Learned or Invented? Nurses Strategies for Calculating and Measuring Medicine Doses

Transcription

1 Learned or Invented? Nurses Strategies for Calculating and Measuring Medicine Doses Roslyn Kay Gillies BSc, Dip Ed, Grad Dip Ed Studies, MEd (Hons) Submitted in fulfilment of the requirements for the degree of Doctor of Philosophy Deakin University May, 2017

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4 Acknowledgements To my grandchildren: Graham Hamilton, John Macquarie, Thomas Hamilton, Abigail Emelia, Gemma Christine, and Olivia Scarlett. May you strive to be the best you can. No thesis was ever achieved through the work of one person alone. My thanks are apportioned between many members of a great team. To my beloved, long-suffering husband, John: you deserve a large chunk of the credit for this study. Your fine editorial skills have been called on frequently. But most of all, thank you for being my constant companion and best friend through thick and thin, and for your practical and moral support. You have ungrudgingly kept me fed and watered, and taken on almost full responsibility for the mundane things of life, such as keeping the household going. To my family: your patience, technical assistance, and problem solving advice have helped me through many difficult periods. And somehow, despite my limited input, you have managed to grow the family from a single grandchild when I started to six on completion. To my ever-supportive supervisors, Principal Supervisor Associate Professor Susie Groves from the mathematics education discipline, and Associate Supervisor Professor Trisha Dunning from the nursing discipline: I remain forever grateful for your expertise, advice, constructive criticism, and constant support throughout the planning and execution of the research, and the writing of the thesis through to final production. The relationship within our thesis team has gone beyond a focus solely on the research project to one, I feel privileged to say, that has evolved into friendship. To my extended family and friends (and even the daughter of a friend): my gratitude to those of you who provided technical advice on the design and implementation of the online questionnaire and/or assisted in piloting it. My thanks also to those who graciously accepted my rationed time availability and my reluctant decisions from time to time, to decline the enjoyment of your company and opportunities to do all the things we love to do together. The names of many I hold dear or in high regard appear as pseudonyms for nurses in the study a strategy I have used to protect the anonymity of some and acknowledge others.

5 I offer my sincere gratitude to the academic staff of universities in every state and territory of Australia who provided the data for the University Phase of the study. I am grateful too, to the validation panel who kindly reviewed the two questionnaires I used to collect data. To the nurses in three Australian hospitals who provided the data for the Hospital Phase of the study: Without your patient explanations of the calculation methods you use in your routine medicine rounds there would be no thesis. You provided the key to unlocking the calculation methods nurses use in clinical practice. To the supervising staff in those hospitals, thank you for providing me with much needed support and guidance. My thanks go to those in the nursing profession who gave so generously of their time and expertise. You have taught me so much about the unstinting contribution to society that nurses and nurse educators make. To my colleagues at Western Sydney University: my gratitude for your support, friendship and encouragement over a great many years, and for the joys of collegiality in working together towards a common goal of supporting nurses through their education. I acknowledge my late parents Nel, for passing on to me something of her gift with numbers, and Ross, for providing such an outstanding model of life-long learning. I also acknowledge Russell Miller, in whose pharmacy I worked for many years as a high school and university student. Thank you for introducing me to the world of medicines a fortuitous link between my career as a mathematics educator and the medicine calculation and administration tasks nurses perform. Finally, to the family of Glendon A. Lean: thank you for your generosity in making available the Glendon A. Lean Memorial Award. Without your bountiful gift of this mathematics education scholarship, my study would not have been possible.

6 Table of contents Acknowledgements Table of contents List of tables List of figures Abstract 1 1 Introduction The origins of my study The problem context Skills needed for accurate dose calculation and measurement Nurses proficiency in dose calculation and measurement Teaching and assessing calculation skills Teaching and assessing measurement skills Statement of the problem The proposed study 12 2 Literature Review Safe administration of medicines Medication error: A problem with multiple causes The role of nurses in medicine administration The incidence of dose calculation and measurement error Patients at high risk of harm from calculation error Perspectives on the effective learning of mathematics Contemporary and traditional views of learning mathematics Social constructivism and situated cognition Learning mathematics with understanding Classrooms promoting effective learning of mathematics Mathematics in vocational and everyday settings Solving dose calculation problems A problem of proportionality Methods used to solve out-of-school proportion problems The dose calculation strategies taught The Formula, its origins, and reasons for its use Alternative dose calculation methods Summary of possible dose calculation methods Assessing dose calculation skills Calculation errors in tests as predictors of errors in practice Nurses proficiency in dose calculations Teaching and assessing dose measurement skills Proportional reasoning in and out of school Formal acquisition of skills for proportionality problems Intuitive proportional reasoning Preferred strategies for solving out-of-school problems Investigation of nurses dose calculation strategies Nurses strategies for solving written dose calculation problems Nurses strategies for calculating and measuring doses in practice Summary and purpose of proposed study The research questions 96 iv v ix xi v

7 3 Methodology Philosophical assumptions underpinning the study Interpretive framework for the current study Research methodologies Quantitative research Qualitative research Mixed-methods research The Research Process Overview of the study Hospital Phase The settings for data collection Recruitment strategy Data collection methods Data management and analysis procedures Ethical issues relating to the Hospital Phase University Phase The settings for data collection Recruitment strategy for the questionnaire Data collection methods Data management and analysis procedures Ethical provisions relating to the University Phase Summary of the research process The Strategies Nurses Use to Calculate Medicine Doses Observation of nurses as they administered medicines Calculations associated with medicine administration Nurses calculation of the dose to administer Classifying nurses dose calculation strategies The proportional reasoning strategies nurses used Scaling processes Overview of nurses dose calculation strategies The dose-to-stock ratio for a medicine administration Factors influencing choice of calculation strategy Relationships between DSR and calculation strategy used Varied DSRs: Two-product dose calculations Factors influencing nurses use of the formula Relationship between formula use and other factors Relationship between formula use and calculation of doses for paediatric patients Summary: Frequency of dose calculation strategy by DSR Nurses innovative dose calculation strategies Creating mathematically convenient liquid solutions when reconstituting medicines Proportional reasoning using body parts Using a syringe scale as an aid to proportional reasoning Nurses use of functional strategies Calculator use in clinical practice The impact of medicine packaging on dose calculation Nurses performance on pen-and-paper medicine administration tasks Nurses dose calculation strategies and calculator use The errors nurses made 231 vi

8 5.16 Nurses descriptions of their calculation methods: Comparing the evidence Evidence from focus groups Comparison of calculation methods: Student versus practising nurse Nurses perceptions of their use of calculators The apparent contradictions between nurses calculation methods The invisible nature of dose calculations One method to calculate, another method to check The impact of mandatory checking on calculation methods Nurses varied capabilities to self-check Calculation methods: Clinical practice versus mandatory tests Summary of nurses dose calculation strategies Measuring Medicine Doses Types of measurement task observed Measuring instruments and techniques Multi-stage measuring processes Measurement issues emerging from the study Volume of liquid in ampoules Selecting syringes for measuring small volumes Nurses performance on measurement aspects of pen-and-paper tasks Nurses measurement errors Summary of nurses measurement of medicine doses The Teaching of Medicine Dose Calculation and Measurement Skills Participants and their universities Campuses represented in the data Employment status and role of participants Units of study Extent of focus on calculation of medicine doses Entry level mathematics prerequisites for students Teaching medicine dose calculations Resources used to support student learning Staff delivering instruction Basis for selecting staff The calculation strategies taught Policy on calculation strategies Determining the calculation strategies taught Including measurement units in formula Variants of the formula Methods used to assess dose calculation skills Student difficulties learning dose calculations Areas of difficulty, contributing factors and solutions Staff difficulties teaching dose calculation skills Problem areas, solutions and staff selection issues Use of calculators The numeracy skills teachers routinely teach The staff who provide instruction Teaching and assessing measurement skills Approaches to assessing dose measurement skills Participants final comments Summary of the teaching of medicine dose calculation and measurement skills 344 vii

9 8 Discussion The strategies nurses use to calculate medicine doses The strategies nurses use to calculate medicine doses in clinical practice The invisible nature of nurses dose calculations Factors influencing the need for a dose calculation Factors influencing nurses choice of strategies for calculating medicine doses The strategies nurses use to solve written medicine dose calculations Comparison between nurses strategies in different contexts The strategies nurses use to measure medicine doses The strategies nurses are taught to calculate and measure medicine doses Strategies taught to calculate medicine doses Strategies taught to measure medicine doses Calculating medicine doses: The theory practice divide Nurses dose calculation methods Written word problems versus authentic practice problems Computational skills needed for formula use versus scalar strategies Conceptual difficulties: A formula problem Determinants of nurses dose calculation strategies: An emerging theory Conclusion Significance of the study Implications for practice Limitations of the study Implications for future research Concluding remarks 384 References 387 Appendices 401 Appendix 1: Nurses invitation to participate 401 Appendix 2: Sample of completed observation schedule 402 Appendix 3: Sample page from questionnaire for nurses 403 Appendix 4: Discussion points for focus groups 404 Appendix 5: Extract from spreadsheet recording observations 409 Appendix 6: Sample pages from questionnaire for university participants 410 Appendix 7: Examples of nurses use of the formula: Details from spreadsheet 416 Appendix 8: Variations of the formula provided by university participants 421 Appendix 9: Staff perceptions of student difficulties: Sequence of responses from participants 426 Appendix 10: Staff perceptions of difficulties experienced by staff: Sequence of responses from participants 431 viii

10 List of tables Table 2.1 Table form of the function relating mass and the number of tablets 50 Table 2.2 Examples illustrating possible methods for calculating medicine doses 66 Table 3.1 Characteristics of interpretive lenses for my study 104 Table 3.2 Features of a multi-strategy approach considered valuable in designing my study 118 Table 4.1 Summary of the research process 152 Table 5.1 Details of the Hospital Phase of the study 155 Table 5.2 Examples of medicine administrations and the types of calculation they required 157 Table 5.3 Frequency of medicine administrations requiring calculation of the dose to administer 162 Table 5.4 Frequency of medicine administrations and dose calculations 163 Table 5.5 Frequency of use of the Nursing Formula 164 Table 5.6 Frequency of integer scalar strategies used to scale up and down from stock mass 167 Table 5.7 Frequency of dose calculation strategy 169 Table 5.8 Frequency of DSR 174 Table 5.9 Frequency of dose calculation strategies DSR 2:1 177 Table 5.10 Frequency of dose calculation strategies DSR 3:1 178 Table 5.11 Frequency of dose calculation strategies DSR 4:1 180 Table 5.12 Frequency of dose calculation strategies DSR 1:2 182 Table 5.13 Frequency of dose calculation strategies DSR 3:2 186 Table 5.14 Dominant calculation strategies for commonly occurring DSRs 187 Table 5.15 Pattern of formula use across hospitals, wards, and nurses 191 Table 5.16 Distribution of medicine administrations requiring dose calculation by calculation strategy used and dose-to-stock ratio 198 Table 5.17 Examples of dose calculations simplified by the creation of a mathematically convenient solution 206 Table 5.18 Medicine administrations for which a functional strategy may have been used 214 Table 5.19 Frequency of enoxaparin and heparin doses administered by hospital 218 Table 5.20 Features of questionnaire medicine administration Items Table 5.21 Nurses dose calculation strategies and calculator use on pen-and-paper medicine administration tasks 223 Table 5.22 Frequency of types of error made 233 Table 6.1 Frequency of use of primary measuring instruments, and associated administration routes 266 Table 6.2 Administration routes for which a syringe was used to measure the dose 268 Table 6.3 Overfill recorded for iloprost, morphine, and noradrenalin ampoules 281 Table 6.4 Appropriateness of syringe capacity for task: by syringe type and hospital 287 Table 6.5 Types of measurement error made and the number of nurses making them, by item 293 ix

11 Table 6.6 Type of poor syringe selection, and the number of nurses making them, by item 294 Table 6.7 Three ways in which nurses split a volume between two syringes 295 Table 7.1 Number of universities, campuses and participants by state and territory 300 Table 7.2 Participants by role and other similar units coordinated or taught 301 Table 7.3 Program type and length 302 Table 7.4 Mathematics achievement level required on entry to program 303 Table 7.5 Modes used to deliver instruction in medicine dose calculations 304 Table 7.6 Types of prescribed and recommended learning resources used 305 Table 7.7 Learning resources described by participants 306 Table 7.8 Responsibility for instruction in medicine dose calculations 307 Table 7.9 Reasons staff are usually selected to teach units involving dose calculations 308 Table 7.10 Policy on the calculation strategies taught to students 310 Table 7.11 Calculation strategy prescribed or recommended by School 311 Table 7.12 Personally preferred calculation strategy by role in unit 313 Table 7.13 Table 7.14 Table 7.15 Number of attempts permitted to pass medicine dose calculation component 317 Is it possible to fail the dose calculation component but pass the unit? 318 Staff endorsement of students experiencing difficulties learning dose calculations 320 Table 7.16 Aspects of medicine dose calculations students find most difficult 322 Table 7.17 Factors that contribute to student difficulties in dose calculations 324 Table 7.18 Suggested solutions to address student difficulties 325 Table 7.19 Staff endorsement of difficulties experienced by staff teaching dose calculations 328 Table 7.20 Types of problems staff experience in teaching dose calculations 329 Table 7.21 Solutions to staff difficulties in teaching dose calculations 330 Table 7.22 Advice to students regarding calculator use 332 Table 7.23 Specific numeracy skills routinely taught 333 Table 7.24 Number of numeracy skills routinely taught 334 Table 7.25 Participants feelings about teaching mathematical skills 336 Table 7.26 Mathematical techniques participants wish to learn more about 337 Table 7.27 Approaches taken to teaching measurement skills 340 Table 7.28 Methods used to assess measurement skills 342 Table 8.1 Dominant calculation strategies for different DSR classes 376 x

12 List of figures Figure 2.1. Proportional reasoning strategies for solving missing value problems 45 Figure 2.2. Diagrammatic representation of a scalar operator, applied in parallel operations within each measure space 48 Figure 2.3. Diagrammatic representation of a functional operator applied between measure spaces 49 Figure 2.4. Graphical representation of the linear relationship between mass and number of tablets when t 1 m Figure 4.1. Administrative details of observed medicine administrations 133 Figure 4.2. Details concerning the medicines administered 134 Figure 4.3. Progression from prescribed dose to dose to administer via stock formulation 135 Figure 4.4. Details concerning the calculations nurses performed 136 Figure 4.5. Details concerning the measurement instrument/s used 137 Figure 4.6. Additional information concerning the medicine administration 138 Figure 5.1. Nurses assumed decision process for determining the need for a dose calculation 161 Figure 5.2. Final classification of nurses observed dose calculation strategies 170 Figure 5.3. Water for injections: contents of ampoule used to dissolve tablet 185 Figure 5.4. The manufacturer s instructions for reconstituting flucloxacillin powder 202 Figure 5.5. Thinking in milligrams on a millilitre scale 210 Figure 5.6. Thinking in vials as well as milligrams on a millilitre scale 211 Figure 5.7. Confirming a dose in milligrams on a millilitre scale 213 Figure 5.8. Function rule: The number of millilitres is the same as the number of milligrams. 215 Figure 5.9. Formula method: Calculator used to perform entire calculation 227 Figure Formula method: Calculator used to perform last step only 227 Figure Proportional reasoning: Calculator used in last step only 228 Figure Formula method: Calculator used for metric conversion 229 Figure The rule of three (ratio version): calculator not used 229 Figure Number of nurses who made each type of error on pen-and-paper tasks 232 Figure Emmy s incorrect metric conversion and fudged answer 234 Figure Emmy s shading of the incorrect answer of five tablets 235 Figure Display of the heparin scenario and Scenarios Figure Scenario Figure Scenarios Figure Quan s version of the formula for calculating the dose 243 Figure Gail s application of the formula, combined with written and mental arithmetic processes 244 Figure Formula and calculator to calculate; proportional reasoning to check 253 Figure Proportional reasoning and mental arithmetic to calculate; formula and calculator to check 253 xi

13 Figure Formula and written steps to calculate; formula and calculator to check 254 Figure Formula and calculator to calculate; proportional reasoning and reversing the calculation process to check 255 Figure Formula to calculate; proportional reasoning and written arithmetic to check 256 Figure Gail s written application of the formula to check a dose with another nurse 257 Figure Formula to calculate; formula with calculator, and reversing processes to check 260 Figure 6.1. A brightly coloured 1 ml oral syringe to which a needle cannot be attached 269 Figure 6.2. An enoxaparin (Clexane) prefilled syringe (Image provided courtesy of NSW Therapeutic Advisory Group. Visit Figure 6.3. An electronic pump and apparatus administering an intravenous infusion to a paediatric patient 272 Figure 6.4. Flowchart showing the four-stage measurement process 274 Figure 6.5. Ampoule and packaging information for heparin 5000 IU in 0.2 ml 276 Figure 6.6. Packaging information for morphine 10 mg in 1 ml 276 Figure 6.7. The scale on a 100-unit insulin syringe graduated in international units of insulin 284 Figure 6.8. Reverse side of 100-unit insulin syringe indicating that 100 international units of insulin are contained in 1 ml of liquid 284 Figure 6.9. The scale on a 50-unit insulin syringe graduated in international units of insulin 285 Figure Reverse side of 50-unit insulin syringe indicates that 50 international units of insulin are contained in 0.5 ml of liquid 285 Figure The scale on a 1 ml syringe 286 Figure The graduations on the scales of 1 ml and 3 ml syringes 288 Figure Comparing the accuracy of 1 ml and 10 ml syringes 290 xii

14 Abstract Administering medicines is a core nursing role, one in which dosage accuracy is essential for patient safety and the efficacy of medicine therapies. Nurses calculation proficiency is a cause of continuing concern and has sparked debate about teaching and assessment methods. Developing and retaining sound dose calculation skills has long been a challenge for students, educators and employers of nurses. Some educators question whether the traditional teaching model, involving application of a specialised Nursing Formula, may be part of the problem, particularly in relation to the widespread conceptual difficulties evident in test performances. Research is needed to compare the effectiveness of the formula approach with that of possible alternative dose calculation methods. The aim of my study was to identify the strategies experienced nurses use to calculate and measure medicine doses in clinical practice, the factors that influence their choice of calculation strategy, and the dose calculation and measurement strategies students are taught in Australian pre-registration nursing programs. A qualitative multi-strategy research design employed naturalistic observation to explore nurses dose calculation strategies during routine administration of medicines in three Australian hospitals. These data were supplemented by interviews, a questionnaire, and focus groups. An online questionnaire gathered data from academic staff of Australian universities about their teaching practices relating to calculation and measurement of medicine doses. Compelling evidence emerged indicating a preference for informal scalar calculation strategies, performed mentally, rather than using the Nursing Formula. Nurses chose scalar strategies that allowed them to keep the problem variables separate and retain the meaning of the problem at every step in the solution process. Nurses strong preference for informal strategies over formal algorithmic methods was at odds with the findings from the online questionnaire that confirmed the Nursing Formula as the principal dose-calculation method taught in universities. The key findings from my study indicated that each nurse made a selection from their personal repertoire of calculation strategies in response to the particular numerical characteristics of the problem to be solved. The single dominant factor influencing the nurse s choice of strategy was the ratio between the two quantities of mass in the problem, namely the prescribed mass of medicine and the mass of the 1

15 stock formulation, indicated by the concentration of the medicine on the product label. The three principal scalar strategies the nurses used were initiated in response to ratios of the form n:1, 1:n, and n:2 respectively. The consistency of nurses responses to the numerical characteristics of medicine administration tasks led to the formulation of an emerging theory explaining why nurses choose one calculation strategy for a particular medicine administration and a different strategy for another. Examination of nurses measurement practices revealed several areas of inaccuracy, notably in relation to the use of syringes to measure fluid volumes. The findings are consistent with the single other study 1 identified that investigated dose-calculation strategies nurses used in professional practice, which also found that nurses made little use of the Nursing Formula, preferring instead a variety of informal proportional-reasoning strategies. The findings also support those of other studies that have shown problem solvers use informal strategies to solve outof-school proportionality problems in preference to formal algorithmic methods which conflict with their native conceptions of proportionality. My study also provides new insights into a previously under-researched aspect of the nursing curriculum. It identifies a theory-practice divide in the teaching, learning and assessment of dose calculations, and identifies the potential for trialling novel ways of approaching instruction that accord with students pre-existing proportionality schema and exploit their intuitive problem-solving capabilities. The findings also strengthen the case to re-examine the methods used to judge nurses fitness to practise in the area of medicine administration, adding to existing concerns about the validity and reliability of traditional assessment methods. 1 Hoyles, Noss & Pozzi (2001) Proportional reasoning in nursing practice. Journal for Research in Mathematics Education, 32(1),

16 1 Introduction Nurses daily confront the possibility of making mathematical errors with potentially serious consequences when they calculate and administer drugs as part of their routine work. Hoyles, Noss, & Pozzi (2001, p. 9) The focus of my study is the strategies nurses use to calculate and measure medicine doses in clinical practice, and the strategies student nurses are taught in education programs for these tasks. Accuracy in all aspects of medicine administration, including the mathematical aspects, is critically important to protect patients from harm and assure the clinical effectiveness of treatments (Weeks, Lyne & Torrance, 2000). 1.1 The origins of my study The seed of my study was sown on a March morning well over twenty years ago. It was my first day as a newly appointed member of staff in a newly created position of Mathematics Lecturer in the Student Learning Centre at a suburban campus of a Sydney university. My role was to single-handedly support 4000 students across a wide range of disciplines in the mathematical requirements of their tertiary studies. Before I had even sat down in the chair at my desk, there was a knock on the door and several nursing students asked me for help. They had a sheet of dosage calculations they were trying to work out. We ve got the formula but we don t have a clue what to do with it, they explained. With no prior exposure to the mathematics of nursing, I perused the word problems with great interest, but through the eyes of an absolute novice. The memory of that event and my reaction to it is still vivid today: Why would you need to use a formula to calculate these medicine doses? They can be worked out quite easily using everyday mathematical problem-solving techniques such as the proportional reasoning approaches I use when I am shopping. To this day, I have been fascinated, curious, and determined to learn more about how nurses calculate medicine doses, as teachers, students, and practitioners. I remain committed to 3

17 Chapter 1: Introduction finding better ways of supporting student nurses in their learning of dose calculations, and, to that end, better ways of teaching the necessary skills. I soon became aware that students were taught three principal formulae for their calculations, which were invariably posed as word problems. The first formula was the Nursing Formula, used to determine the dose to administer based on the dose prescribed and the formulation of the stock of medicine used. Two additional formulae enabled the calculation of the flow rate for an intravenous infusion; one in millilitres per hour and the other in drops per minute. The formula for calculating the drip rate in drops per minute was the most complex and involved multiplying two fractions together. The nurse is required to substitute the volume of liquid to be infused (in millilitres), the time for the infusion to run (in minutes, which usually requires conversion of the number of hours to minutes), and the drop factor for the particular intravenous giving set apparatus the nurse will use to administer the infusion. The drop factor is the number of drops required to deliver a volume of one millilitre of the liquid to be infused, and is most commonly 15, 20, or 60 drops per millilitre. What disturbed me about the way students learnt to use the Nursing Formula was that typically it was taught with little or no attempt to derive it or justify it in any way, or explain why it worked. It appeared to be invoked as a magical method that nurses must use to solve all dose calculation problems. I found that many students lacked an understanding of how the component parts or terms in the formula related to the quantities described in the word problem they were attempting to solve. Nor did they have any understanding of how the multiplication and division operations represented in the formula related to the problem being solved. Why divide these terms and multiply these? Further, when students applied the formula it was sometimes apparent that their arithmetical and calculator skills were poor, yet they often did not check that the answer they had obtained was reasonable. These factors, when combined, resulted in a situation where calculation errors were likely to be made, and remain undetected. Frequently, when teaching staff modelled the formula, the focus was on numbers; I observed teachers making little or no reference to units of measure until they obtained the answer in the final step of the calculation process at which point they attached a unit, almost as if at random. The lack of focus on units of measure appeared to me to be dangerous, particularly when the prescribed dose and the 4

18 Chapter 1: Introduction formulation of the stock to be used were expressed in different units. In such circumstances, the nurse needed to perform a conversion so that the two quantities to be substituted into the formula were expressed in the same unit. I felt it was best to highlight the need for a conversion by attaching the units of measurement to quantities from the point at which they were first substituted into the formula. My early concerns about the difficulties student nurses experienced learning dosage calculation skills resulted in my first publication in the area of nursing mathematics: Drug calculations for nurses: More than a formula and a calculator? (Gillies, 1994). This paper presented the results of an analysis of the performance of 210 first-year students on a medication calculation 2 test, conducted as part of their assessment program, and the results of a survey of academic staff of universities who were concerned with teaching units of study involving calculation of medicine doses. Some of my concerns related to the strong focus on formula-based methods in the teaching of medication calculations, a focus reflected in the resources recommended to students to support their learning. Students were encouraged, and more often required, to apply formulae to calculate medicine doses and intravenous flow rates. Yet, from the outset these methods and the mechanical way in which students applied them sat uncomfortably alongside the beliefs and practices that underpinned my work as a mathematics educator, with its fundamental focus on learning mathematics with understanding. Applying formula-based calculation methods appeared to result in students developing only procedural understanding of the computations they performed, consequently, many students experienced difficulties in developing sound calculation skills. I felt increasingly uneasy about supporting students solely by reinforcing the methods they were taught within the nursing program. The reliance on formula-based calculation methods seemed to be at the expense of the mathematical problemsolving skills students brought to their nursing studies. Students appeared to be actively discouraged from applying skills such as proportional reasoning that they had developed at school and possibly had continued to hone in their everyday lives. The practices and attitudes of the nurse educators seemed to result in students thinking that their intuitive mathematical problem-solving skills were not of value, 2 I use the broad term medication calculation to describe all calculations associated with medicine administration, including calculation of intravenous flow rates and dose calculations. I use the term dose calculation specifically in reference to calculating the quantity of medicine either a number of tablets or a volume of liquid required to administer a prescribed dose of medicine. 5

19 Chapter 1: Introduction and were inadequate or unsuitable for the mathematical tasks nurses performed. Students came to believe that using the specialised formulae they were taught in their pre-registration studies was the proper way, the safe way, possibly the only way, for nurses to perform calculations. Through their attitudes and actions, nurse educators reinforced the belief that nursing mathematics was a separate branch of mathematical endeavour that demanded specialised nursing formulae. Another area of concern was that I saw little recognition that accurate measurement of the dose was also an important aspect of accurate medicine administration. For example, I wondered about the ability of nurses to accurately and confidently use the scale on a syringe to measure a volume of liquid. This concern stemmed partly from evidence in the test results students showed me that some had a poor understanding of the decimal number system which forms the basis of most scale reading. I saw little evidence of measurement skills being assessed as part of the penand-paper word problems routinely used to test students calculation skills, and wondered whether students measurement skills were being adequately developed and appropriately assessed. At one university, my colleagues and I sought to ensure students were skilled in the measurement aspect of medicine administration by including authentic measurement activities requiring the use of syringes and other scales in the annual mathematics preparation program for nurses. Student feedback showed that this part of the program was always well received because it gave students the opportunity to identify their misconceptions and address them. Up to the point in my teaching career when I first encountered the difficulties many tertiary nursing students experienced in mastering medicine dose calculations, my career had comprised many years of teaching mathematics to a variety of students in high schools and TAFE colleges. My teaching practice was founded on a solid understanding of mathematical content from my undergraduate study (a Science degree with majors in Pure Mathematics and Mathematical Statistics). This was followed by comprehensive training in mathematics teaching and learning through a Diploma in Education that included two units in mathematics teaching. Then some years later, a Graduate Diploma in Education (Learning Difficulties) equipped me to better assist students experiencing learning difficulties. My background, both as a student and teacher of mathematics, had led me to the firm belief that any given mathematical problem may be solved in many different ways. Some ways may be more sophisticated or elegant than others, but, provided 6

20 Chapter 1: Introduction the student was confident in using a particular method and that method was based on sound reasoning and resulted in the correct answer, that method should be regarded as a valid method, and possibly the best method for that person and that problem. The value of learning mathematics with understanding (Hiebert & Carpenter, 1992) was the cornerstone of my teaching practice, particularly in later years. My personal belief was that a model of good practice was to justify the mathematical methods we employ. Good teaching should dispel the belief that a formula is something magical handed down from expert mathematicians. Rather, if students are taught to use a formula, the teacher should first derive it, or at least provide adequate justification for its use. Also, the problem solver may choose to calculate the quantity in other ways that do not involve use of a formula. My experiences over five years working to support students in their learning medication dose calculations led me to undertake research (Gillies, 2004) which established that student nurses could draw on their existing problem-solving skills to find appropriate methods to solve a variety of problems requiring calculation of medicine doses and intravenous flow rates. 1.2 The problem context Nurses play a key role in the administration of medicines to the patients in their care. Nurses competence in dose calculation and measurement is paramount for the safety of patients (Coben, 2010; Hoyles, Noss, & Pozzi, 2001; Marks, Hodgen, Coben & Bretscher, 2016). Accuracy in the quantity of medicine administered optimises the therapeutic effect of the medicine, protects the patient from the potentially damaging effects of an incorrect dose, and the nurse and healthcare facility from the personally devastating and costly consequences that can result from a medication error (Adhikari, Tocher, Smith, Corcoran & MacArthur, 2014; Anderson & Webster, 2001; Eisenhauer, Hurley & Dolan, 2007; Hughes, 2008). Potential costs to employers include longer hospitalisation, additional treatment, and litigation (Eastwood, Boyle, Williams & Fairhall, 2011; World Health Organization [WHO], 2009). Fortunately, only a small percentage of medicine administration errors result in serious harm to the patient or, at worst, their death (Adhikari et al., 2014). 7

21 Chapter 1: Introduction Nurses work in an error-critical environment, in that there is little or no room for error (Coben, 2010; Hoyles et al., 2001). An overarching policy framework prioritising quality use of medicines and patient safety governs all aspects of healthcare provision, including medical interventions involving the administration of medicines (Australian Government, 2002a, 2002b; WHO, 2011). Safety in healthcare provision has become increasingly challenging for nurses and other health professionals as a result of the increasing complexity of the work environment, the nature of medicine therapies, the vast number of medicines now used to treat patients, new technologies that are progressively introduced, and the increasingly complex ways in which medicines are administered (Adhikari et al., 2014; Anderson & Webster, 2001; WHO, 2010) Skills needed for accurate dose calculation and measurement To be safe practitioners nurses need to accurately calculate and measure the medicines they administer (Nursing and Midwifery Board of Australia, 2006, 2016b; Wright, 2012b, 2007b, 2006). Accurate calculation of a medicine dose begins with a prescribed amount of medicine, most often expressed as a quantity of mass (for example, a number of milligrams or micrograms), which is then translated by the nurse into the quantity of the available medicine stock needed to deliver the dose prescribed (Glaister, 2016). The concentration of the available stock (for example, 80 mg per tablet, or 100 micrograms per 2 ml) mediates the calculation process. The nurse then measures the correct quantity of medicine prior to administering it to the patient (Cartwright, 1996; Coben, Hutton et al., 2010; Hoyles et al., 2001; Macdonald, Weeks & Moseley, 2013; Weeks, Hutton, Coben, Clochesy & Pontin, 2013). Accurate measurement of the medicine may require simply counting the correct number of tablets or capsules, or it may require drawing the correct volume of liquid into a syringe. Administration of a medicine becomes a far more complex and mathematically demanding process if the medicine is supplied in powdered form that must first be reconstituted to a liquid form prior to administration (Kee, Marshall, Forrester & Woods, 2016; Saxton, Ercolano-O Neill & Glavinspiehs, 2005). The calculation and measurement processes needed before a medicine supplied in powdered form are closely connected, first, to the mass of the powder 8

22 Chapter 1: Introduction reconstituted by the nurse, and then subsequently, to the concentration of the reconstituted solution. When nurses administer liquids by intravenous infusion, they must also factor in the period of time over which the medicine is administered. This is done by calculating the constant rate at which the infusion is to be delivered. The nurse then sets an electronic infusion pump, keying in the numerical values that will deliver the prescribed volume of liquid at a constant rate over the nominated period of time (Kee et al., 2016) Nurses proficiency in dose calculation and measurement Assessing competence in the mathematical aspects of medicine administration has traditionally focused strongly on calculation skills, with little focus on the measurement aspects of accurate medicine administration. Deficits have been identified in students skills (Coben, Hutton et al., 2010; Fleming, Brady & Malone, 2014; Kohtz & Gowda, 2010; Macdonald et al., 2013), with conceptual difficulties being identified as a major cause of error in students dose calculations (Fleming et al., 2014; Gillies, 1994; Hutton et al., 2010; Weeks et al., 2000; Wright, 2006). Conceptual difficulties, or problem set-up errors (Weeks, Clochesy, Hutton, & Moseley, 2013, p. e44), are evidenced by students not being able to relate elements of word-based problems to the formula they are applying, resulting in erroneous setting up of dosage calculation equations and incorrect doses (Weeks, Hutton, Young, Coben, Clochesy & Pontin, 2013, p. e27). Studies analysing the performances of students and nurses on tests of numeracy skill and dose calculation competence suggest continuing problems with competence. Reports of high rates of calculation error in tests are an ongoing cause of concern to the profession, tertiary education institutions and healthcare facilities globally (Adhikari et al., 2014; Alsulami, Conroy & Choonara, 2012; Weeks et al., 2000; WHO, 2011). Stakeholders fear the potential consequences of medication error for patients, and the cascading sequence of negative impacts that may follow, affecting the patient, the nurse and the organisation (WHO, 2009). Educational institutions and healthcare facilities continue to commit considerable time and resources to improving nurses calculation skills through interventions (Hoyles et al., 2001) such as one-on-one tutoring, providing opportunities for intensive practice, using online learning packages for skill 9

23 Chapter 1: Introduction development and assessment, and opportunities to repeat calculation tests (Ramjan et al., 2014). Concern among healthcare administrators about the association between calculation error and patient safety (Department of Health, 2000) led to a focus on developing policies and protocols that promote safe administration of medicines and minimise errors (Anderson & Webster, 2001; Deans, 2005; Hoyles et al., 2001). Awareness of the importance of dose calculation competence, and the need for all nurses to have calculation skills they can retrieve when needed, are also reflected in the widespread practice of requiring nurses to pass a calculation test on entry to employment, and possibly annually thereafter (Calliari, 1995; Coben, Hall, Hutton et al., 2008; Ludwig-Beymer, Czurylo, Gattuso, Hennessy & Ryan, 1990). 1.3 Teaching and assessing calculation skills Approaches to teaching and assessing calculation skills for medicine administration have come under increasing scrutiny as the importance of presenting problems in authentic contexts has been recognised as essential for meaningful learning and valid assessment (Macdonald et al., 2013; Ramjan et al., 2014; Rodger & Jones, 2000; Weeks, Higginson, Clochesy & Coben, 2013; Wright, 2012a). The methods students are taught to calculate doses have been questioned in light of the recurring nature of students difficulties mastering dose calculation (Ramjan et al., 2014), the high incidence of calculation errors in tests, and the difficulties students and nurses experience retaining their skills, once mastered (Blais & Bath, 1992; Jackson & De Carlo, 2011; Sherriff, Wallis & Burston, 2011; Wright, 2007b, 2012a). Teaching student nurses formulaic methods to prepare them for calculating medicine doses and intravenous flow rates in clinical practice is a long-standing tradition in Australia and other countries (Hoyles et al., 2001; Stolic, 2014; Wright, 2007b). Alternative calculation methods are seldom taught. The fact that formulaic methods have been taught almost exclusively for decades suggests that educators regard these as best practice calculation methods. But where is the evidence to support such a belief? Without proof of the effectiveness of formula methods in clinical practice, the continued practice of teaching formulaic methods may not be giving students the best preparation for professional practice. Moreover, the focus on formula methods continues despite claims that alternative methods may offer 10

24 Chapter 1: Introduction advantages over formulae (Best & Moore, 1988; Hoyles et al., 2001) particularly if students can see a clear connection with practice (Crookes, Crookes & Walsh, 2013). Optimal calculation methods are likely to be tailored closely to the demands of clinical practice. They should be efficient, accurate, reliable, utilitarian and transferable to the diverse range of problem situations that nurses are likely to encounter. Nurses need to feel comfortable and confident in the calculation methods they use. Evidence of recurring problems relating to calculation errors and poor results in mathematical and dosage calculation tests has prompted some authors to question the validity of the methods used to assess nurses competence for clinical practice (Hutton, 1998a; Wright, 2007b, 2009c, 2012a). In particular, the use of traditional pen-and-paper tests in which dosage calculation problems are posed as word problems, has come into question on the grounds that they do not accurately predict or reflect the nurse s ability to calculate doses in clinical practice. Nurses demonstrate poor skills in written assessments that are not found in clinical practice (Hoyles et al., 2001; Wright, 2007b, 2009c). Wright attributed this discrepancy to the fact that the skill set required to solve written word problems is different from the skill set required to solve actual dose calculation problems in practice. This situation, which exists in many countries (Coben, Hodgen, Hutton & Ogston-Tuck, 2008), highlights the need to fill a knowledge gap concerning the cognitive processes and the mathematical and problem-solving strategies associated with successful dose calculation in practice. For assessments to be valid and reliable, it is crucial that they test skills that mirror those that define competence in clinical practice. 1.4 Teaching and assessing measurement skills Concern about the competence of nurses in the measurement aspect of medicine administration, and whether students are taught the necessary skills for accurate dose measurement, was raised at least as long ago as 1996 (Cartwright, 1996). Until quite recently there has been little evidence of any greater awareness of the importance of the measurement aspect of medicine administration. 11

25 Chapter 1: Introduction A computer-based learning and assessment program developed by a team of researchers and educational resource developers (Weeks, Hutton, Young et al., 2013) reflects a growing recognition of the importance of technical measurement competence (p. e25). One of few comprehensive reports on the results of assessing students dose measurement skills was a study by the same UK team (for example, Coben, Hutton et al. (2010) and Sabin et al., (2013)) who revealed a range of student errors, mainly involving liquid medicines and caused by inexperience in using measuring equipment such as syringes. Most of the errors students made were of minor magnitude and did not compromise patient safety or the therapeutic effect of the medicine. 1.5 Statement of the problem We know very little about the methods nurses use to calculate and measure medicine doses in the practice environment, how effective those methods are, and how they relate to the methods they are taught as students. A review of the literature located only one study investigating the calculation strategies nurses employ when administering medicine doses in professional practice. As part of a broader study of workplace mathematics in the UK, Hoyles et al. (2001) followed twelve paediatric nurses in a specialist children s hospital as they went about their routine functions. They found that rather than using the single taught nursing rule, experienced nurses used a range of correct proportional-reasoning strategies based on the invariant of drug concentration (p. 4). The findings of Hoyles et al. (2001) are supported by recent evidence obtained through interviews with students (Marks, Hodgen, Coben, & Bretscher, 2016), suggesting the formulaic methods learnt at university differed from calculation methods the students mentors used on a daily basis in clinical practice. Experienced nurses solving problems posed as word problems have also been found to make greater use of alternative calculation methods rather than using the Nursing Formula (Wright, 2013). The studies by Marks et al. (2016), Wright (2013), and Hoyles et al. (2001) were the only ones found that investigated nurses cognitive processes when they calculate medicine doses (Wright, 2013), or reported on the problem-solving methods nurses use in clinical practice (Hoyles et al., 2001; Marks et al., 2016). 12

26 Chapter 1: Introduction Through three entirely different methodological approaches, these researchers reached very similar conclusions, namely that nurses make extensive use of methods other than the traditionally taught formula. Although these three studies were small, nevertheless they raise the question of whether the methods students learn in tertiary programs differ from those nurses use in clinical practice. They point to the need for further investigation of how nurses approach dose calculations in clinical practice, rather than simply assume that if students are taught to use the formula, that is the method they will continue to apply throughout their professional careers. What is lacking is robust empirical evidence concerning the dose calculation practices of competent nurses (Hoyles et al., 2001; Wright, 2012a, 2007b) and the extent to which the specialised Nursing Formula forms part of those practices. We need to know when and why nurses employ particular calculation strategies. If nurses choose to use alternative calculation strategies (Hoyles et al., 2001; Wright, 2008), what are they, where do they come from, and how widespread is their use? These issues are at the heart of my study. Rigorous investigation of the mathematical skills and subskills that constitute accurate dose calculation in clinical practice will result in a sound knowledge base from which to equip future cohorts of nurses for the demands of clinical practice (Coben, Hall, et al., 2008; Wright, 2012a). Establishing an evidence-based model of competent dose calculation practice will provide a benchmark against which current teaching and assessment practices can be reviewed (Coben, Hall, et al., 2008; Wright, 2007b). Rather than teachers accepting in good faith the age-old tradition of using a specialised formula without credible evidence of its usefulness in practice, such evidence-based information will equip educators with knowledge critical for (a) devising effective approaches to skill development, and (b) creating valid and reliable assessment instruments by which to judge competence (Wright, 2007b, 2012a). Knowledge of the dose calculation strategies nurses use in clinical practice will also allow reassessment of the relative importance of the many mathematical skills and subskills that, for so long, have been regarded as essential for dose calculation (Coben, Hall, et al., 2008; Wright, 2007b), but have so consistently been found lacking in student and graduate nurses (McMullan, 2010; Wright, 2013). In relation to contemporary approaches to developing skills for calculation and measurement of medicine doses in universities, the scant indicators in the literature 13

27 Chapter 1: Introduction point to the fact that in most countries, including Australia, a heavy emphasis remains on teaching the formula to calculate medicine doses (Hoyles et al., 2001; Weeks, Lyne, Mosely & Torrance, 2001; Wright, 2008d, 2013). This presumption should be verified, however. Little comprehensive empirical evidence has emerged in recent years investigating the dose calculation and measurement strategies taught in tertiary education programs (Stolic, 2014). The last known data collected in Australia was over twenty years ago, the result of a small study I conducted (Gillies, 1994) focusing only on the teaching of calculation skills, not measurement skills. An up-to-date picture of the dose calculation and measurement methods currently taught in Australia will enable comparison of the strategies taught with the strategies used by practising nurses. It will assist educators to make informed judgements about the adequacy of current teaching models. Personal goals are a primary force driving my study: gaining a greater understanding of how experienced nurses calculate and measure doses will allow me to develop more effective ways of supporting nursing students in their learning of the mathematics of medicine administration, and by implication, more effective ways of teaching it. However, I expect other people, too, to benefit from my study, including nurse educators and future nursing students. I also hope that the patients these nurses care for will also benefit through a reduction in nurses wrong-dose errors, as will the institutions employing nurses, and all those engaged in the ongoing education and professional development of nurses. 1.6 The proposed study The overall aim of my study was to examine the strategies Australian nurses use in the clinical setting to calculate and measure the quantity of medicine to administer, and how these strategies compare with those taught in pre-registration education programs. My study also investigated factors that influence nurses choice of calculation strategy. The research was conducted in two phases. One phase focused on observing nurses as they carried out dose calculation and measurement activities in clinical practice. The other phase sought information about current teaching and assessment practices from academic staff in Australian universities who coordinated or taught nursing units involving calculation and measurement of medicine doses. 14

28 Chapter 1: Introduction The calculations nurses regularly perform include calculation of the dose of medicine to administer and calculation of intravenous flow rates. The latter skill is an important aspect of accuracy in medicine administration and a cause of considerable difficulty for many students, particularly in relation to expressing flow rates in drops per minute. However, my study was limited to investigating only those calculations related to determining the dose to administer, that is, the quantity of medicine the nurse should administer to the patient to deliver the dose prescribed. Calculation of intravenous flow rates was not examined in any detail. 15

29 2 Literature Review What one thinks mathematics is will shape the kinds of mathematical environments one creates, and thus the kinds of mathematical understandings that one s students will develop. Schoenfeld,(1992, p. 341) Chapter 2 presents a literature review that analysed, interpreted and assessed the body of literature relevant to nurses application of mathematics to calculating and measuring medicine doses. The function of the review was to situate the existing literature in the context of the rationale for the topic of my research, introduced in Chapter Safe administration of medicines One of the greatest challenges today is not about keeping up with the latest clinical procedures or the latest high-tech equipment. Instead, it is about delivering safer care in complex, pressurized and fast-moving environments. In such environments, things can often go wrong. Adverse events occur. Unintentional, but serious harm comes to patients during routine clinical practice, or as a result of a clinical decision. Dr Margaret Chan, Director-General, World Health Organisation (2011, p. 8) Safe administration of medicines relies on medicines management, a system aimed at maximising the benefits of medicines for patients, while minimising potential harm (Nursing and Midwifery Council [NMC], 2010, p. 4). Many government and other agencies are involved in medicines management from manufacture to administration and ultimately disposal of medicines (Adhikari, Tocher, Smith, Corcoran, & MacArthur, 2014; Department of Health, 2002; NMC, 2010). At the institutional level, medicines management is a complex multi-stage and multi-disciplinary process, involving doctors, pharmacists, nurses and patients (Adhikari et al., 2014). In Australia, the National Medicines Policy (NMP) and Quality Use of Medicines (QUM) are the overarching regulatory and policy frameworks relating to the medicine therapy. Stimulated by the World Health Organization as part of a global scheme to implement national medicinal drug policies, the NMP has initiated 16

30 Chapter 2: Literature Review partnerships between governments, educators, health practitioners, the healthcare and medicines industries and consumers, with the goal of working together to promote the objectives of the policy. Nationally standardised regulation of medicines aims to ensure appropriate practices are followed in the development, production, supply and disposal of medicines under the responsibility of the Therapeutic Goods Administration and in cooperation with State and Territory Governments and with industry. Quality Use of Medicines (QUM), and within it the QUM Strategic Action Plan, are central objectives of Australia s NMP promoting wise use of medicines in health management. QUM means selecting health management options wisely by: considering the place of medicines in treating illness and maintaining health; choosing medicine therapy, taking into account the best available treatment options for the individual; and using medicines safely and effectively to get the best possible results. The patient is the final step in the process of administering a medicine, and as a QUM partner, plays a role in the quality, safety and efficacy of medicine use by making the best possible use of medicines. Medicines are the most common treatment used in health care and are associated with a higher prevalence of errors and adverse events than other medical interventions (Australian Commission on Safety and Quality in Health Care and NSW Therapeutic Advisory Group Inc., 2014; Runciman, Roughead, Semple, & Adams, 2003; WHO, 2009). The potential for serious harm when a medication error occurs means medicine administration is one of the highest risk areas of nursing practice and an ongoing cause of concern to both managers and healthcare professionals (Anderson & Webster, 2001; Davis, Keogh, Watson, & McCann, 2005). Nurses play a key role in administering medicines. In Australia, the activities, education and registration of nurses are controlled within a tightly regulated national structure. The Australian Health Practitioner Regulation Agency regulates health practitioners in partnership with the relevant National Board, the Nursing and Midwifery Board of Australia being the relevant Board for nurses. The Australian Nursing and Midwifery Accreditation Council (ANMAC) is the independent accrediting authority determining the professional responsibilities of nurses and midwives (Nursing and Midwifery Board of Australia, 2017). National standards at the point of registration, including those related to competence in 17

31 Chapter 2: Literature Review medicine administration, are controlled by the Nursing and Midwifery Board of Australia (Nursing and Midwifery Board of Australia, 2016b) Medication error: A problem with multiple causes In medicine therapy, medication errors can occur at any stage of the process from prescribing, dispensing, and administering, to recording, monitoring, and reporting (Adhikari et al., 2014). Significant numbers of patients are harmed every year as a result of their health care (WHO, 2009, p. 10). It is difficult to ensure safe care when so many different health care providers are involved in providing successful treatment for each patient (Anderson & Webster, 2001; WHO, 2009). The complexity of administering medicine therapy makes it error-prone, with the result that medication error remains a major challenge to patient safely in healthcare facilities globally (Adhikari et al., 2014; Alsulami, Conroy, & Choonara, 2012; WHO, 2011). Adverse medication events are frequently multifactorial in nature (Anderson & Webster, 2001; WHO, 2011), highlighting the importance of understanding all contributing factors so strategies to improve medication safety can target multiple points in the process (WHO, 2011). Efforts to identify the causes of adverse events affecting patients have shifted over recent years to systems failures rather than focusing on individual blame and the personal deficits of the health professionals involved. Such an approach is credited with reducing the likelihood of error by introducing checks in the system that can intercept errors before they reach the patient (Fortescue et al., 2003). Organisations at national and global levels have identified education as a core strategy to address medication error, with the World Health Organization leading the way in stimulating educational initiatives (WHO, 2011). Factors associated with medication error include the following (Härkänen, Ahonen, Kervinen, Turunen, & Vehviläinen-Julkunen, 2015; National Patient Safety Agency [NPSA], 2007; Runciman et al., 2003; WHO, 2011, p ): personal factors (e.g. rushing, interruptions); workplace design (e.g. inappropriate storage of medicines) ; medicine design (e.g. tablets similar in name or appearance) ; certain classes of medicine, especially those intended for paediatric patients; 18

32 Chapter 2: Literature Review where, and by whom, the medicine is prepared (e.g. by the nurse in a clinical area rather than by the pharmacist in a ready-to-use form); and how and when the medicine is administered (e.g. intravenously/during a morning shift) (Hughes & Edgerton, 2005). Injectable medicines carry additional risks of calculation error. These risks relate to specific actions performed during preparation and administration (Beaney & Black, 2012), including: diluting a concentrate; reconstituting a powder with a liquid; using part of a vial/ampoule or multiple vials/ampoules; performing complex calculations involving more than one step; and using a volumetric pump or syringe driver The role of nurses in medicine administration Nurses and pharmacists are credited with providing a critical barrier to medication administration errors in hospitals by reviewing medicines before they are administered. Nurses are generally believed to assume primary responsibility for patient safety by ensuring the correct dose is given (Deans, 2005; Elliott & Joyce, 2005). A common perception is that nurses are responsible for detecting all medication errors regardless of where they originate. Nurses responsibilities include detecting errors originating outside nurses roles in calculating and preparing the correct quantity of medicine for administration. This perception is prevalent not only among doctors, pharmacists and administrators, but among nurses themselves (Cook, Hoas, Guttmannova, & Joyner, 2004). However, it may not be realistic to rely on nurses to identify all errors, (Whitehair, Provost, & Hurley, 2014); nurses operate in a complex, often chaotic work environment making it difficult for them to remain entirely focused on the task during medicine administration (Berman et al., 2015). Administering a medicine is not simply a mechanistic task (NMC, 2010). The actual act of administering a medicine is only a small part of the medicine administration process (Eisenhauer, Hurley, & Dolan, 2007), which may involve as 19

33 Chapter 2: Literature Review many as fifty identifiable steps to have the medicine in a ready-to-use form (Hughes & Edgerton, 2005). Safe administration of a medicine requires application of knowledge, multiple clinical judgements, professional vigilance, and highly complex thinking (Hayes, Jackson, Davidson, & Power, 2015; NMC, 2010; Eisenhauer et al., 2007). Nurses draw on their knowledge, experience, and ability to anticipate problems, integrating these competencies with an understanding of the individual patient s clinical history (Eisenhauer et al., 2007). High levels of professional vigilance are needed to identify clinically significant signals for intervention, and act on cues to minimise risks and respond to threats (Meyer & Lavin, 2005). As well as cognitive skill, medicine administration demands effective communication with patients and other health care professionals, and psychomotor skill, for example, to administer medicines by injection or intravenous infusion with the least amount of pain (Wolf, 2014) The incidence of dose calculation and measurement error It is very difficult to determine the extent to which nurses incorrect calculations, or their measurement errors, contribute to the overall incidence of medicine administration error in practice (Cartwright, 1996). Barriers to developing a clear picture of the negative impact of calculation and measurement error largely relate to inconsistencies in defining error types and methodological differences in collecting and reporting evidence. After a comprehensive search of the literature, it seemed to me dose calculation and measurement errors were most likely to be included by researchers in error categories labelled: dosing error, improper dose, wrong/incorrect dose, wrong dose, strength or frequency, wrong/unclear dose or strength, or wrong frequency, dose miscalculation, overdose, and underdose (Cartwright, 1996; Cousins et al. 2002; Deans, 2005; Ghaleb et al. 2006; Kaushal et al. 2001; Kozer et al. 2002; NPSA, 2007a, 2009a; Wolf et al., 2006). However, my conjecture was impossible to confirm because of a lack of clarity about how nurses miscalculations and measurement errors are classified and where they are recorded. Nevertheless, the evidence examined suggested few errors affecting patients involved nurses. Many errors classified as incorrect dose originated in the prescribing stage and resulted from causes such as poor use of abbreviations used to 20

34 Chapter 2: Literature Review represent quantities, illegible writing, and incomplete or ambiguous prescription instructions (NPSA, 2007a). Doctors prescribing errors were more frequent than errors made by nurses in the administration stage (Ghaleb, Barber, Franklin, & Wong, 2010; Wright, 2009). It also seemed clear very few of the latter resulted from incorrect calculation or measurement of the dose. The results of several studies supported these conclusions. Dose miscalculation accounted for 8% of the human factors reported in a self-report survey of medication errors by 154 registered nurses employed at a major regional hospital in Victoria (Deans, 2005). Calculation errors accounted for 7% of the medication errors made by 274 nurses over a three-year period following their employment at a hospital in the USA (Calliari, 1995). Incorrect doses (which possibly included miscalculation or measurement error) accounted for just 1% of the errors identified in a study (Härkänen et al., 2015) involving 32 registered nurses administering 1058 medicines to 122 inpatients in a university hospital in Finland. Even in the error-prone administration of medicines to paediatric patients (Ghaleb et al., 2010), incorrect dose has not been found to be a major cause of medication administration error, despite nurses frequently needing to perform complex calculations to tailor the dose to the patient, thus increasing the likelihood of calculation error. Incorrect dose accounted for 9% of the 429 medication administration errors observed in a study involving ten wards across five hospitals in the London area caring for paediatric patients (Ghaleb et al., 2010). Few studies identifying nurses calculation and measurement errors were found. Exceptions were a UK and a Finnish study. Both studies revealed the contribution of incorrect dose errors to the overall incidence of medication administration error was exceeded by causes such as incorrect preparation, omission, incorrect time, medicine left by the beside without the nurse administering it, and defunct medicine. Indeed, the absence of calculation error as a category in its own right in error studies may be considered evidence it is not a major problem in clinical practice (Wright, 2009). Yet, despite the lack of evidence of calculation and measurement errors being a significant problem in practice (Hoyles, Noss, & Pozzi, 2001; Wright, 2007b, 2009a), errors made by nurses in dose calculation assessments have long been seen as signifying a problem in practice. Consequently, student and graduate nurses dose calculation errors continue to be the target of remediation efforts among educators and employers of nurses (Wright, 2013). 21

35 Chapter 2: Literature Review Patients at high risk of harm from calculation error Children and older people are particularly vulnerable to harm from medication administration error (Ghaleb et al., 2010), the most common type of adverse event affecting hospitalised children. Medication error is more likely to result in death when it affects a child than when it affects an adult (Hughes & Edgerton, 2005). Hughes et al. (2005) found inability to calculate the correct dose caused the majority of paediatric medication errors (Hughes & Edgerton, 2005), with ten-fold errors in the dose a particular problem (Lesar, 2002; NPSA, 2007a). Ghaleb et al. (2010) confirmed the high prevalence of dose calculation errors impacting paediatric patients. They analysed over 1500 doses administered to 265 paediatric patients by 161 nurses in five different types of hospital in the London area of the UK caring for paediatric inpatients. I determined that faulty mathematical procedures may have been implicated in two categories when I conducted an examination of the nine listed error categories. These categories were wrong rate of intravenous administration, which accounted for 20% of administration errors (the second most frequent error type following incorrect preparation errors), and incorrect dose, which accounted for 9% of errors (the fifth most frequent error type after incorrect time and drug left by the bedside without administering it). Other errors included incorrect administration technique, omission error, extra dose error, and incorrect drug. 2.2 Perspectives on the effective learning of mathematics When the workplace is the site of safety-critical judgements by professionals (Coben, 2010), effective education for numeracy is paramount if employees are to develop the characteristics of being numerate. Coben et al. (Coben, Fitzsimons, & O'Donoghue, 2000) defined numeracy thus: To be numerate means to be competent, confident, and comfortable with one's judgements on whether to use mathematics in a particular situation and if so, what mathematics to use, how to do it, what degree of accuracy is appropriate, and what the answer means in relation to the context. (p. 35, emphasis in the original) In the quest to develop nurses who are truly numerate and capable of accurately calculating medicine doses several questions arise. What knowledge, 22

36 Chapter 2: Literature Review skills and attitudes do nurses need to possess to be deemed competent to administer medicines in clinical practice, and what type of teaching, learning, and assessment is likely to be most effective in developing competence? To answer these questions, an appropriate starting point is to consider contemporary perspectives on effective learning of mathematics and the type of approaches to instruction and classroom practice most effective in fostering successful learning. It is informative to contrast contemporary views of mathematics and effective learning with traditional views many current educators seek to replace and consider how contemporary views might be applied to nurses learning strategies for calculating medicine doses Contemporary and traditional views of learning mathematics For several decades there has been general acceptance among mathematics educators that one of the goals of learning mathematics is for students to become competent problem solvers. However, the task of setting appropriate goals for mathematics instruction depends on what one believes mathematics is, and what it means to understand mathematics (Schoenfeld, 1992). A further question to be resolved is how problem solving fits within those goals. Several authors have suggested mathematics is problem solving and problem solving should be the basis of the mathematics curriculum (Pólya, 1945; Romberg & Kaput, 1999). Hiebert et al. (1997, p. 11) advocated that, ideally, learning skills should be viewed as a problem-solving activity, rather than an exercise in transmitting rules and procedures. The term problem solving evokes many different meanings ranging from performing rote exercises to undertaking mathematical activities as a professional (Schoenfeld, 1992). Consequently any discussion of problem solving should include a definition of the term. One definition is: developing a mathematical point of view and the tools to go with it (Schoenfeld, 1992, p. 334). As they reflect on learning and assessment of dose calculations, nurses educators will meet significant challenges in their efforts to construe dose calculation as problem solving, articulate what mathematics is in the context of dose calculations, and define a mathematical point of view and the tools to go with it in relation to dose calculation. Educators will meet similar challenges as they endeavour to identify what constitutes appropriate mathematics instruction for dose 23

37 Chapter 2: Literature Review calculation, and what it means to understand mathematics in relation to dose calculations. To many people, mathematical knowledge is a body of facts and procedures, and knowing mathematics is having mastered those facts and procedures (Schoenfeld, 1992). Schoenfeld regarded teaching mathematics based on the concept of it being a rigid, absolute, closed body of laws to be memorised as trivialising mathematics and that a curriculum based on mastering a corpus of mathematical facts and procedures was severely impoverished (p. 335). By contrast, Schoenfeld viewed mathematics as an exploratory, dynamic, evolving discipline (p. 335). Schoenfeld described the desired focus in learning mathematics as: seeking solutions, not just memorising procedures; exploring patterns, not just memorising formulas; formulating conjectures, not just doing exercises (Schoenfeld, 1992, p. 335). From a contemporary perspective, learning mathematics is empowering and leads to quantitatively literate students capable of making balanced judgements and applying mathematics in practical ways such as using proportional reasoning. Schoenfeld suggested such students are flexible thinkers with a broad repertoire of techniques and perspectives for dealing with novel problems and situations (p. 335). Approaching dose calculation instruction from a perspective aligned with the image portrayed by Schoenfeld has significant implications for the formula-based approach and the didactic transmission methods traditionally used to teach dose calculations. Cultural assumptions shaped by formal learning experiences include the perception that mathematics is associated with certainty. Doing mathematics means following the rules laid down by the teacher, and knowing mathematics means remembering and applying the correct rule, and being able to get the right answer quickly (Lindquist, 1997; Schoenfeld, 1992). Schoenfeld (1992) illustrated how such cultural perceptions might translate into classroom practice: a task is used to introduce a technique, the technique is illustrated and more tasks are provided for practice, after which the student has a new technique in their mathematical tool kit. The sum total of such techniques reflects the student s mathematical knowledge and understanding. Similar descriptions of how students attempt to learn to learn dosage calculations abound in the literature (Weeks, 2001; Weeks, Clochesy et al., 2013). My examination of current text books on the topic provided further evidence confirming this approach. Consistent experiences of the type described by these authors may lead to students giving up trying to make sense of mathematics, accepting a passive role, and 24

38 Chapter 2: Literature Review forming the view mathematics is handed down by experts for them to memorise (Schoenfeld, 1992). According to Schoenfeld, students may perceive the methods teachers and texts impose on them as arbitrary and in conflict with the methods they might have attempted themselves. This perception is likely if students are taught a single method different from how they might have approached the calculation problem. Repeated experiences resulting in the type of conflict described may give rise to beliefs such as the following: doing mathematics requires lots of practice in following rules; there is always a rule to follow to solve mathematics problems; there is only one correct way to solve any mathematics problem, the method provided by the teacher or text; mathematics is a solitary activity done by individuals in isolation; mathematics learned in formal settings has little or nothing to do with the real world; and ordinary students cannot expect to understand mathematics, rather, they should expect simply to memorise and apply what they have learned mechanically and without looking for meaning (Schoenfeld, 1992, p. 343). Students taught using traditional talk and chalk classroom pedagogy often have no experience of the practical applications of the calculation strategies they are attempting to learn until much later. When that exposure occurs, they are expected to immediately be capable of transferring their learned skills to an unfamiliar clinical practice environment (Weeks, Clochesy, et al., 2013). When students experiences of mathematics follow the traditional approach described, they may be unable to attempt problems for which they have no ready solution method, or give up trying after a brief attempt without success (Schoenfeld, 1992). Many student nurses enter the domain of nursing numeracy against this background of prior experiences of mathematics and mathematics learning. They find their previous experiences of mathematical endeavour continue unchanged: they learn the formula by rote then gain practice in applying it mechanically. Therefore it should not be surprising that students whose instruction in dose calculation is similar to that described by Schoenfeld (Schoenfeld, 1992) fail to master dosage calculation, 25

39 Chapter 2: Literature Review as has so frequently been reported in the literature (Hutton, 1998a; Savage, 2015; Weeks, Hutton, Young et al., 2013; Weeks, Lyne, & Torrance, 2000) Social constructivism and situated cognition Theories concerning the social construction and social transmission of mathematics, the situated nature of cognition (Brown, Collins, & Duguid, 1989; Nasir, Hand, & Taylor, 2008) and cognitive apprenticeship (Collins, Brown, & Newman, 1989) were widely accepted by the end of the 1980s as being well grounded in empirical evidence (Schoenfeld, 1992). According to Resnick (1988), becoming a good mathematical problem solver may be as much a matter of acquiring the habits and dispositions of interpretation and sense-making as acquiring any particular set of skills (p. 58). Resnick suggested teachers would do well to consider mathematics education less as an instructional process in the traditional sense and more as a socialisation process in which developing a mathematical point of view and desired behaviour patterns is socially mediated (Resnick, 1988; Schoenfeld, 1992). Socialisation or enculturation is the process of entering and picking up the values of a community or culture (Resnick, 1988, p. 39). Learning in any domain proceeds not through absorption but is culturally shaped and defined: people develop their understandings of any enterprise from their participation in the community of practice within which that enterprise is practiced (Schoenfeld, 1992, p. 341). The clinical practice environment in which medicine doses are calculated and administered provides an environment rich in opportunities for student nurses to enter a community of practice and learn values and skills appropriate for safe, accurate medicine dose calculation. However, the potential for positive learning opportunities in which students develop their understandings of dose calculation, are counterbalanced by equally potent opportunities for the reverse to occur. The apprenticeship model has the potential to enculture students in a community of practice characterised by negative values and procedural calculation methods, rote learned and devoid of meaning. Constructivism implies a belief all knowledge is a product of our own cognitive acts (Confrey, 1990, p. 108); knowledge is constructed through our experiences, rather than simply through absorption. Applying constructivism in teaching means one must reject the transmission model of learning (Barnes, 1998) or 26

40 Chapter 2: Literature Review empty bucket theory (Eppler, 2003, p. 81) that assumes one can simply pass on information to learners and understanding will result (Confrey, 1990). Guided discovery and meaningful application in a problem-solving environment are most effective in facilitating mathematical learning, rather than imitation and the rote application of algorithms (Goldin, 1990, p. 31). Reflection and communication are two key cognitive processes in learning (Hiebert et al., 1997). Accordingly, Hiebert et al. (1997, p. 11) advocated part of the teacher s role is to facilitate class discussions, encouraging the sharing of alternative methods and the examination of whether, and why, they work. As part of the journey to becoming a powerful user of mathematics, students need to feel free to hold their own opinions, change their minds, build on others thinking, invent their own methods, and adopt the methods of others. This is all a natural part of the problem-solving process. (Hiebert et al., 1997, p. 127). Social interaction, learning in a problem-solving setting, and an emphasis on cognitive and affective development are central concepts in the sociohistorical theory of learning of Vygotsky, whose work came into prominence in the latter part of last century (Taylor, 1993). If nurses are to become powerful users of mathematics, many of the elements Hiebert and Vygotsky proposed as essential to the process pose significant challenges in terms of current practices relating to dose calculation instruction. The importance of learning dose calculations in problem-solving settings was recognised at least as long ago as 1939 (Faddis, 1939). Faddis advocated orientating students by supplying them with medication cards for hypothetical patients for whom they selected medicines from available stock, and then presented to their peers for verification the card, the bottle, the figuring for dosage, the technic (sic) of administration, and any other significant points (p. 1222). Other early exponents of discovery learning in groups using a hands-on approach utilising the specialised artefacts and terminology of nursing practice include Best and Moore (1988) and Blais and Bath (1992). The intellectual practice of teaching abstract mathematics is the antithesis of approaches recognising the value of real-world contexts in learning. Such an approach limits the learning of students, particularly those of lower socio-economic status (Heckman & Weissglass, 1994, p. 29). Brown et al. (1989) likened the situated nature of knowledge, including mathematical knowledge, to the situated nature of words. Words are situated in that 27

41 Chapter 2: Literature Review their meaning comes from the context in which they are used. Knowledge is similarly situated, contend Brown et al. (1989). A concept, like the meaning of a word, is always under construction and continually evolving. With each new occasion of use the concept is recast in a more densely textured form. Thus adequate contextualisation of dose calculation problems is needed for students to attach meaning to them. Exploiting the situated nature of dose calculations could be the key to the distinction Brown et al. (1989) drew between the acquisition of inert concepts and the development of useful, robust knowledge. They suggested students commonly acquire algorithms, routines and decontextualised definitions bearing no relationship to everyday or vocational mathematical situations. When students find no use for algorithms, routines, and definitions, they lie inert. Reliance on didactic transmission and the use of word problems to represent dose calculation scenarios (Weeks, 2001, p. 32) is common in all modes of dose calculation instruction, including face-to-face teaching, textbooks, and online learning (Rodger & Jones, 2000). However, these approaches fail to enable students to connect calculation processes with authentic problem contexts. Weeks noted that, nevertheless, such approaches are congruent with the novice-to-expert practice whereby students are introduced to new situations by teaching them context-free rules to guide them in their actions. Only through teaching mathematics in the context of authentic practice can teachers avoid sending a message to students that mathematics has no connection to the real world, and mathematics exists without the need to be concerned about whether, and how, it is used (Heckman & Weissglass, 1994). Heckman and Weissglass added a cautionary note, however, that with the goal of providing students with authentic activity comes the weighty responsibility of deciding what is authentic activity, a responsibility they suggested is a curricular and ethical choice. A growing awareness of the importance of learning medication calculations in authentic problem contexts (Coben, 2010) is reflected in recent studies evaluating the effectiveness of learning environments created to embrace the concept of situated cognition. These initiatives took different forms, including laboratory-like settings simulating the clinical environment (Grugnetti, Bagnasco, Rosa, & Sasso, 2014; Ramjan et al., 2014; Rodger & Jones, 2000; Wright, 2005a), and online learning environments attempting to emulate the key features and artefacts of authentic medicine administration (Grandell-Niemi, Hupli, Leino-Kilpi, & Puukka, 2003; 28

42 Chapter 2: Literature Review Macdonald, Weeks, & Moseley, 2013; McMullan, Jones, & Lea, 2010; Weeks, Clochesy, et al., 2013). Simulation of authentic clinical practice environments aims to create learning environments complete with the artefacts and visual cues of clinical practice, thus facilitating contextualisation and conceptualisation of problems being solved. In this way, simulation enables students to better relate the mathematics within nursing practice to problem contexts (Ramjan et al., 2014; Wright, 2005a). Students typically have access to equipment, or images of equipment associated with medicine administration, such as prescriptions written on patient charts, measurement tools such as syringes to actually measure, or measure on-screen, the volume to be administered. Real or placebo medicines in packages or bottles, or images of them, allow the student to see the label describing the medicine and its concentration, and relate that information to the problem (Wright, 2005a). Rodger and Jones (2000) described an approach to the teaching and assessment of medication calculations at their Australian university that sought to create a quasi-real-world (p. 84) learning and assessment environment in contrast to more traditional didactic approaches. Students were exposed to a hands-on practical approach using real medicines and measuring equipment. The approach trialled was a response to the belief among educators at the university the primary cause of dose calculation errors lay in students being unable to conceptualise the problem and relate the calculations they were performing to the clinical context in which they were set. Students in the control group were exposed to traditional didactic lecture delivery with overhead projector presentations, textbook assistance, and computerassisted learning packages. They were assessed using traditional pen-and-paper testing, in contrast to the experimental group who were tested in the simulated clinical setting. The researchers reported that a measure of the success of the new practical approach was all 34 students in the experimental group exposed to it passing the medicine dose calculation exam on their first attempt. This was in contrast to 53% of the 154 students in the control group passing, some of whom required a further two attempts to achieve a pass. Rodger and Jones (2000) concluded that, in comparison to students exposed to traditional didactic teaching and pen-and-paper testing, the practical approach to teaching and assessment compensated to some extent for the limited amount of exposure students have to clinical practice. The additional 29

43 Chapter 2: Literature Review exposure to authentic contexts allowed them to better conceptualise and contextualise medication calculation problems, and this resulted in greater accuracy and reduced anxiety. A different approach to investigating ways to facilitate students learning of dose calculations through simulation of the practice environment (Ramjan et al., 2014) involved implementing instructional interventions of varying levels of authenticity, in the clinical practice unit of the nurses program. The interventions included simulated medication calculation scenarios in the first clinical practice classes, a one-hour cross-disciplinary visually enhanced didactic remediation workshop, and a hands-on contextualised numeracy workshop (p ). Some opportunities were available to all students, and some were offered to support students who had failed to demonstrate competence in the medication calculation tests. Following the interventions, 74% of the 390 students tested achieved the 100% pass requirement on their first attempt, while all but one student passed within the three permitted attempts. An approach to teaching, learning, and assessment of dose calculations trialed by a UK team including Macdonald et al. (2013) and Weeks, Sabin, Pontin, and Woolley (2013) investigated the use of a computer-assisted program designed to expose students to authentic clinical practice scenarios. The approach, like that of Rodger and Jones, was designed to simulate real-world practice. The two approaches differed, however, in that one used the real artefacts of the practice environment (Rodger & Jones, 2000), the other, computer-generated images of artefacts (Macdonald et al., 2013). Both studies instructed students in applying the formula to calculate medicine doses. However, a major difference existed between the approach to assessment taken by Macdonald et al. and that customarily used in other studies (Macdonald et al., 2013). Macdonald et al. assessed performance in the virtual computer-based clinical environment, whereas other studies use traditional paper-based tests to evaluate medicine dosage calculation skills. A separate aspect of the research compared students performance on the computer-based assessment instrument with performance in the practical assessment environment where students were provided with authentic artefacts associated with medicine administration. The study confirmed assessment in the virtual practice environment produced similar results and was a valid alternative to assessment in the simulated practical environment (Coben et al., 2010). 30

44 Chapter 2: Literature Review Learning mathematics with understanding Traditional approaches to teaching and learning mathematics have not resulted in students learning mathematics with understanding. Curriculum documents in several countries reflect attempts to correct past failings and redefine school mathematics and what is important for students to know and understand (Romberg & Kaput, 1999). Among the difficulties in teaching and learning mathematics is the perception, not only among some students, but also among some teachers, the focus should be on immediate results rather than on a need for mathematics to make sense (Lindquist, 1997). The philosopher John Dewey is among the many psychologists, philosophers and educators who have long warned about the damaging effects of teaching without understanding on students ability to reflect and to make sense of what they were doing. According to Lindquist (1997), in 1910 Dewey said: Sheer imitation, dictation of steps to be taken, mechanical drills may give results most quickly and yet strengthen traits likely to be fatal to reflective power (p. viii). A focus on achieving performance without understanding the mathematical underpinnings supporting it is likely to lead to difficulties, as explained by Schoenfeld (1992): A reliance on schemata in crude form When you see these features in a problem, use this procedure may produce surface manifestations of competent behaviour. However, that performance may, if not grounded in an understanding of the principles that led to the procedure, be error prone and easily forgotten. (p. 352). Several authors, in apparent confirmation of Schoenfeld s warning, reported consistent mechanical drills, either in the form of pen-and-paper exercises (Adams & Duffield, 1991) or completion of online quizzes (Sherriff, Burston, & Wallis, 2012), frequently fail to result in mastery of dosage calculations and long-term retention of skills. Others have noted the common phenomenon of nurses failing in tests after having previously demonstrated apparent mastery of dosage calculations (Blais & Bath, 1992; Jackson & De Carlo, 2011; Pierce, Steinle, Stacey, & Widjaja, 2008; Sherriff, Wallis, & Burston, 2011; Wright, 2012a, 2007b). However, a downside to teaching in a way that promotes learning with understanding is the payoff is likely to be long-term. It needs articulation across multiple levels of the educational pyramid, a change in expectations of what students 31

45 Chapter 2: Literature Review will learn and how they will learn it, and a change from commonly held perceptions of accountability (Lindquist, 1997). A comprehensive framework for thinking about mathematical understanding proposed by Hiebert and Carpenter (1992) is useful for considering how medicine dose calculation might be taught in ways promoting learning with understanding. Hiebert and Carpenter proposed that growth of mathematical knowledge can be viewed as a process of constructing internal representations of information and, in turn, connecting the representations to form organised networks (1992, p. 80). Internal networks are dynamic and constantly undergo realignment and reconfiguration in a chaotic process as new relationships are created. Mathematical understanding can be characterised by the types of connections and relationships constructed between ideas, facts, and procedures. Hiebert and Carpenter (1992) distinguished between two types of knowledge crucial for mathematical expertise: conceptual knowledge and procedural knowledge. Conceptual knowledge is knowledge rich in relationships and connected networks. A unit of conceptual knowledge is not stored as an isolated piece of information: it is conceptual knowledge if it is part of a network. By contrast, procedural knowledge is a sequence of actions such as those followed in standard computational algorithms used in arithmetic; minimal connections are needed to create internal representations of succeeding actions in the procedure. The benefits of learning mathematics with understanding have been described by Hiebert and Carpenter (1992) as well as other authors (e.g. Gould, 1996; Southwell, 1998; Skemp, 1986) and have particular implications for nurses learning of dose calculation skills and for addressing recurrent problems concerning still development (Ramjan et al., 2014). For nurses to learn dose calculations with understanding, the process should typically commence in the university learning environment and continue during supervised clinical practice. Learning with understanding should continue to be developed through experience in clinical practice after qualifying as a Registered Nurse. According to Hiebert and Carpenter (1992), understanding is: generative; promotes remembering; enhances transfer; and 32

46 Chapter 2: Literature Review influences beliefs. Understanding is generative: When a nursing student invents a new technique or procedure based on their existing understandings, this may generate new understandings, suggesting a generative effect. As neural networks grow and become more structured, they increase the potential for invention. This argument highlights the importance of building understanding right from when dose calculation is first encountered. New representations are more likely to connect with rich networks of knowledge than with impoverished networks, simply because there is more to which they can relate. Understanding promotes remembering: A problem reported in the literature is nurses failure to remember how to calculate medicine doses, even after testing has indicated mastery (Rice & Bell, 2005). This phenomenon highlights the value of nurses understanding the dose calculations they perform. Memory is a constructive or reconstructive process, rather than a passive activity of storage. When connections are created between new information and existing knowledge, new information that is well-connected to existing knowledge is remembered better. Hiebert and Carpenter (1992) offered two explanations for this. First, an entire network of knowledge is less likely to deteriorate than an isolated piece of information. Second, retrieval of information is enhanced if it is connected to a larger network: there are simply more routes of recall. Understanding enhances transfer: In the calculation of medicine doses, as in other mathematical endeavours, nurses cannot possibly learn a separate strategy for every type of problem they may encounter. According to Hiebert and Carpenter (1992) transfer is essential for mathematical competence because new problems need to be solved using previously learned strategies. Transfer from one task to another is high if a large number of the elements making up the tasks are alike. Understanding influences beliefs: As well as the cognitive consequences of understanding, Hiebert and Carpenter (1992) postulated understanding also has important yet subtle affective consequences. For example, the way nurses approach medicine dose calculation is likely to influence their beliefs about mathematics and their role in calculating and administering medicines. If nurses are encouraged to construct connections between pieces of information within a representation system or between different representation systems, they may come to realise mathematics is 33

47 Chapter 2: Literature Review a cohesive body of knowledge and information acquired in one setting will connect with information acquired in another Classrooms promoting effective learning of mathematics The type of classroom environment the teacher creates mirrors the teacher s sense of the mathematical enterprise. That environment, in turn, moulds students beliefs about what mathematics is: students adopt the perspectives and prejudices of the community in which they learn (Schoenfeld, 1992, p. 365, 339). According to Schoenfeld, this generally accepted belief carries important ramifications for the types of classrooms and learning experiences teachers should strive to create to facilitate students understanding. It highlights, too, the unfortunate consequences likely to follow if students become part of the wrong kind of community of practice (Schoenfeld, 1992, p. 360). Classroom mathematics should mirror the desired type of sense-making if students are to understand mathematics and use it in meaningful ways (Schoenfeld, 1992, p. 340). In their classrooms, teachers should strive to create communities of practice modelling the types of mathematical sense-making we hope the students will develop (Schoenfeld, 1992, p. 345). Lindquist (1997) observed the convergence of five dimensions tasks, teacher s role, social culture, tools, and equity provides a framework for creating mathematical classrooms providing all students with the opportunity to build mathematical understandings they can use throughout their lives (Lindquist, 1997, p. xv). Teachers allow students the time needed to develop their own procedures and do not expect all students to use the same ones. Class discussions involve sharing alternative methods and examining why they work (p. 11). Reflection and communication are two key cognitive processes. The importance of well-defined learning goals Good teaching is always associated with well-defined learning goals (Ermeling, Hiebert, & Gallimore, 2015). Applying this belief to the task of facilitating development of effective dose calculation skills implies educators should be asking questions such as: What is the goal of learning? Is it to have students correctly execute the substitution of values into a prescribed formula, use a calculator to obtain correct answers, and be able to repeat this process with many different combinations of values? Is the learning goal something more than students being 34

48 Chapter 2: Literature Review able to mechanically use the formula provided? Is the learning goal that students develop procedures they are able to apply as needed, without loss of skills over time, adapting them to solve variants of the same problems as they encounter them in the future? Different learning goals are better achieved by different teaching approaches (Ermeling et al., 2015). The former goal of mechanically applying a formula to obtain correct answers is best achieved through error-free repetition combined with feedback. However, these authors contended the goal of long-lasting, adaptable skills is better achieved if students are required to exert some intellectual effort in making sense of the procedures, perhaps wrestling with the question of why the procedures work (Ermeling et al., 2015, p. 50). Students are more likely to gain durable learning (p. 50) with the capacity for retention and transfer over time through instructional methods encouraging thought to understand the mathematical principles underpinning procedures. The principle that some methods are more effective in achieving certain learning goals than others applies even to very young children (Ermeling et al., 2015). Ermeling et al. gave the example of children s learning of arithmetic skills, arguing it is likely to be more effective if they are encouraged to invent their own way of solving simple story problems rather than being taught the necessary arithmetical skills through processes such as filling in the blanks in number sentences (e.g. 8 3 =. ). In the context of nurses learning to calculate medicine doses, educators and employers of nurses may need to shift away from a goal of students learning to use a single calculation strategy in a mechanical way to get correct answers. Nurses need to have control over the strategies they use to calculate doses. They need robust skills that equip them to successfully tackle the vast diversity of dose calculations they will encounter in their careers. They need solution techniques they feel secure using, can easily recall, and can adapt to many medicines, doses and clinical situations. Designing instructional approaches According to Schoenfeld (1992, p. 345), instruction that is most likely to result in the development of mathematical power is aimed at: developing conceptual understanding rather than mere mechanical skills; providing opportunities to explore a broad range of problems and exploratory situations and to respond with flexibility and resourcefulness; 35

49 Chapter 2: Literature Review providing students with a broad range of approaches and techniques ranging from the straightforward application of the appropriate algorithmic methods to the use of approximation methods; helping students develop their analytical skills, and the ability to reason in extended chains of argument; preparing students to become independent learners, interpreters, and users of mathematics; and helping students develop mathematical modes of thought that are both versatile and powerful. The role of the teacher Perceptions concerning teachers roles in the classroom have gradually changed from earlier notions suggesting teachers were passive conveyors of facts and information (Hoyles, 1992, p. 33) to a role focused on developing independent learners whose skills are durable, flexible and adaptable. This change is reflected in two approaches to introducing a new concept to students in the classroom described by Ermeling, Hiebert and Gillimore (2015). Ermeling, Hiebert and Gillimore (2015) proposed that ideally students are given the opportunity to grapple with novel and challenging problems before they are introduced to specific formulae or rules. In contrast to this approach, is the approach of another teacher who reduces potentially rich and challenging problem scenarios to purely mechanical tasks by introducing specific formulae and procedures and asking students to apply them to obtain correct answers. Students then further consolidate their skills through repetition by working through exercises in learning resources. In classrooms supporting effective learning the teacher should see their role as one of posing problems, coordinating discussions, and joining students in asking questions and suggesting alternatives (Hiebert et al., 1997, p. 11). The teacher will also allow students the time they need to develop their own procedures, rather than expecting all students to use the same procedures. Recommendations for teachers proposed by Schoenfeld (1992, p. 365) include: modelling problem-solving behaviours whenever possible, exploring and experimenting along with students; 36

50 Chapter 2: Literature Review creating a classroom atmosphere in which all students feel comfortable trying out ideas; inviting students to explain their thinking at all stages of problem solving; and presenting problem situations closely resembling real situations in their richness and complexity so the experience students gain in the classroom will be transferable. Beliefs and attitudes play an important role in mathematics teaching and learning, both for students and teachers. Students beliefs shape their behaviours in ways that have extraordinarily powerful (and often negative) consequences. Students form their beliefs largely from their classroom experiences and from the community in which they learn (Schoenfeld, 1992, p ). Teachers must ask critical questions to uncover implicit beliefs, such as what it means to learn mathematics, how the curriculum has been created and by whom, the relevance of the curriculum to the needs of all students, and whether the instructional model predisposes some groups to succeed and others to fail (Heckman & Weissglass, 1994). When educators select resources and devise educational experiences, they invariably express their own beliefs and values about the mathematics being taught and how it should be taught (Heckman & Weissglass, 1994). No material or learning environment is free from judgemental decisions about what is valuable. According to Heckman and Weissglass: To effectively teach and effectively learn in situated cognition and/or cognitive apprenticeships, many traditional values and beliefs must make way for more democratic concepts in which assumptions of the dominant culture are questioned and cultures of the students are respected. (p. 31) The way mistakes are viewed is a distinguishing feature of the type of classroom environment teachers have created. Hiebert et al. (1997) contended mistakes are important sites for learning (p. 126), sometimes serving as stepping stones from which students construct their solutions. Ideally mistakes should come to be regarded as: methods that could be improved, as useful starting points rather than dead ends. Mistakes often signal differences in students opinions and these 37

51 Chapter 2: Literature Review differences generate arguments and trigger attempts to justify and explain. These justifications and explanations provide the real learning opportunities, both for the speaker and for the listeners. (Hiebert et al., 1997, p. 126). Teachers attitudes to students inadequacies and failures may also have a critical impact on learning (Heckman & Weissglass, 1994). Heckman and Weissglass recommended teachers view difficulties as the result of past experiences of failure, the effects of ridicule and criticism that have disempowered students, and lack of opportunities to learn in a situated environment. 2.3 Mathematics in vocational and everyday settings Studies of adults mathematical practices in workplace and everyday situations have highlighted just how far removed mathematics in these setting is from mathematics taught in school (Pozzi, Noss, & Hoyles, 1998). In their everyday lives, people engaged in a wide variety of mathematical endeavours in different countries have demonstrated the widespread use they make of mathematical concepts and techniques they have not learned in school (Nunes, Schliemann, & Carraher, 1993) or other formal settings. Since the 1980s, research in the field of situated cognition has yielded rich insights into how adults use mathematics in the workplace. The focus of these studies has included dairy workers, carpenters, civil engineers, and nurses (Hoyles, Noss, Kent, & Bakker, 2010). Another strand of enquiry by Nunes et al. (1993) revealed how Brazilian children operating as street vendors used mathematics in ways quite different from their school mathematics. Lave (1988) attributed the distinction between everyday mathematical practices and school mathematics to the absence of constraints placed on the strategies able to be used in everyday situations: adults use any technique available to them to perform the desired calculations. By contrast, school mathematics is regulated in regard to both strategies and resources. The regulation-free situation of shopping mathematics was the explanation Lave gave for the essentially error-free shopping strategies of adults in her study compared to their more error-prone calculations performing the same tasks posed as written problems. Most adults use mathematics in everyday life in ways vastly different from the mathematics learned in formal settings (Hoyles et al., 2010; Lindquist, 1997; Nunes 38

52 Chapter 2: Literature Review et al., 1993). They make sense of situations in ways that differ quite radically from those of the formal mathematics of school, college and professional training, and make far greater use of informal methods. Problem-solving at work is characterised by pragmatic goals to solve particular types of problems using techniques that are quick, efficient and adapted to the workplace problem context, rather than being focused on striving for consistency and generality, which is stressed by formal mathematics (Hoyles et al., 2010). Pozzi et al. (1998) likened the techniques nurses and other users of numeracy in the workplace employ for the sake of expediency (Coben, 2010) to the fast and frugal heuristics described by Gigerenzer et al. (2001): simple and adaptable problem-solving techniques that use realistic mental resources. The application of knowledge in workplace practices is often invisible (Coben, 2010; Hoyles et al., 2010; Marks et al., 2016). In the case of mathematical knowledge, the invisibility of mathematics adds to the difficulty of investigating how adults use mathematics in out-of-school settings. Hoyles et al. (2010, p. 8) observed that mathematical knowledge is judged to be invisible in many situations as it tends to be deeply embedded within the representational infrastructures of the models, tools and artefacts of the workplace. Nurses, for example, may no longer see the calculations they perform as part of their routine care (Hutton, 1998b; Marks et al., 2016) because the embedded nature of the calculations renders them invisible (Sabin, 2013, p. e3). Similarly, nurses often do not identify taking observations such as weight, girth, temperature, blood pressure, respiratory rate, and pulse oximetry reading as measurements (Cartwright, 1996). Teaching and learning of mathematics for workplace application should be very different from traditional school-based approaches (Hoyles et al., 2010). Hoyles et al. argued learning experiences should be designed to exploit the richness of the workplace context, utilising the multitude of meaningful problem contexts to motivate mathematical thinking and harness the expertise of learners. Utilising workplace problem contexts to facilitate learning was a theme echoed by Coben (2010): Where mathematics is situated in professional/vocational practice it should be taught, learned and assessed in relation to that practice, both directly in practice and through authentic and comprehensive simulation of practice; the latter enables individuals to be exposed to the full range of problems associated with 39

53 Chapter 2: Literature Review the use of mathematics in their professional practice, something which may be impossible to do safely, comprehensively and effectively in real world, real time contexts. (p. 18) Hoyles et al. (2010) noted, however, the highly didactic nature of much of the workplace numeracy training they observed, and the disturbing practice in which much of workplace training in mathematics in the UK is dominated by the delivery of general techniques out of context, which employees were invited to apply to their work-based problems (Hoyles et al., 2010, p. 9). Such an approach, they warned, mitigates against effective training by ignoring the whole richness of the workplace context in which employees are working (p. 184) and the huge potential for meaningful learning it offers. Delivering general techniques without locating them in meaningful contexts is also likely to evoke negative reactions from students who have already been alienated by their school mathematics experiences. In relation to such an approach applied to nursing numeracy, Hoyles et al. (2010) proposed that, like other forms of workplace mathematics, the kinds of knowledge and skills required for dose calculation are not easily or effectively developed by an approach that teaches generalised context-free strategies. This is the contemporary vocational educational framework within which current teaching of dose calculation should be considered. The mathematics in the work of nurses and pilots (Hoyles et al., 2001; Noss, Hoyles, & Pozzi, 2002) and professional engineers (Kent & Noss, 2002) was the subject of earlier investigations of the workplace mathematics of professionals. The most common observation of these researchers was the situated nature of the mathematical reasoning these professionals used, compared to the formal and generalised nature of traditional workplace training (Hoyles et al., 2010). They found general mathematical techniques were often rejected in favour of techniques adapted to the particular types of workplace problems to be solved. The formula nurses had been taught by educators who considered it efficient (Hoyles et al., 2010, p. 7) was among the rejected techniques. Hoyles et al. (2010) summarised their findings concerning the process of meaningful learning and application of mathematics in workplace settings: Mathematics learning becomes meaningful when learners (whether young people in school, or adults in workplaces) are given the space to express, share and develop their own ideas, and teaching becomes effective if, for example, it 40

54 Chapter 2: Literature Review builds on the knowledge learners already have, and develops appropriate mathematical language through communicative activities and higher-order questioning. (p. 9) In relation to nursing numeracy, Coben (2010) stressed the innate potential for nurses to develop the necessary mathematical expertise, given the right learning environment. She called for a move to: a more open, democratic holistic approach that recognizes the strengths of capable, experienced professionals and the potential of novices to develop expertise and experience through an appropriate programme of teaching and learning founded on a deep understanding of the requirements of the work in question. (Coben, 2010, p. 19) The benefits and satisfaction associated with valuing the prior knowledge and expertise of learners was evident in a project focusing on development of technomathematical literacies undertaken by Hoyles et al. (2010). They found giving voice and autonomy to the expertise of employees (p. 186) resulted in unexpected benefits to participants who reported experiencing a heightened feeling of job satisfaction and sense of empowerment. 2.4 Solving dose calculation problems Accurate calculation and measurement of the quantity of medicine are vital aspects of medicine administration. The calculation requirements may be simple or complex, and may involve one step or many steps. The quantity to be administered may be a number of tablets or capsules, or a number of millilitres of liquid. The first step in determining the dose to administer is often conversion of one quantity to the same unit of measure as another (Coben et al., 2010; NPSA, 2007a, 2007b; Simonsen, Daehlin, Johansson, & Farup, 2014; Wright, 2005b). Some medicine administrations require several calculations, increasing the complexity of the calculation process. Medicines for paediatric patients, for example, are often ordered by way of instructions from doctors indicating how nurses should determine the prescribed dose, rather than by stating a prescribed dose as such. Doctors state a milligram per kilogram (mg/kg) value on the patient chart and nurses use that rate to calculate the mass of medicine required, based on the child s weight (Hughes & Edgerton, 2005; Starkings & Krause, 2015;). Nurses then perform a 41

55 Chapter 2: Literature Review second calculation to determine the quantity of medicine needed to administer the calculated mass. Measurement of the dose is the final step in readiness for administering the medicine. Some medicines, typically antibiotics, are supplied as a vial of powder because the medicine is unstable in liquid form (Saxton et al., 2005). The nurse first reconstitutes the powder with a diluent, such as sterile water for injection (possibly allowing for displacement) in accordance with the manufacturer s instructions (Saxton et al., 2005). The nurse then works out the concentration of the reconstituted solution, the two key quantities being the mass of the powder contained in the vial (for example, 1 gram), and the final volume of the reconstituted solution (for example, 1 gram per 10 millilitres). Using this concentration, the nurse then calculates the quantity of the solution needed to deliver the dose prescribed (Kee, Marshall, Forrester, & Woods, 2016; Saxton et al., 2005). Accuracy in medication calculations is an essential requirement for the safe administration of medicines and the clinical efficacy of the treatment. Nursing curricula have not always included mathematics (Hek, 1994), however there is now widespread acceptance educational institutions and students themselves bear the responsibility for ensuring the skills of graduate nurses are adequate for their role in medicines management (Ramjan et al., 2014). As a consequence, effective teaching, learning and assessment of the necessary mathematical skills are regarded as an important goal of the nursing curriculum to ensure nurses are competent and confident in the administration of medicines in clinical practice A problem of proportionality Medicine dose calculations are essentially problems of proportionality (Hoyles et al., 2001). Together with those who solve the many problems of proportionality encountered in workplace and everyday situations, nurses, too, need proportional reasoning skills either formal or informal to solve dose calculation problems. They must calculate the missing value in the problem, namely the quantity of medicine the nurse needs to administer. Calculating medicine doses falls within a set of mathematical problems described by Vergnaud (1983) as multiplicative structures, a conceptual field encompassing multiplication, division, fraction, rational number, decimal, linear function, dimensional analysis, and vector space (Behr, Harel, Post, & Lesh, 1992; 42

56 Chapter 2: Literature Review Vergnaud, 1983). According to Vergnaud, these concepts cannot be regarded as independent of one another and may be present simultaneously in problems of proportionality. The basis of proportional reasoning lies in the relationship existing between two quantities where one quantity changes in direct 3 proportion to the other. Problems of proportionality typically involve dealing with two measure spaces. In the case of medicine doses, the first measure space is most commonly mass (measured in grams, milligrams or micrograms). The second measure space is usually volume (measured in litres or millilitres) in the case of a liquid medicine, or another vehicle containing the mass, such as a tablet or capsule, if the medicine is in solid form. The nature of the proportional relationships involved in the calculation of medicine doses is illustrated by the following examples. Example 1: A solid medicine is available in 25 mg tablets. Thus 75 mg of the medicine is contained in three tablets (following parallel tripling operations in each measure space) mg is contained in half a tablet (following parallel halving operations in each measure space). Example 2: A medicine is available in a liquid formulation of 10 mg per 2 ml. Thus 20 mg is contained in 4 ml of liquid (following parallel doubling operations in each measure space). 5 mg is contained in 1 ml of liquid (following parallel halving operations in each measure space). The calculation strategies used to solve proportional problems such as those illustrated in the previous examples, are possible because the measure spaces are isomorphic 4. Isomorphism of measures is characterised by a relationship of simple direct proportion between two measure spaces, M 1 and M 2 (Vergnaud, 1983). According to Vergnaud (1983), many situations found in everyday and technical contexts exhibit a relationship of direct proportion involving two measure spaces. Vergnaud offered the following examples (the two applicable measure spaces appear in parentheses): sharing objects (persons-objects); constant price (goods- 3 4 Direct proportion involves one quantity, y, increasing as another quantity, x, increases. Alternatively, one quantity, y, decreases as another quantity, x, decreases. Direct proportion can be expressed as an equation: y = a x, where a is the constant of proportionality. Isomorphic: being of the same or of like form; isomorphism: the state or property of being isomorphous or isomorphic (Macquarie Dictionary). 43

57 Chapter 2: Literature Review cost); uniform speed (duration-distance); and constant density or concentration (various measure spaces are possible). The last example is most relevant to the nursing context. In the calculation problems nurses solve involving solid and liquid medicines, proportional relationships are manifest in the form of the constant density of solid medicines, and the constant concentration of liquid medicines. For example, a tablet is assumed to have uniform density (e.g. 100 mg is spread uniformly throughout a single tablet), and a liquid medicine is assumed to have uniform concentration (e.g. 10 mg is spread uniformly throughout 2 ml of liquid) Methods used to solve out-of-school proportion problems Examination of the literature reveals a number of problem-solving methods identified by researchers as strategies problem solvers use to solve out-of-school problems of proportionality. These methods are of particular interest because some of them, or variants of them, have already been identified as methods nurses use as alternatives to the traditionally taught formula (Hoyles et al., 2001; Wright, 2013). Given evidence of their use in a variety of problem situations and by a variety of problem solvers, both adults and children, it is possible nurses use others of them to solve dose calculations. A sample of secondary school students of different grade levels successfully used five of the solution processes Vergnaud (1983) identified in his work on proportionality to solve a series of direct proportion problems. The everyday problems the students solved involved finding the amount of oil consumed by a central heating system over a given number of hours, and have direct parallels to the problems nurses solve when they calculate medicine doses. The processes the students used were: rule of three; scalar operator; functional operator; unit value; and scalar decomposition. The processes Vergnaud (1983) identified for solving missing value proportionality problems are illustrated in Figure

58 Chapter 2: Literature Review Figure 2.1. Proportional reasoning strategies for solving missing value problems (after Vergnaud, 1983, pp ) Three of these solution processes, scalar operator, functional operator, and the rule of three, were identified by Nunes et al. (1993) as the methods Brazilian fishermen (n = 22) used for calculations closely resembling their routine use of mathematics in their work. The procedures identified by Vergnaud (1983) are now explored in more detail with reference to how they might be used to calculate medicine doses. Rule of three Problems involving direct proportion are sometimes referred to as missing value problems (Schliemann & Carraher, 1993) or rule-of-three problems 5 (Vergnaud, 1983). The rule of three is a method commonly taught in schools and other educational settings for solving missing value proportion problems (Shield & Dole, 2002). Karplus, Pulos and Stage (1983) reported no clear evidence could be found in the research literature indicating the origins of this widely taught algorithmic 5 Also referred to, primarily by authors from the USA, by names such as the ratio-proportion method (Kohtz & Gowda, 2010; Rice & Bell, 2005; Brotto, 2012). 45

59 Chapter 2: Literature Review approach to solving proportionality problems. However, ancient arithmetic texts indicate in the fifteenth and sixteenth centuries the rule of three, also known as the Golden Rule or the Merchant s Rule, was regarded as a powerful mathematical technique for solving many mathematical problems (Swetz, 1992). Several forms of the rule of three are used. One is the equivalent ratios form 6 (Karplus et al., 1983): Another form used is the equivalent fractions form (Karplus et al., 1983; Schliemann & Carraher, 1993; Touriniare & Pulos, 1985): In each of these forms, a and c are elements of one measure space, such as mass, and b and x are elements of a different measure space, such as volume. In the context of a liquid dose calculation problem, the missing value (x) is the unknown number of millilitres of liquid the nurse needs to administer to deliver c milligrams of medicine using stock expressed as a milligrams in every b millilitres of the medicine. a : b c : x where a, b, and c have known values and x is unknown. a c, where a, b, and c have known values and x is unknown. b x The rule of three takes its name from the fact that, in the proportional relationship (represented by either of the two forms illustrated), if three of the four values are known, the fourth value (x) can be found. This is achieved by solving the resultant equation, known also as solving for x (Kohtz & Gowda, 2010, p. 83). Solving an equation in the equivalent ratio form proceeds by equating the product of the means (b and c) and the product of the extremes (a and x). Thus: ax = bc. Solving an equation in the equivalent fractions form proceeds as follows. 6 The equation is solved by equating the product of the means and the product of the extremes: ax = bc 46

60 Chapter 2: Literature Review a c b x (Eqn 1) Multiply both sides of the equation by bx: ax bc (Eqn 2) Divide both sides by a: bc x (Eqn 3) a The value of x can thus be found by substituting the values of the three quantities, a, b and c into the equation and evaluating x. Eqn 2 is most often obtained by the shortcut process of cross multiplication, also known as the cross-product algorithm or rule (Cramer, Post, & Currier, 1993), a process illustrated below. a c (Eqn 1) b x a c (equivalent to multiplying both sides by bx) b x ax bc (Eqn 2) bc x (Eqn 3) a Scalar operator Application of a scalar operator (Vergnaud, 1983) may be illustrated through the following problem: One tablet contains 100 mg, how many tablets will be required to administer 300 mg? If we apply Vergnaud s model of a scalar operator, we see that within the measure space M 1 (mass), the value 300 is obtained from 100 by multiplying it by the scalar operator, 3. We now move to the measure space M 2 (tablets). In a parallel operation within that measure space, we apply the same scalar operator, 3, to the value 1 (corresponding to 100 in measure space M 1 ). We obtain the value, 3, as the value of the unknown, x, the number of tablets to be administered. The problem and its solution, illustrated diagrammatically after Vergnaud (1983), are shown in Figure

61 Chapter 2: Literature Review Figure 2.2. Diagrammatic representation of a scalar operator, applied in parallel operations within each measure space Application of a scalar process is confirmed by the fact the scalar operator, 3, was only ever used within a measure space, never between (or across) measure spaces. Carrying out parallel transformations (multiplication by 3) on the value in each measure space maintains a constant ratio (Nunes et al., 1993) between mass and number of tablets. A scalar operator has no dimension, being a ratio of two magnitudes of the same kind. Thus 300 mg is 3 times 100 mg, and the mass contained in 3 tablets is 3 times the mass contained in 1 tablet. Applying a scalar operator can also be achieved by an additive process (Nunes et al., 1993; Vergnaud, 1983), thus 300 mg is perceived as: (3 times). Vergnaud observed that although this process is clearly not a multiplicative procedure, it demonstrates the scalar procedure relies on iteration of addition. Steinthorsdottir (2005) noted this additive or buildup strategy (p. 227) is the dominant strategy used by children and adolescents for solving proportions. Following Steinthorsdottir s model, the solution process might be represented as follows: mg: tablets: Chunking (p. 21, 22) was the name Hoyles et al. (2001) gave to a similar scaling up process nurses in their study used: A certain chunk of mass (which may not necessarily be one unit) is related to a specific volume. The chunk is added 48

62 Chapter 2: Literature Review repeatedly or multiplied by an integer to reach the required dose, and the equivalent operations are performed on the volume (p. 21). Although not explicitly examined by authors such as Vergnaud (1983) and Nunes et al. (1993), probably because the activities of participants in their studies mainly involved scaling up processes, it seems clear the scalar operator they described can also be used to scale down from a known quantity to an unknown quantity. Using a scalar operator to scale down requires a division process, the inverse of the multiplication process used to scale up. Alternatively scaling down can be achieved if the scalar operator applied is in the form of a fraction less than unity. Functional operator Another option for solving the problem illustrated is to apply a functional operator 7 (Vergnaud, 1983). Nurses might observe that division by 100 provides a link between 100 mg in measure space M 1 and 1 tablet in M 2. The nurse can then apply a parallel operation on the 300 mg in M 1 to obtain the unknown number of tablets in M 2, namely 3 tablets. This process, illustrated diagrammatically after Vergnaud, is shown in Figure 2.3. Function rule: Divide the mass by 100 to get the number of tablets Figure 2.3. Diagrammatic representation of a functional operator applied between measure spaces A functional process is a between-measures process in which mathematical operations are carried out between (or across) two measure spaces, such as mass and volume (Vergnaud, 1983; Nunes et al., 1993; Hoyles et al., 2001). 7 Termed functional operator/strategy/solution by Hoyles et al. (Hoyles, Noss, & Pozzi, 2001) and Nunes et al. (Nunes, Schliemann, & Carraher, 1993), and function operator by Vergnaud (Vergnaud, 1983). 49

63 Chapter 2: Literature Review Vergnaud s illustration of how a functional operator may be applied to solve problems of proportionality, including medicine dose problems, provides the impetus for further exploring the mathematical foundations of this method. The significance of the term functional operator derives from the mathematical model in which the number of tablets is a linear function of the mass to be administered. In the example illustrated in Figure 2.3, the applicable function rule was: Divide the mass by 100 (or 1 multiply the mass by ) to get the number of tablets. 100 The linear relationship between mass (m) and number of tablets (t) may be represented in three forms: as a two-column table format (Schliemann & Carraher, 1993; Vergnaud, 1983), as an algebraic equation, and as a graph. Table 2.1 shows values of mass, m, that might be administered, and the corresponding number of tablets, t, that should be given to administer that mass. The values in the table form part of a (theoretically) infinite set of ordered pairs illustrating the function. Table 2.1 Table form of the function relating mass, m, and the number of tablets, t Mass (mg) m No. of tablets t ½ ½ ½ If we wish to express the proportional relationship between mass (m) and number of tablets (t) in formal algebraic terms we might say: the variable t is directly 50

64 Chapter 2: Literature Review proportional to m, or t varies directly with respect to m. This relationship can be expressed algebraically in the form of an equation (Schliemann & Carraher, 1993; Vergnaud, 1983): t = f ( m) = am, where t is the number of tablets, m is the mass to be administered, and a is the constant of proportionality In words, this algebraic interpretation means: The number of tablets to be given, t, is a function of the mass to be administered, m. The value of t is always a times the value of m, where a is the constant of proportionality. Put another way, the function maps a set of values from the measure space of mass onto a set of values from the measure space of tablets, as illustrated in Table 2.1. In this example, the functional operator is the constant of proportionality, a. It is also called the coefficient of the linear function, and is the gradient of the straight line whose equation is: t m 100 1, or t m. 100 These two equations are equivalent, since dividing m by 100 is equivalent to 1 multiplying m by. 100 Figure 2.4 is a graphical representation of the values of mass and the corresponding number of tablets appearing in Table 2.1. The straight line is the linear function: t m

65 Chapter 2: Literature Review Figure 2.4. Graphical representation of the linear relationship between mass and 1 number of tablets when t m 100 All straight lines passing through the origin (0,0) of the Cartesian coordinate represent direct proportionality (Schliemann & Carraher, 1993). In the context of calculating medicine doses, the graph of the linear function linking the mass to be administered to the vehicle delivering that mass (i.e. a volume of liquid or a number of tablets) similarly always passes through the origin. The self-evident reason for this is that if nurses administer zero mass, then patients will receive nothing, that is, zero tablets or zero volume. Rather than being dimensionless, as a scalar operator is, the dimension of a functional operator is the quotient of two other dimensions. In the nursing example represented in Table 2.1 and Figure 2.3, these two dimensions are milligrams and tablets, resulting in a functional operator whose value is one-hundredth of a tablet per milligram. Function notation (Schliemann & Carraher, 1993; Vergnaud, 1983) can assist in explaining the mathematical underpinnings of two of the scalar problem-solving approaches described earlier, namely the multiplicative and additive scalar approaches. The multiplicative approach can be explained as follows. If represents the number of tablets needed to administer a mass of m milligrams, then application of a scalar operator is encapsulated in the following equation: f( m) 52

66 Chapter 2: Literature Review f ( am) = a f ( m), where a is a constant. Thus if 300 mg is to be administered using 100 mg tablets, then: mg will be contained in 3 1 tablet, that is, 3 tablets. The alternative additive approach (Nunes et al., 1993; Vergnaud, 1983) for solving this problem can be explained as follows. If f( m) represents the number of tablets needed to administer a mass of m milligrams, then: f ( m m ) = f ( m) f ( m ) (Eqn 2.2) Thus if 300 mg is to be administered using 100 mg tablets, then: 100 mg mg mg will be contained in 1 tablet + 1 tablet + 1 tablet, that is, 3 tablets. Unitary method 8 The unitary method is a scalar procedure applied to find the value in the measure space M 2 corresponding to a unit value in measure space M 1 (Vergnaud, 1983). Schliemann and Carraher (1993) described the process as deriving a unit ratio, n:1. Using a liquid dose calculation problem to illustrate, consider a medicine available in a concentration of 10 mg per 2 ml. Dividing by 10, we see 1 mg is contained in 2 10 ml or 0.2 ml. The volume required for any multiple of 1 mg can then be determined by applying the scalar operator, 0.2. For example, 12 mg will be contained in a volume of ml, or 2.4 ml. The unitary method can also be applied to find the number of milligrams contained in one millilitre of the medicine (i.e. 5 mg in 1 ml in the preceding example). However this application of the unitary method is only productive if the prescribed mass can be easily related to the quantity of mass (i.e. 5 mg) contained in 1 ml of medicine. 8 Most commonly referred to as the unitary method (Hoyles et al., 2001), but termed the unit value method by Vergnaud (Vergnaud, 1983) and the unit ratio strategy by Karplus et al. (1983). 53

67 Chapter 2: Literature Review Scalar decomposition This approach to solving problems of direct proportion involves breaking down or decomposing the quantity for which a corresponding value is to be found into several parts, typically multiples or fractions of the quantity for which the value is known. Situated in a nursing context and using the most recent example (a liquid medicine available in a concentration of 10 mg per 2 ml), consider the problem of finding the volume needed to administer 25 mg of the medicine. Following Vergnaud s (1983) model of scalar decomposition, 25 mg is broken down into multiples and fractions of the stock mass, 10 mg, for which the corresponding volume is known to be 2 ml. The nurse then performs identical transformations on the volume of 2 ml, in the manner illustrated (Karplus et al., 1983): 25 mg = 20 mg + 5 mg 1 = 2 10 mg + 10 mg 2 1 Volume = 2 2 ml + 2 ml 2 = 4 ml + 1 ml The process of scalar decomposition can be expressed in formal mathematical terms, after Schliemann and Carraher (1993), as follows. If f( m) = 5 ml is the volume needed to administer a mass of m, then: f ( m m ) = f ( m) f ( m ) Thus, if (20 mg + 5 mg) is to be administered using a liquid medicine whose concentration is 10 mg per 2 ml, then it follows that: the volume needed to administer (20 mg + 5 mg) is the volume needed to administer 20 mg + the volume needed to administer 5 mg. In abbreviated form, we could state: Vol (25 mg) = Vol (20 mg) + Vol (5 mg) = 4 ml + 1 ml = 5 ml 54

68 Chapter 2: Literature Review A scalar approach to dose calculation using a syringe In their investigations of how nurses solve dose calculation problems, two authors, Wright (2013) and Cartwright (1996), identified a highly visual solution method in which nurses utilise a syringe to assist in the calculation. This technique was used by one of the eight experienced nurses in Wright s study who applied it consistently to calculate liquid doses. The technique involves nurses using the scale on the syringe to visualise the proportional relationship between mass and volume and to apply scalar procedures to calculate the dose (this technique is illustrated in Table 2.2 appearing later in ) In the case of a liquid medicine available in a concentration of 10 mg/ml, the nurse described visualising a 1 ml syringe as containing the entire 10 mg mass. Then the nurse mentally divided the syringe into ten equal parts so each part (i.e. containing 0.1 ml of liquid) corresponded to 1 mg of medicine. Thus, a total of six of the ten parts along the scale (i.e. measuring up to the 0.6 ml mark on the syringe scale) contained the required 6 mg of medicine ordered. The last example in Table 2.2, 2.4.3, illustrates use of a syringe scale to assist in calculating a medicine dose. For another dose calculation involving a liquid medicine available in a concentration of 20 mg in 2 ml, the nurse mentally divided a 2 ml syringe into quarters so each quarter (corresponding to 0.5 ml) contained 5 mg. Thus the required dose of 5 mg was contained in the first quarter of the syringe, coinciding with a volume of 0.5 ml on the syringe scale. Cartwright reported nurses in her Australian study (Cartwright, 1996) using a similar visual break down when drawing up medication for injection (p. 140), adding they never used the formula, which some claimed they did not know. 2.5 The dose calculation strategies taught Medication calculation is an area in which graduate nurses must meet required standards of competence to enter the nursing register (Hutton, 1998b; Wright, 2012a). Around the world traditions for educating nurses have evolved differently in different countries in response to many factors, resulting in differences in the approaches taken to educating nurses in the calculation of medicine doses. 55

69 Chapter 2: Literature Review Factors possibly leading to these differences include different systems of measurement in everyday use, and differences in the school curriculum, particularly in relation to the topic of proportion. An international literature review (Hunter Revell & McCurry, 2013) identified three traditional methods nurses are taught to calculate doses: the formula method, dimensional analysis, and the ratio-proportion method The Formula, its origins, and reasons for its use In Australia, the United Kingdom and many other countries, the most commonly taught method for calculating medicine doses is the formula 9 (Gillies, 1994; Hoyles et al., 2001; Hughes & Edgerton, 2005; Macdonald et al., 2013; Weeks, Hutton, Coben et al., 2013; Wright, 2013). A possible exception is the USA where other methods may be more prevalent than the formula (Stolic, 2014). Many different versions of the formula exist (Weeks, 2001), most of them expressed in words or abbreviated representations of words rather than conventional algebraic symbols. All versions are, in essence, identical in structure. Weeks, Hutton, Young et al. (2013, p. e26) described three variations of the formula in use at their study site in the UK: What you want, over what you ve got, times what it s in; N Need over Have times Supply (NHS), or S ; and H Prescribed dose over Dispensed dose times by Quantity the dispensed dose is contained in (PDQ). The version of the formula reported by Hoyles et al. (2001) is: Amount to give = What you want What you've got The amount it comes in. In their interviews with senior nurses, Hoyles et al. (2001) found the formula appeared again and again, as it did in widely used nursing texts they examined. The centrality of the formula in dose calculations, as perceived by Weeks et al. (2000), is evident in their statement that possessing skills in the application of formulae is 9 Also referred to as the nursing rule (Hoyles et al., 2001, p. 4) 56

70 Chapter 2: Literature Review critical to ensure patients received the correct medicine doses. These authors expressed the view that students must develop an understanding of not only the key components in real-world dose calculation problems, but also the abstract word problems, formulae and equations that are used to represent, explain and solve these problems (p. 25). Some authors claim a lack of consistency in the methods taught for calculating doses results in students becoming confused, and compounds problems that stem from the traditional methods used to transmit knowledge of calculation processes (Weeks, 2001). The formula is derived from the mathematical rule of three (see 2.4.2). The invariance of the stock concentration (Hoyles et al., 2001) defines the proportional relationship between mass and volume, which can be represented using the equivalent fraction model: Prescribed mass Amount you need to give Mass of available stock Amount the stock mass comes in (Eqn A) The left-hand side of the equation relates to the patient s dose, and the righthand side to the available stock of the medicine. The unknown is the Amount you need to give. On the right-hand side of the equation Amount the stock mass comes in is most commonly 1 tablet or 1 capsule for a solid medicine, and a number of millilitres such as 1, 2, 5, or 10 ml for liquid medicines. To see the progression to the formula taught to nurses, we first need to reverse the two sides of the equation: Mass of available stock Amount the stock mass comes in Prescribed mass Amount you need to give We now transform the equation, following the same steps used in relation to the rule of three, so the unknown is the subject of the equation. The resulting equation is the formula nurses use: Prescribed mass Amount you need to give Amount the stock mass comes in Mass of available stock An alternative version of the formula is that reported by Hoyles et al. (2001): Amount to give = What you want What you've got The amount it comes in. 57

71 Chapter 2: Literature Review The formula is frequently taught, memorised, and recalled in a form that omits the left-hand side of the equation, the subject of the formula. Students frequently learn just the expression on the right-hand side of the equation, a practice reinforced by the way it is frequently shown in text books and other learning materials as a mathematical expression rather than a true formula with the subject on one side and the means to calculate it on the other. It is apparent the formula is a time-honoured tradition for calculating doses in nursing practice. However, evidence of how and when it came into common usage is not readily available. In essence, applying the formula involves a small number of apparently simple steps. It requires the nurse to identify three pieces of numerical information in the problem statement, substitute them into the formula correctly, and simplify the expression on the right-hand side of the formula. According to Hoyles et al. (2001), the purpose for teaching the nursing rule was not its widespread applicability. It was taught to bypass the need to appropriate or understand any mathematical structure and to impose consistency on what were seen to be dangerous variations in strategy. If nurses followed the rule, they will make error-free calculations provided they possess either a calculator or the appropriate computational skills with arithmetic. (Hoyles et al., 2001, p. 13) There may be additional reasons attracting nurse educators to teaching a single, apparently simple rule for calculating dosages. Wright (2005a) highlighted the difficulties experienced by nurse educators as they struggle to find effective ways of teaching the mathematical concepts required for dosage calculations. When one considers the limited preparation many nursing educators have for teaching the mathematical aspects of medication administration, it is not surprising the formula offers great appeal as a simple, one size fits all calculation method. The careers of the majority of academic staff teaching in nursing programs have grown from successful professional practice in the healthcare system. Accordingly, their strengths in educating pre-registration nurses commonly lie in aspects of the profession other than the mathematical processes of medication administration. The mathematical backgrounds of nurse educators vary widely, as does their ability to teach and support students in the mathematical concepts required for dose calculation, a proposition supported by Coben (2010, p. 14): 58

72 Chapter 2: Literature Review The quality of teaching and mentoring in any mode is dependent on the skills, knowledge and understanding of the teacher or mentor and his or her ability to communicate these to the student. Since the literature indicates a lack of proficiency amongst some qualified nurses it would not be surprising if some of those teaching or supporting nursing students had an inadequate grasp of numeracy or were unable to communicate their knowledge to novices even if they themselves understand what is required. Coben s contention accords with reports from several authors of difficulties experienced by teachers in teaching medicine dose calculations (Gillies, 1994; Wright, 2005a). In response to my earlier survey seeking information about teaching practices relating to medication calculation (Gillies, 1994), 53% of respondents from eight Australian universities reported staff experienced difficulties in teaching the topic, and another 19% were unsure. Twelve percent of respondents said they made no attempt to teach the mathematical aspects of the topic, and a further 7% said they personally did not feel comfortable doing so. The adequacy of teachers skills for teaching mathematical concepts was perhaps reflected by the fact that almost onethird of respondents had not studied mathematics to the end of secondary school. As an experienced nurse educator, Wright (2005a) explained how the magnitude of the task she faced in teaching medication calculations had prompted her to seek more effective ways of developing the necessary skills in students, and in supporting them in their mathematical needs. Wright described feeling overwhelmed by students lack of mathematical knowledge and ill-equipped to deal with the level of difficulty students experienced in applying the formula she taught them for calculating medicine doses. Given the likelihood many teachers feel ill-equipped to teach the mathematical skills required for medication calculation, it is also likely there is a perception among educators their task in teaching and assessing dose calculation skills is made considerably easier if solution methods are limited to just one. This translates to just one method the teacher needs to learn, understand, be able to demonstrate to students, and provide appropriate support to students in performing the associated computations. Indeed there is pressure for uniformity in the teaching approach used (Jackson & De Carlo, 2011), and the version of the formula taught (Cartwright, 1996; Weeks, 2001). Assessing students medication calculation competencies is simplified if the teacher needs only to make sense of, and assess, the application of 59

73 Chapter 2: Literature Review one calculation method, especially if students are encouraged, or even required, to use that method. When one searches for the origins and history of the practice of teaching the formula, the answers appear to lie at least in part in the rituals surrounding the practice of medicine administration, some of which have no basis in research (Baker & Napthine, 1994). Historically, the formula appears to be one of the rituals of practice handed down through many generations of nurses, possibly commencing within the hospital training system in which nurses learned entirely from other nurses, and a large part of nurses education took place in the practice environment. Anecdotal evidence suggests the requirement for nurses to calculate doses on a regular basis may have been considerably less for past generations of nurses than it is today, with some doctors practicing in Australian hospitals in the 1960s and 1970s recalling they always calculated doses themselves and informed the nurse of the dose to administer via the patient chart so the nurse had only to administer the stated quantity. The rule of three is an ancient, efficient and very useful rule for solving proportion problems. However, developing meaning for the rule in contemporary education settings has been linked to problems in developing conceptual understanding of proportion (Shield & Dole, 2002). Students perceptions of the value of the formula as a method for calculating medicines doses appear to be mixed. On the one hand, knowing the formula and how to set up the problem was the most frequent reason given by students for their ability to correctly calculate medication dosages and intravenous flow rates (Rice & Bell, 2005). On the other hand, Rice and Bell noted amongst the same sample of nursing students, the most frequently reported reason for confusion was not being able to remember the formula. A perception of students is that having a formula to use is essential because it gives them a starting point for solving the dose calculation problem: without the formula they would not know where to start (Gillies, 2003) Alternative dose calculation methods In addition to the formula, two methods are sometimes taught to students to calculate medicine doses, primarily in the USA. These methods are dimensional analysis (DA) and a method frequently referred to as ratio-proportion a variant of the rule of three (Hunter Revell & McCurry, 2013; Stolic, 2014). 60

74 Chapter 2: Literature Review Dimensional analysis DA is used in the sciences to determine or check the unit of measurement of a calculated quantity. Another application of DA is in medication calculation where it is sometimes referred to as the factor-label method (Arnold, 1998; Rice & Bell, 2005), unit factor method, or dimensionless unit conversion (Wang, 1998). The mathematical principles underpinning the DA method described by Olsen, Giangrasso, and Shrimpton ( 2012) were: any non-zero number divided by itself equals 1; when a quantity is multiplied (or divided) by 1, the quantity is unchanged; and cancelling is possible, not only between numbers, but also between identical measurement units. Arnold (1998) described the essence of the DA method. It involves setting up an equation in which the desired form of the medication, expressed as a fraction, is placed on the left side. The right (computational) side commences with a starting factor, also expressed in the form of a fraction. All other known quantities are arranged in fraction form in a sequence on the right side, and units are successively cancelled until the desired denominator label appears, at which point the process stops. In this way, the prescribed quantity is expressed in the form in which the nurse will prepare the medication for administration (for example a number of tablets or millilitres per dose). Fully worked examples of the DA method appear later in Table 2.2, and in Appendix 6 in the extracts from the questionnaire used to collect data in the University Phase of the study. Reported advantages of DA over other dose calculate methods include that DA: is well-suited to problems involving conversion factors including dose calculations and IV flow rates (Arnold, 1998; Greenfield, Whelan, & Cohn, 2006;); can be used to systematically convert the units on the medication package to the units of the prescribed dose (Greenfield et al., 2006); and allows systematic organisation of data in a single method by entering relevant factors as fractional quantities on a single line (Arnold, 1998). 61

75 Chapter 2: Literature Review Mixed results have been reported from studies comparing students performances on dose calculation problems using DA with those using the traditional formula method (Greenfield et al., 2006). Small scale studies have found (a) students using DA made significantly fewer errors than students using the formula (n = 65; Greenfield et al., 2006), and (b) students experienced less frustration and made fewer errors when the method of DA was used to solve dose calculation and IV flow rate problems Craig (2005). However, contrary evidence came from a small study conducted in the USA (n = 79; Kohtz & Gowda, 2010) that found no significant difference, either in students performance of the conceptual errors they made when they compared two approaches to dose calculation: DA and the formula. DA may have advantages in the USA because in the environment of multiple measurement systems that prevails there. Historically, there has been no regulated or consistent system for ordering or supplying medicines in the USA (National Council for Prescription Drug Programs, 2014). Medicines might be ordered in the metric, apothecary or household systems of measurement but supplied in a different measurement system, resulting in nurses frequently having to make conversions between the three different systems (Greenfield et al., 2006). The resulting confusion has led to many medication errors such as recording a patient s weight in pounds but entering the numerical value as kilograms when performing a milligram per kilogram calculation. A dose more than twice that intended results from such an error (Institute for Safe Medication Practices, 2011). Despite the claim by Olsen et al. (2012) that DA is rapidly becoming the most popular method of dosage calculation (p. 76), there is little evidence that DA is known or used for dose calculation outside the USA. Further, in relation to nursing programs, including many in Australia, where students do not study a prerequisite physics or chemistry unit which might expose them to DA techniques, there is little valid argument to support introduction of DA as a dose calculation method. Perhaps the greatest strength of DA is its emphasis on including units of measurement throughout the entire solution process. This is a feature often lacking when teachers and students apply the formula, substituting numbers stripped of their units of measurement into the formula for numerical calculation, thus rendering the calculation task largely devoid of meaning and context (Wright, 2008a). However this problem can be readily overcome simply by including units of measurement consistently throughout the solution process. 62

76 Chapter 2: Literature Review Many claims about the benefits of DA were made without adequate explanation or substantiation, including claims that DA: conceptualises the principles of problem solving (Greenfield et al., 2006, p. 92); supports critical thinking (Cookson, 2013; Craig, 2009; Greenfield et al., 2006); and prevents medication errors by allowing visualisation of all parts of the medication problem (Craig, 2009). A counter argument is that DA is essentially a procedural technique in which formal mathematical formats in the form of products of fractions are used to represent the numerical data in the problem statement. DA makes considerable mathematical demands on students, requiring them to perform multiple cancellations to simplify the sequence of fractions that results from its application. This involves processes known to cause difficulty to many students (Cartwright, 1996) and which are therefore likely to alienate many student nurses. Rather than applauding DA, one mathematics educator, Thompson (1994) went so far as to suggest DA should be condemned and banned, at least when proposed as arithmetic of units, its aim is to help students get more answers, and it amounts to a formalistic substitute for comprehension. In terms of the claim DA conceptualises the principles of problem solving, the reality is that after the first line of the equation, all connection to the problem situation is severed and the process of solution becomes purely mechanical. A further detraction of DA is it demands a lengthy and intensive written process, even for calculations that could be executed far more quickly and simply using other, possibly mental, processes. The written structure demands accuracy in each of the steps required to manipulate the many fractions progressively introduced, a process that is difficult for the problem solver to check, even with the aid of a calculator. Ratio-proportion method (rule of three) The ratio-proportion method 10 (Brotto, 2012; Hunter Revell & McCurry, 2013; Jackson & De Carlo, 2011) is identical to the rule of three and expresses, either in fraction or ratio form, the relationship between quantities central to problems of 10 Also referred to as desired dose/dose on-hand methods (Craig & Sellers, 1995) and solving for x (Craig & Sellers, 1995, p. 83). 63

77 Chapter 2: Literature Review proportionality. Like DA, ratio-proportion is prominent in the USA, as a method taught in schools (Karplus et al., 1983) and as a method for calculating medicine doses (Craig & Sellers, 1995; Kohtz & Gowda, 2010). Kohtz and Gowda indicated they viewed the method of ratio-proportion, together with calculation formulas (p. 83), as being conventional calculation methods. Some textbooks, again mainly those emanating from the USA, confirm the teaching of this method, sometimes in addition to DA and/or the formula (e.g. (Brotto, 2012; Berman et al., 2015, Volume 2). An exception is Glaister (2016), an Australian textbook mainly modelling the ratio and proportion method (p. 69) for solving dose calculation problems. It also offers informal proportional reasoning methods to check calculations, and the formula as an alternative strategy to ratio and proportion. Glaister illustrated the ratio and proportion method by finding the volume to administer if 40 mg is administered from liquid stock of concentration 8 mg per ml. The equation may be set up in ratio (or linear) form (see Glaister, 2016, p. 23): 1 ml: 8 mg = x ml: 40 mg p. 22): Alternatively the equation may be set up in fraction form (see Glaister, 2016, 1 ml x ml 8 mg 40 mg Solving the equation for x yields 5 ml as the volume to be administered. (See solution methods for both ratio and fraction forms in ) The claimed success of the ratio-proportion method for solving dose calculations (Jackson & De Carlo, 2011), like similar studies investigating the success of DA, relates only to short-term outcomes. Reports of success typically refer to students performance on tests immediately following or a short time after the teaching intervention. Some studies have compared pass rates of students exposed to the rationproportion method with pass rates of previous cohorts taught to calculate doses using the method the teacher had been taught (Jackson & De Carlo, 2011). Other studies 64

78 Chapter 2: Literature Review have compared the performance of two groups of students exposed contemporaneously to two different methods for calculating doses (Greenfield et al., 2006; Kohtz & Gowda, 2010). A common failing of studies comparing the success of the DA and rationproportion methods with that of the formula method is the lack of detail provided clarifying the exact form of the method taught and how it was applied to dose calculation problems. Further, few studies have investigated the long-term effectiveness of calculation methods such as DA and ratio-proportion. The focus of most studies has been on students performance on tests conducted immediately or soon after the teaching intervention. However given retention of skills is a welldocumented problem (Sherriff et al., 2011; Wright, 2012a, 2007b), without evaluating the long-term effectiveness of these dose calculation methods, it is impossible to judge their value in preparing student nurses for professional practice Summary of possible dose calculation methods Table 2.2 summarises calculation methods described in the literature for solving problems of direct proportion discussed in In the table, an example from the nursing context is used to illustrate how each method might be used to solve a medicine dose calculation problem. All problems in Table 2.2 relate to a medicine, metoclopramide, available in liquid form in a concentration of 10 mg per 2 ml, to be administered by intravenous infusion. Three different prescribed doses 11, 20 mg, 15 mg, and 7.5 mg, are used to illustrate different calculation processes. In each case the dose has been selected to best illustrate the particular calculation process demonstrated. The table shows how a nurse might set out a written solution using the particular calculation method. At least one key source or reference in the literature is nominated for each calculation method. 11 The prescribed dose may not be clinically appropriate. 65

79 Chapter 2: Literature Review Table 2.2 Examples illustrating possible methods for calculating medicine doses (table continues over four pages) Prescribed dose & administration route Stock formulation Calculation strategy References Calculation process Calculated volume to administer Metoclopramide 20 mg IV infusion 10 mg per 2 ml Formula Hoyles et al. (2001) What you want Dose = What you've got 20 mg = 10 mg 2 ml = 4 ml The amount it comes in 4 ml Metoclopramide 20 mg IV infusion 10 mg per 2 ml Dimensional analysis Cookson (2013) 4 ml 20 mg 2 = dose dose = 4 ml per dose 1 ml mg 4 ml Metoclopramide 20 mg IV infusion 10 mg per 2 ml Scalar operator Vergnaud (1983) 2 M 1 Mass (mg) M 2 Volume (ml) ml 66

80 Chapter 2: Literature Review Prescribed dose & administration route Stock formulation Calculation strategy Reference/s Calculation process Calculated volume to administer Metoclopramide 20 mg IV infusion 10 mg per 2 ml Functional operator (Hoyles et al., 2001; Nunes et al., 1993 Vergnaud, 1983) M 1 Mass (mg) M 2 Volume (ml) ml Function rule: Divide the mass by 5 to get the volume. Metoclopramide 20 mg IV infusion 10 mg per 2 ml Unit value (Vergnaud, 1983) 20 M 1 Mass (mg) M 2 Volume (ml) ml

81 Chapter 2: Literature Review Prescribed dose & administration route Metoclopramide 20 mg IV infusion Stock formulation Calculation strategy 10 mg per 2 ml Unitary method/unit ratio approach/one unit rule References Calculation process Calculated volume to administer (Hoyles et al., 2001; Lapham & Agar, 2009; Schliemann & Carraher, 1993) 10 mg in 2 ml 10 mg 2 ml in mg in 0.2 ml 20 1 mg in ml 20 mg in 4 ml 4 ml Metoclopramide 20 mg IV infusion 10 mg per 2 ml Rule of three 12 (Berman et al., 2015; Vergnaud, 1983) 10 mg 20 mg = 2 ml x ml = 2 x 10 x = x = 10 x = 4 4 ml Metoclopramide 20 mg IV infusion 10 mg per 2 ml Chunking: Multiplicative process (Hoyles et al., 2001); 10 mg in 2 ml 2 : 20 mg in 4 ml 3 ml 12 Referred to as the ratio-proportion method by Hunter Revell (2013), Jackson and de Carlo (2011) and Brotto (2012). 68

82 Chapter 2: Literature Review Prescribed dose & administration route Stock formulation Calculation strategy References Calculation process Calculated volume to administer Metoclopramide 20 mg IV infusion 10 mg per 2 ml Chunking: Additive or build-up process (Hoyles et al., 2001; Vergnaud, 1983; Schliemann & Nunes, 1990; Steinthorsdottir, 2005) 10 mg in 2 ml 10 mg + 10 mg in 2 ml + 2 ml 20 mg in 4 ml 3 ml Metoclopramide 15 mg IV infusion 10 mg per 2 ml Scalar decomposition (Vergnaud, 1983) 1 15 mg = 10 mg + 10 mg 2 1 Volume = 2 ml + 2 ml 2 = 3 ml 3 ml Metoclopramide 7.5 mg IV infusion 10 mg per 2 ml Syringe scale used also a scale for mass (mg) (Cartwright, 1996; Wright, 2013) 1.5 ml 69

83 Chapter 2: Literature Review 2.6 Assessing dose calculation skills Evidence relating to nurses dose calculation abilities has rarely been based on their performance in the practice environment. Rather, declarations of nurses competence have traditionally been based on assessments of abstract numeracy skill (McMullan, 2010) or tests of dose calculation competence relying on written problems that use words in an attempt to depict real practice scenarios (Sherriff et al., 2011; Weeks et al., 2000; Wright, 2005b) Calculation errors in tests as predictors of errors in practice Some have argued traditional assessment methods fail to reflect nurses performance on dose calculation problems in clinical practice (Conti & Beare, 1988; Coombes et al., 2005; Hoyles et al., 2001; Wright, 2009a, 2008a, 2008b). These authors have challenged the belief competence in theory predicts competence in practice, claiming it is not supported by evidence. By contrast, assessments conducted in simulated clinical environments following exposure to computer-based learning environments incorporating images of artefacts associated with medicine administration have been found to be predictive of performance in clinical practice (Weeks, Clochesy, et al., 2013). It seems clear the extent of calculation error found in written tests is not reflected in professional practice (Hutton, 1998b; Wright, 2009a), a conclusion reached despite the difficulties, identified earlier, of accurately gauging the incidence of calculation and measurement error in clinical practice. Wide variability in the quality of assessment instruments used to assess fitness for practice in respect to dose calculation competence poses serious risks to patient safety (Coben, Hodgen, Hutton, & Ogston-Tuck, 2008). At worst, some tests have been judged mathematically and/or professionally inappropriate (Coben et al., 2008, p. 38), with one test found to be neither reliable or valid (Coben et al., 2008, p. 40) Nurses proficiency in dose calculations Nurses proficiency in calculating doses has been the subject of much literature, with conceptual and computational errors accounting for most errors (Blais & Bath, 1992; Hutton, 1998a; Savage, 2015; Segatore, Edge, & Miller, 1993; Weeks 70

84 Chapter 2: Literature Review et al., 2000; Weeks, Hutton, Young et al., 2013). A strong association between students conceptual difficulties and the formulaic methods they use to solve dose calculation problems (Gillham & Chu, 1995) is apparent in portrayals of conceptual difficulties. Example of such portrayals illuminating the association include: inability to provide or to set up a correct formula (Blais & Bath, 1992, p. 13); misconceptions of the relationship between elements of word-based problems and formulae, and erroneous setting up of dosage calculation equations (Weeks, Hutton, Young et al., 2013, p. e27); misunderstanding the logic of the problem they were attempting to solve, that is, misunderstanding of the basic word problems and formulae (Weeks et al., 2000, p. 25); inability to use information given to formulate an equation in order to solve problems (Hutton, 1998a, p. 26); and formula wrong; figures misplaced in formula (Savage, 2015, p. 650). The difficulties students experience relating the terms of the formula to the words used to describe the problem scenario were illuminated in one students description of their exposure to the formula method for dose calculation: There were words like prescribed over dispensed and then suddenly we were using numbers and a formula but I couldn t see where they came from and it wasn t just me we were sat there (sic) and everybody was looking at each other and there were blinkers coming up with lots of people (Weeks et al., 2000, p. 26) Computational difficulties involve: fractions, decimals, and conversions between them, place value, misplacement of the decimal point (Cartwright, 1996; Fleming, Brady, & Malone, 2014; Hughes & Edgerton, 2005; Hutton, 1998a; Lesar, 2002; Pierce et al., 2008; Savage, 2015; Weeks et al., 2000; Wright, 2005a). multiplying, dividing, and ratios (Fleming et al., 2014; Hughes & Edgerton, 2005; Savage, 2015; Wright, 2005a; ), and multiple computations (e.g ; Macdonald et al., 2013, p. e71); 71

85 Chapter 2: Literature Review percentages, and multiplication and division of numbers by powers of ten (needed for metric conversions; Wright, 2005b); converting quantities from one metric unit to another (Coben et al., 2010; Hutton, 1998a; Lesar, 2002; Rodger & Jones, 2000; Simonsen et al., 2014; Wright, 2007a, 2007b, 2009, 2012b); and estimation techniques (needed to judge the reasonableness of a calculated quantity and detect errors; Cartwright, 1996; Hoyles et al., 2001; Pierce et al., 2008). 2.7 Teaching and assessing dose measurement skills The dose calculation skills of students and nurses have attracted much attention in the literature. However, nurses accuracy in measuring medicines has received little attention, despite being an important component of competent medicine administration (Cartwright, 1996; Hoyles et al., 2001). The scant attention educators pay to this aspect of dose accuracy in medicine doses is mirrored in commonly used text books and other learning resources (for example, Glaister, 2016; Gatford & Phillips, 2011; and Hext, 2003). The apparent failure to recognise the potential for the measurement aspect of medicine administration to contribute to errors has prompted one author to question whether the required skills are taught in nursing programs, possibly because of a general assumption nurses are able to accurately measure doses (Cartwright, 1996). In a departure from traditional approaches to teaching and assessing medicine administration skills focusing almost exclusively on calculation competence, a small number of authors have acknowledged the importance of skill in selecting and using appropriate measuring devices, estimating and accurately measuring quantities using a range of calibration systems, and recording measurements correctly on charts (Cartwright, 1996; Coben et al., 2010; Hoyles et al., 2001; Macdonald et al., 2013; Nicholls, 2006; Weeks et al., 2013). Using syringes to measure volumes requires sound skills in the decimal number system, fractions, and converting between decimals and fractions to correctly interpret the calibrations on scales (Nicholls, 2006). Technical measurement competence ( dosage-measurement ) is one of three essential sub-elements that combine with conceptual or cognitive competence 72

86 Chapter 2: Literature Review ( dosage problem-understanding ) and calculation competence ( dosagecomputation ) to form competence in administering correct medicine doses (Weeks, Hutton, Young et al., 2013, p. e23). In clinical practice, an error in any one of these sub-elements, if undetected, will result in a medication error (Macdonald et al., 2013). Only one study (Coben et al., 2010) was found investigating assessment of students dose measurement skills. The mainly minor measurement errors made by the 63 students tested largely revealed students inexperience. For example, Coben et al. reported a lack of dexterity in using syringes to draw up liquids, and poor judgement in selecting a suitable vehicle for measuring the calculated volume of liquid, for example, selecting a 30 ml medicine cup to measure a 5 ml dose, or a 5 ml syringe to draw up a 1 ml volume. A more serious error, undoubtedly also the result of inexperience, resulted from students holding the needle tip above the liquid level in the ampoule as they drew liquid into the syringe. Although the plunger was at the correct mark, the actual amount in the syringe was negligible. This problem, observed mostly in relation to 1 ml syringes, had the potential to result in the patient receiving a significant underdose. 2.8 Proportional reasoning in and out of school Problems involving the concepts of ratio and proportion have captured the attention of researchers in mathematics education and developmental psychology over the last century. Research investigating approaches to solving problems of proportionality used by school students in and out of school settings, and adults in workplace and other out-of-school settings is informative in several ways. First, nurses have all been exposed to proportional problems in their school education. Second, they also have much experience in responding to real-world problems of proportionality, the most commonly encountered problems being purchasing items of known unit cost. Examining the literature relating to how adults and children approach problems of proportion provides a framework for considering how nurses approach problems of proportionality when they calculate medicine doses. Some of the early work by developmental psychologists, Inhelder and Piaget (1958), involved investigation of how students learn to solve problems involving 73

87 Chapter 2: Literature Review proportion, and attempting to locate the development of proportional reasoning within their framework of concrete and formal operational thinking (Schliemann & Carraher, 1993). A series of multinational studies in countries including the USA, Switzerland and Britain (Karplus et al., 1983) investigated proportional reasoning in secondary school students in the 1970s and 1980s. The focus on how proportionality is applied in, and out of, formal settings intensified during the last part of the 20th century with work by Vergnaud (1983) in France, and Karplus (1983), Schliemann and Nunes (1990), Schliemann and Carraher (1993), and Nunes, Schliemann and Carraher (1993) in Brazil. More recent studies by Hoyles et al. (2001) and Wright (2013) in the UK have led the way in investigating how nurses solve problems of proportionality in the context of medicine doses. Karplus et al. (1983) summarised the results of a number of investigations using a study method involving school students measuring the heights of Mr Tall and Mr Short figures using paper clips and buttons. The results of these and similar studies revealed much about students use of proportional reasoning. These authors found differences between students in the reasoning approaches they used relating to socio-economic status, educational status, age, and the context of the problem. A number of factors were identified influencing the level of difficulty experienced in proportional reasoning, such as whether the numerical value of one variable is an integral multiple of the other, the type of fractions involved (e.g. unit fractions such as etc., or composite fractions such as 3,,, which increases difficulty), and the magnitude of the numerical values involved. In relation to the last point, the difficulty level of the problem increases if the unknown is smaller than the given values, or the problem involves numerical values larger than about 30 (Karplus et al., 1983). Differences between countries in the school curriculum have also been found to impact on the development of proportional reasoning skills. Extensive use of an instructional model in the USA known as ratio-proportions (Hunter Revell & McCurry, 2013) involving solving an equivalent fraction equation by crossmultiplying was reported by Karplus et al. (1983) (see also 2.5.2). This model was confirmed by their examination of school mathematics textbooks widely used in the USA. 2 74

88 Chapter 2: Literature Review In their own study, Karplus et al. (1983) found clear evidence that additive reasoning replaced proportional reasoning to a very large extent on more difficult problems. In their investigation of children s responses to problems involving the price of purchased items, Schliemann and Carraher (1993) found differences relating to the backgrounds of the three groups of children they studied, the types of scalar strategy used, the use of calculators, and the use of written or oral (i.e. mental) computational routines. Street vendor children from poor families with little prior formal instruction on proportionality tended to use informal strategies and successive additions involving a building up approach involving step-by-step transformations in both variables till the answer was reached (Schliemann & Carraher, 1993, p. 66). The children did not use calculators or written computations. Children in the same age group of 11 to 14 years who were from middle- and upper-class schools, some of whom had received instruction on proportions and some who had not, were more likely to use calculators, written computations, the strategy of computing the price of one item, and multiplicative procedures rather than successive addition. Karplus (Karplus et al., 1983) summarised earlier studies, including those by him and his colleague, Kurtz (Kurtz & Karplus, 1979), and concluded proportional reasoning was more frequently used by students in countries where teaching of the unitary method is used, specifically countries other than the USA. The unitary method has two distinct steps, the first being to find how much of one quantity delivers a unit of the other; the second being to apply that ratio to find the missing value. Karplus et al. found this strategy to be useful as a starting point for a teaching process based on gradually increasing the complexity of problems, connecting the problem variables with everyday experience, and establishing secure connections between newly learned strategies and students existing knowledge. Australian researchers Fielding-Wells, Dole, and Makar (2014) exposed grade 4 students (aged 9 years) to informal experiences of proportion mediated by an inquiry and argumentation classroom culture. They found students additive strategies progressively shifted to proportional reasoning thinking. The context of the students experience of proportionality centred on how human a Barbie doll was in terms of the proportionality of the doll s dimensions in relation to those of a human. Fielding-Wells et al. argued these informal experiences would support the students in later years as they applied their proportional reasoning thinking more formally. 75

89 Chapter 2: Literature Review Formal acquisition of skills for proportionality problems In the Australian curriculum, proportional reasoning is seen as an important goal of primary school mathematics (Fielding-Wells et al., 2014). Proportional reasoning skills have been described as the capstone of children s elementary school arithmetic and the cornerstone of all that is to follow (Post, Behr, & Lesh, 1988, p ). Proportion and ratio are critical ideas for students to understand (Steinthorsdottir, 2005) and are foundational to almost all of secondary and higher mathematics (Confrey, 2008; Shield & Dole, 2002). Proportional reasoning is required for other school subjects such as chemistry (Ramful & Narod, 2014), and is used in many everyday and workplace applications of mathematics (Nunes et al., 1993; Schliemann & Carraher, 1993; Vergnaud, 1983). Yet proportional reasoning is a notoriously difficult concept to master (Schliemann & Carraher, 1993). The development of proportional reasoning The literature on proportional reasoning reveals a broad consensus that qualitative reasoning strategies based on an informal or intuitive knowledge of relationships and without numerical quantification, precedes multiplicative reasoning and quantitative thinking (Fielding-Wells et al., 2014; Kieren, 1993; Steinthorsdottir, 2005). Learning to view something in proportion or in proportion with precedes the acquisition of the proper concept of ratio (Streefland, 1985, p. 83). Correspondingly, students qualitative descriptions give way to more quantitative language as their thinking progressively shifts from additive strategies to proportional thinking (Fielding-Wells et al., 2014). Understanding the multiplicative structure inherent in proportion situations is the essence of proportional reasoning; it requires the problem solver to see, for example, 4 in relation to 8 as multiplying by 2, as distinct from seeing 4 in relation to 8 as adding 4 (Behr et al., 1992). According to English and Halford (1995), fractions are the building blocks of proportion (p. 254). The concept of ratio and proportion is complex because it is intertwined with many mathematical concepts including multiplication, division, fractions and decimals (Behr et al., 1992, p. 80). It relies on prior knowledge of these underlying concepts (Shield & Dole, 2002). Studies in the development of proportional reasoning, while not always fully supportive of the developmental theories of Inhelder and Piaget (Inhelder & Piaget, 1958), have nevertheless pointed to a multi-stage pattern of slow and incremental 76

90 Chapter 2: Literature Review development (Karplus et al., 1983; Steinthorsdottir, 2005; Vergnaud, 1983). The development of proportional reasoning only commences at the beginning of adolescence when students are in the early years of secondary school (Schliemann & Carraher, 1993; Vergnaud, 1983). Students are able to solve increasingly complex problems by applying increasingly complex and more mathematically sophisticated problem-solving strategies (Steinthorsdottir, 2005). Kieren (1993) identified four levels of proportional reasoning, the most rudimentary of which is characterised by limited ratio knowledge and the use of incorrect additive strategies within or between ratios (see also for descriptions of transformations within and between measures). Students operating at the highest level understood proportion in terms of multiplicative relations and could take into account both within and between ratio relationships and choose the relationship that was easier to calculate. Karplus et al. (1983) described a similar progression to competent proportional reasoning, commencing with non-use or illogical use of data, followed by additive or constant difference approaches, a transitional stage involving iterative or graphic processes and/or partial use of proportions, and a final stage of explicit use of equal ratios. Although most students progress consistently and have achieved considerable proficiency by the end of early secondary school, some fail to master even the simplest of problems by that point in time (Vergnaud, 1983). The contexts in which students encounter proportional relationships are important for developing their schema of proportion (Schliemann & Carraher, 1993). Schliemann and Carraher concluded proportional reasoning may develop first in a limited range of contexts and in relation to particular contexts. Then, given the right conditions, transfer and generalisation may become possible as similarities in relationships are detected. Recognition of similarities may act as a bridge for the transfer of procedures to novel contexts. The knowledge of how students proportional reasoning develops has implications for nurse educators. By identifying contexts in everyday life in which nurses use proportional reasoning that mirror dose calculation contexts, educators can support the development of students skills and facilitate skill transfer to nursing settings. 77

91 Chapter 2: Literature Review The effectiveness of traditional teaching approaches The effectiveness of traditional approaches to teaching proportional reasoning in schools has been questioned by a number of authors (Cramer et al., 1993; Hoyles et al., 2001; Shield & Dole, 2002; Vergnaud, 1983). Examination of two mathematics textbooks by Shield and Dole (2002) revealed little connectivity of ideas between proportion-related topics, confusing definitions, and frequently illogical calculations, raising questions about the messages such texts send to students, and possibly providing some explanation for why many middle school students struggle with topics based on proportional reasoning. The generally poor understanding of proportion by students (Shield & Dole, 2002) may largely be attributed to the standard solution procedure of crossmultiplying and solving for x having little meaning (Cramer et al., 1993; Shield & Dole, 2002;). When cross-multiplication is used in association with the rule of three (or ratio-proportion method (Craig & Sellers, 1995; Kohtz & Gowda, 2010), it is evident this technique is poorly understood by students as well as some educators. The technique is frequently incorrectly applied, as evidenced by incorrect interpretations I identified in several textbooks. While acknowledging the efficiency of the cross-product algorithm, Cramer et al. (1993) questioned its usefulness. They argued: It is impossible to explain why one would want to find the product of contrasting elements from two different rate pairs. The cross-product rule has no physical referent and therefore lacks meaning for students and for the rest of us as well. Teachers need to step outside the textbook and provide hands-on experiences with ratio and proportional situations. Initial activities should focus on the development of meaning, postponing efficient procedures until such understandings are internalized by students. (p. 170) Karplus et al. (1983) concluded the rule of three approach to teaching ratio and proportion dominant in the United States at the time of their 1983 study was an effective teaching strategy for only a small minority of students. They regarded the unitary method as more successful even though its effectiveness was also limited. The limited effectiveness of the rule of three as a solution method for adolescent students has direct implications for its usefulness for nurses dose calculations, given the formula is derived from it. 78

92 Chapter 2: Literature Review Vergnaud s (1983) warnings concerning illusions that persist among mathematics teachers regarding the development of proportionality concepts have implications for teachers of dose calculations also. One illusion is that in teaching mathematics, the teacher s role is to present neat, formal theories, and that when this job is well done, students should understand mathematics (p. 172). The reality is the development discernible from younger students to older ones is slow, and concepts develop through problem solving. Another illusion is the natural development fallacy (p. 173) of postponing teaching proportional reasoning until students reach the right stage. According to Vergnaud, there is no reason to believe students will develop complex concepts without meeting complex situations. The role of algorithms in solving out-of-school problems Algorithms, such as those used for addition, subtraction, multiplication, and division in arithmetic, abound in school mathematics (Usiskin, 1998). An algorithm is a step-by-step process that guarantees the correct solution to a given problem, provided the steps are executed correctly (Barnett, 1998, p. 69). Algorithms allow us to solve classes of problems; they are reliable, accurate and fast; they yield the correct answer time after time (Usiskin, 1998). The power of an algorithm derives from the breadth of its applicability (Usiskin, 1998, p. 10). There are inherent dangers in the use of algorithms, however (Kamii & Dominick, 1998; Morrow, 1998; Usiskin, 1998). Algorithms may encourage children to give up their own thinking, thereby preventing children from developing number sense (Kamii & Dominick, 1998). Among the dangers of algorithms noted by Usiskin (1998, p ) are: blind acceptance of results, highlighting the importance of performing a check, for example, by using a second method to confirm the answer; overzealous application, where another method would be more sensible; and helplessness if technology for the algorithm (for example the formula or a calculator) is not available. When problem solvers use the algorithm specifically designed for solving problems of proportionality, the tendency is for them to make more errors than when other methods are used (Nunes et al., 1993). Further, when children used schooltaught algorithms, once they had written down their answers they rarely queried 79

93 Chapter 2: Literature Review answers or related them to the problem situation (Kamii & Dominick, 1998; McIntosh, 1998b; Nunes et al., 1993). According to Nunes et al. the reason for this unquestioning acceptance of answers is that using the algorithm disrupts the problem solver s connection to the problem situation. Failure to check the reasonableness of answers results in errors frequently remaining undetected (Nunes et al., 1993). By contrast, Nunes et al. found children made fewer errors when they solved problems in the oral mode because they kept the meaning of the problem in mind. A similar phenomenon of undetected errors resulting from unquestioning acceptance of patently incorrect answers (e.g. twenty tablets instead of two) and failure to apply checks has been reported in relation to nursing students when they calculate medicine doses (Blais & Bath, 1992; Eastwood, 2011; Savage, 2015) Intuitive proportional reasoning Evidence from many studies investigating proportional reasoning has led to the belief that if students are exposed to real-world proportion problems, development of proportional reasoning is possible even without formal school instruction (Nunes et al., 1993; Schliemann & Carraher, 1993; Schliemann & Nunes, 1990; Vergnaud, 1983). Nunes et al. (1993) concluded in response to their study of the use of proportionality in the everyday lives of fishermen and street vendor children, the concept of proportionality does not have to be taught. It can develop on the basis of everyday experience (p. 126). Schliemann and Carraher (1993) hypothesised that people develop an understanding of proportionality most easily in response to the demands of proportional situations in everyday life, the cost of items purchased being one of the most common examples. The unitary method is one possible approach to solving proportion problems. Frequently, missing value problems are solved through the derivation of a unit ratio, n:1, corresponding to the cost of one unit. Building up strategies based on successive additions that preserve the relationship between variables in the problem are commonly employed by people with little or no schooling. This strategy is indeed correct but the scalar multiplier is implicit rather than explicit (Schliemann & Carraher, 1993, p. 69) 80

94 Chapter 2: Literature Review Preferred strategies for solving out-of-school problems Among the many studies investigating how people solve problems of proportion in out-of-school settings, there has been consistency in several of the findings. The first is that problem solvers reject the school-taught rule-of-three algorithm for solving proportionality problems in everyday contexts (Karplus et al., 1983; Nunes et al., 1993; Schliemann & Carraher, 1993; Vergnaud, 1983). Nurses preference for calculation methods other than the formula, derived from the rule of three, when they calculated medicine doses in clinical practice was reported by Hoyles et al. (2001) and Wright (2013). In all the studies examined focusing on problems of proportion, children and adults preferred to use scalar approaches not taught in schools (Nunes et al., 1993) tailored to the specific problem situation. They also preferred to use mental arithmetic strategies bearing no resemblance to formal algorithms, such as the rule of three, intended for performing the same computations. Preference for invented problem-solving strategies over school-taught algorithms to solve out-of-school problems extends beyond proportionality problems. Nasir et al. (2008) tested the concepts of average and percentage among school basketball players in two different contexts. African American basketball players used invented strategies to compute an average and a percentage for problems posed in a basketball context. However, when the same problems were posed as abstract school mathematics problems, the youths used algorithms, often incorrectly recalled, to calculate the same measures. According to Nasir et al. (2008) the basketball players patterns of solutions illustrated the discontinuity between their everyday cultural knowledge about the concepts of average and percentage and the types of mathematics relating to the same concepts they had been exposed to in school. The dominance of scalar strategies Another area of consistency among the research findings is that people make far greater use of scalar procedures than functional procedures. This finding has been found in relation to studies involving adults and children, whether schooled or unschooled, and relates to early studies by researchers such as (Karplus et al., 1983; Nunes et al., 1993; Schliemann & Carraher, 1993; Schliemann & Nunes, 1990; Vergnaud, 1983). Brazilian fishermen showed a strong preference for scalar solutions (Vergnaud, 1983) as did child street vendors (Nunes et al., 1993). 81

95 Chapter 2: Literature Review An exception was the finding by Hoyles et al. (2001) that the nurses in their study made as much use of functional strategies as they did of scalar strategies. However, in every case, the strategy was inextricably tied to the particular medicine and, by implication, its concentration. Nunes et al. (1993) considered why students do not often draw on the schooltaught rule-of-three algorithm for solving problems of proportion. The researchers asked: Why should such a useful procedure of great applicability be so readily abandoned? (p. 126): It seems that everyday procedures, which are likely to be already available to students before they are taught the algorithm, compete with the algorithm. The conflict stems from the fact that the everyday knowledge uses calculation procedures in which variables are kept separate. No calculations across variables are carried out. The school-taught procedure violates this principle. Thus, it is not easily coordinated with students previous knowledge. This conflict may well be at the root of poor learning of school mathematics for solving proportions problems. (Nunes et al., 1993, p. 126) Even for problems more amenable to a functional solution, the fishermen made only occasional use of functional solutions, favouring scalar solutions that were sometimes both clever and awkward (Vergnaud, 1983, p. 115). Scalar approaches involving parallel transformations of variables had the advantage of preserving the meaning of the problem (Schliemann & Carraher, 1993). By contrast, using a functional solution or the rule of three required setting meaning aside in order to carry out computations across variables (Schliemann & Carraher, 1993). Schliemann and Nunes (1990) formed the belief scalar procedures are used almost universally, both by those without school instruction and those who had been instructed in the rule of three. They hypothesised that this schema for conceptualizing and solving proportions is developed naturally through exposure to everyday, real-world proportionality situations. The strength of the out-of-school proportionality schema is such that it impedes other solution processes. When school-taught procedures come into conflict with the out-of-school model, formal school procedures are poorly learned and quickly forgotten (Schliemann & Nunes, 1990, p. 267). A more formal explanation for the rejection of the rule-of-three algorithm was offered by Vergnaud (1983) who conjectured it it is not natural for students to 82

96 Chapter 2: Literature Review multiply and divide magnitudes. In the rule-of-three algorithm, the value of the unknown, x, is: If a, b, and c are viewed as pure numbers, resolving presents few problems. In real-world problems of proportionality, however, the ratios of numbers are replaced with ratios of quantities (Schliemann & Carraher, 1993; Vergnaud, 1983). Such quantities may be expressed through measures of natural units (e.g. oranges, boys), conventional units of measure (e.g. dollars, metres; Schliemann & Carraher, 1993), or, in the nursing context, through magnitudes of physical quantities such as mass (e.g. milligrams, micrograms) and volume (e.g. millilitres). When a, b, and c are viewed as magnitudes, products and quotients involving these magnitudes have no meaning to problem solvers. Consequently, application of the rule of three, and by inference the formula derived from it, results in multiplying and dividing magnitudes of volume and mass. Such mathematical operations have no meaning to nurses solving problems and lead to conceptual difficulties (Fleming et al., 2014; Hutton et al., 2010; Weeks et al., 2000; Wright, 2006). This disconnection from the meaning of the problem, Vergnaud (1983) postulated, is the reason why the problem solver rejects the algorithmic process offered by the rule of three, and logically the dose calculation formula as well, as being incomprehensible in terms of its relationship to the problem situation. Nunes et al. (1993) concluded their findings appeared to contradict the implicit pedagogical assumption of mathematics educators (p. 22) that students should first learn mathematical operations such as algorithms, and only later gain practice in applying them to word problems and/or real-life problems. Their findings support the view of Hiebert and Carpenter (1992) who argued for meaning before efficiency. x bc, a where a, b, and c are quantities of mass, and b and x are quantities of volume. The conclusions of Nunes et al. (1993) and Hiebert and Carpenter (1992) have important implications for nursing education if student nurse are given the formula followed by opportunities to apply it to word problems that attempt to represent realworld dose calculation problems. bc a 83

97 Chapter 2: Literature Review The influence of problem context on strategy choice and accuracy of solution Several studies have illuminated aspects of proportional reasoning that have potential implications for the dose calculations nurses perform. Of particular interest is the impact of the mode of presentation of the problem on the problem solvers choice of solution strategy and the accuracy of their solution. Among the Brazilian schoolchildren Nunes et al. (1993) studied, all of whom worked as street vendors in their family market enterprises, both the calculation strategy they used and the accuracy of their calculations were influenced by the way the problem was posed as a simulated store problem, word problem, or computation exercise. Children capable of solving a computational problem in the natural situation often failed to solve the same problem when it was taken out of its context. Simulated store problems (e.g. You re selling x cars for y cruzeiros, but I only want one. How much does one car cost? (Nunes et al., 1993, p. 32)) elicited oral arithmetic practices performed mentally using strategies similar to those the children used dealing with closely linked quantities in their work as street vendors. Problems posed as simple mathematical operations without context (e.g ; ) elicited written arithmetic practices. Word problems (e.g. I had x soccer cards in my collection. I lost y. How many do I have now? (Nunes et al., 1993, p. 32)) elicited a mixture of practices of both types. Nunes et al. (1993) found the testing condition (store problem, word problem, or computation exercise) not only influenced the choice of procedure, but also had a striking effect on the accuracy of children s calculations. Children s performance on computation exercises was significantly inferior to their performance on both simulated store and word problems. Further, the type of arithmetic practice the children used was associated with differing levels of success. Statistical analysis revealed oral procedures were far superior to written procedures in terms of the percentage of correct responses. In the formal test conditions where children mostly used pencil and paper, they tried, frequently without success, to follow school-prescribed routines, such as addition and multiplication algorithms, which they sometimes confused. Nunes et al. (1993) remarked that their findings confirmed the results of other studies showing that problem solving in the supermarket was significantly superior to problem solving with pen and paper (Nunes et al., 1993). In respect of the superiority of the street mathematics exhibited by children in their study, Nunes et al. offered as 84

98 Chapter 2: Literature Review an explanation the possibility that through their roles as street vendors, the children had many opportunities to practice oral (i.e. mental) arithmetic, but few opportunities to practice written arithmetic in the school setting. The fact that the manner in which a problem is posed may influence the problem solvers choice of calculation strategy and the accuracy of their calculations has important implications for how students and qualified nurses respond to dose calculation problems, particularly under test conditions. If the same influences impacting the calculation responses of children in the study by Nunes et al. (1993) were found to have similar influences on nurses calculations, four outcomes might be anticipated in relation to their performance on calculations designed to test their dose calculation skills. First, nurses might be expected to respond with different solution procedures depending on whether problems were encountered as real-world problems in the natural setting of the ward, posed as written word problems, or posed as context-free computations. Second, nurses might be expected to have differing levels of accuracy depending on the mode of presentation of the problem. Third, nurses might be expected to achieve differing levels of success in solving the problems according to the type of arithmetic practice they applied mental arithmetic or written algorithmic processes. Fourth, nurses might be expected to have poor outcomes on calculations presented as decontextualised numerical computations compared to dose calculations encountered in authentic practice contexts or as written word problems. Factors influencing the direction of calculation The direction of the calculation was a phenomenon of interest to researchers investigating nurses dose calculation practices. Hoyles et al. (2001) noted the structure of the formula follows the sequence of physical actions nurses take when they apply the formula. By contrast, Wright (2013) found when nurses use scalar processes they work in the reverse direction to that followed when using the formula. Wright (2013) found the formula sequence commences with the prescribed dose and works forward via the stock on hand to find the quantity to be administered. By contrast, nurses using scalar strategies commence with the stock on hand and work backwards until they reach the prescribed dose, using a series of parallel transformations. The explanation Wright gave for the reverse direction of the calculation process when scalar strategies are used rather than the formula was that more confident problem solvers are able to work backwards from the known to the 85

99 Chapter 2: Literature Review unknown, whereas less confident problem solvers tend to work forwards from the unknown to the known (Wright, 2013, p. 456). In their study, Nunes et al. (1993) found the direction or order in which the calculation proceeded differed according to whether the problem solver used mental or written arithmetic procedures, the direction of calculation process affected preservation of the relative values of the quantities involved and the magnitude of errors made. Nunes et al. found: In contrast to written arithmetic, oral [i.e. mental] arithmetic proceeds from larger to smaller and works in ways that preserve the relative numerical value of numbers (1993, p. 48). Moreover, statistical analysis confirmed errors in oral practice tended to be smaller than those generated in written arithmetic. Similar findings in relation to the direction of nurses dose calculations would have potentially significant ramifications for patient harm, since errors of greater magnitude usually pose a greater level of risk of harm or death to the patient than do minor errors. 2.9 Investigation of nurses dose calculation strategies Investigations of nurses responses to dose calculation problems can be divided into two categories. The first category comprises studies focusing on nurses responses to dose calculations posed in narrative form, typically as word problems attempting to represent problems that might be encountered in clinical practice. The second category comprises study of nurses responses to problems encountered in authentic clinical practice environments. In these, the prescribed dose appears on the patient chart and the available stock is in the form of a package, bottle, ampoule, or vial of medicine, on the label of which is printed the strength or concentration of the medicine. A great deal of literature has focused on the first category, however it has centred almost exclusively on the performance of nurses and students rather than the calculation strategies they use. Two studies in the first category will now be examined because of their focus on dose calculation strategies nurses used. These studies, the only such studies identified are those by Wright (2013) and an earlier study I conducted (Gillies, 2006). The focus will then shift to the only study identified in the second category focusing on the dose calculation strategies nurses use in clinical practice, the study undertaken by Hoyles et al. (2001). 86

100 Chapter 2: Literature Review Nurses strategies for solving written dose calculation problems In Wright s study (2013), eight experienced nurse educators solved eight dose calculation problems presented in narrative form without the use of calculators. They verbalised their thinking, which Wright recorded, combining this data with that collected through researcher observation and participants written calculations. Wright identified three types of solution process she classified as: formula, scalar methods, and syringes. The formula was the most commonly used method with six of the eight participants using it as either their sole or dominant calculation method. Yet the formula was used for less than half of the items for which it was an appropriate method. Over half the questions were solved using alternative calculation strategies. Scalar processes dominated with the majority of participants making some use of scalar strategies. One participant used the syringe method, a form of scalar approach, as their primary problem-solving method, applying it to half the items. This strategy, in which a syringe scale is used as a measure of both mass and volume, was also identified by Cartwright (1996). It was discussed earlier in and illustrated in Table 2.2, including: Wright (2013) reported nurses scalar methods taking a number of forms a version of the unitary method (Vergnaud, 1983); a method involving doubling and halving (p. 454); methods that combined strategies in ways similar to Vergnaud s (1983) method of scalar decomposition (see and Table 2.2, 2.5.3); a scalar method involving finding a fraction or performing a division operation, referred to by Wright as relational methods (p. 454) and similar to Vergnaud s (1983) scalar operator method, with the multiplication process replaced by division; and use of a syringe as a visual aid in combination with scalar methods (p. 454). When the results were compared with those of related studies, on the one hand nurses extensive use of scalar methods corroborated the conclusion of Hoyles et al. (2001) that nurses eschewed the formula in favour of informal proportional reasoning 87

101 Chapter 2: Literature Review methods. On the other hand, nurses preference for informal methods rather than the formula was contrary to expectation, based on the conclusions of Nunes et al. (1993) that problems posed in written format were more likely to elicit formal school-taught solutions. Wright s findings (2013) highlighted the computational complexities associated with use of the formula. Because calculators were not permitted, the arithmetical operations the nurses performed needed many steps requiring a variety of algorithms for operations such as multiplication and division, and caused nurses considerable difficulty. Wright postulated these computational complexities explained, at least in part, the high error rate of 35% associated with nurses use of the formula. By contrast, when nurses used scalar methods, for which the error rate was less than 13 21%, they manipulated the available stock mass value until they obtained the prescribed dose. This approach required fewer steps and allowed nurses to keep the problem context in mind. The impact of not having access to a calculator appeared to impact less on the computational complexities of the task when nurses employed scalar solution strategies than when they used the formula. However it could be argued that the requirement that calculations be performed without calculators may, in itself, have contributed to the relatively poor overall success rate of 67% on the 64 test items analysed and the average score of 5.4 correct answers per person of the 8 attempted (68%). These scores were of some concern considering all nurses had a clinical background in the acute care setting and more than half also had experience in intensive care units. Further, their current roles as teachers of pre-registration nurses should have guaranteed a high level of competence in calculating medicine doses. No conclusions were possible concerning the level of success associated with different calculation strategies written or mental because all solutions were required in written form. However the finding that the error rate associated with formula use (35%) was higher than that for scalar methods (at most 21% and probably closer to half that for the formula) confirmed the conclusion of Nunes et al. (1993) that the presentation of the problem (authentic practice, word problem, or computation exercise) influenced the accuracy of the solution. 13 In fact the error rate may have been as low as half that of the formula method because Wright did not include among the scalar methods the four items she classified separately as syringe method. 88

102 Chapter 2: Literature Review The objective of the earlier study referred to (Gillies, 2006) was to investigate first-year students ability to solve medication calculation problems before they were exposed to formal instruction on the topic. As part of a broader study (Gillies, 2004) comparing the effectiveness of two different approaches to teaching medication calculations, 35 first-year nursing students at an Australian university were asked to solve ten calculation problems set in everyday contexts. The everyday tasks, posed in the form of word problems, were designed to parallel typical medication calculation problems involving tablets, liquid doses for oral administration and injection, and intravenous drip rates. The problems included three calculations mimicking the most difficult type of calculation nurses are required to calculate, namely calculation of intravenous flow rates in drops per minute. All 35 students succeeded in applying a correct method to at least one of the ten problems, and 13 students (37%) were able to apply a correct method to at least seven of the ten items. The overall success rate on the test was not good. The proportion of students obtaining the correct answer ranged from 3% on the IV time for the infusion to run parallel question to 97% on an item that paralleled a tablet question. On average, 37% of students obtained the correct answer per item. When application of a correct problem-solving method was used as the criterion for success, the average success rate per item rose to 51%, with the success rates on individual items ranging from 29% for the IV time to run problem to 97% for the easiest tablet calculation. The average increase of 1.4 questions per student on the 10 questions attempted reflected questions for which students used a correct method but failed to proceed to the correct answer because their computational skills were inadequate. The increased success rate translated to 26% of the students adding three or four more successful items to their score. Students applied a broad range of correct problem-solving strategies, including division operations, finding a fraction of a quantity, the unitary method and adaptations of it, the rule of three, ratio methods, proportional reasoning methods, and expressing rates in equivalent forms. In summary, with no prior instruction in dose calculation methods, on average students were able to apply correct problem-solving methods to approximately half of the ten test items using multi-step processes that maintained the proportional relationships and the meaning of the problem situation in each step. 89

103 Chapter 2: Literature Review The findings provide evidence many students come to nursing studies equipped with sound conceptual understanding of proportionality and appropriate problemsolving methods. A few students were successful in applying intuitive problemsolving methods to even the most difficult of the medication calculation problems nurses must solve. In another aspect of the same study, reported separately (Gillies, 2004), I sought to investigate the viability of nurses using the same intuitive problem-solving methods to solve a parallel set of dose calculation problems to the everyday problems they solved. The study compared the learning outcomes of two groups of students, a subset of 19 participants from the study described previously. The students were exposed to two different approaches to teaching medication calculation, one modelled on application of formulae, the other drawing on and further developing students existing mathematical problem-solving skills. Although the formula-based calculation methods learned by the twelve students in the formula group appeared to result in greater learning gains in the short term, application of formulae was associated with a deficit model of learning. Students viewed the availability of a formula as a good way of overcoming their own inadequacies and deficiencies in mathematics. The explanations from students about why they liked the formula approach revealed many negative feelings about their perceptions of their own mathematical competence and their belief that without a formula they would not be able to perform calculations, a common perception among students reported also by Rice and Bell (2005). By contrast, the seven students in the problem-solving group learnt to calculate doses and intravenous drip rates using student-generated methods explored in class. Students were free to select a method of their own choosing to solve the medication problems. The learning that occurred was more closely associated with conceptual understanding and was characterised by personal growth and confidence building. Further, students attitudes to mathematics and medication calculation were more positive at the end of the teaching intervention, compared to students in the formula group. The problem-solving students felt they knew what they were doing at each step of the calculation, and, in contrast to the formula group, they were more confident their answers would be correct. Having the freedom to use their preferred method to solve medication calculation problems meant the students felt they had obtained the correct answer by themselves, giving them a sense of achievement and personal 90

104 Chapter 2: Literature Review satisfaction, thus also boosting their confidence and self-esteem. The findings from the study were congruent with Hiebert and Carpenter s (1992) model of learning mathematics with understanding in which effective learning involves building on existing knowledge so new knowledge is grafted onto existing networks of mathematical concepts and knowledge. Wright s (2013) study and my own (Gillies, 2004) were limited in their scope, sample size, and generalisability. Yet despite these limitations, they demonstrate students and experienced nurses possess sound concepts of proportionality and competence in using informal methods, in particular scalar methods, for solving dose calculation problems posed in narrative form. The findings suggest the same calculation methods may also be used successfully by nurses in the practice environment, a conclusion reached by Hoyles et al. (2001) Nurses strategies for calculating and measuring doses in practice Among all the studies centred on dose calculation skills, just one, that of Hoyles et al. (2001), investigated the dose calculation strategies nurses use in clinical practice. Wright (2013) also reported finding no similar studies similar to that of Hoyles et al. No studies were identified investigating nurses measurement strategies in practice. The study by Hoyles et al. (2001) paints a very different picture of the dose calculation skills nurses use and their mathematical competence from that portrayed by other studies focusing on the performance on graduate and student nurses on traditional tests of dose calculation competence. The Hoyles et al. study revealed nurses competently applying a range of proportional reasoning strategies, tailored to the particular features of the problem scenario, rather than the traditionally taught formula. As part of a broader investigation of workplace mathematics, Hoyles et al. (2001) sought to identify the mathematical processes the nurses used to solve medicine dose calculation problems in clinical practice. This task was one they initially had not intended to undertake. Given the high profile of dose calculation in the professional roles of nurses, they assumed the necessary mathematical strategies had already been well researched and any further investigation by them was unlikely to add anything new. 91

105 Chapter 2: Literature Review The researchers observed twelve paediatric nurses as they calculated routine medicine doses in a specialist paediatric hospital in the UK. Thirty administration episodes were observed, six of which required no calculation because the prescribed dose was identical to the concentration of the available stock (e.g. give 10 mg from stock labelled 10 mg per 5 ml). Despite the relatively small number of doses requiring calculation, Hoyles et al. (2001) remarked on the variety in the prescribed doses, and the stock formulations (or packaged doses) the nurses used to administer them. They observed that values of the scalar ratio of mass-of-drug-prescribed to mass-in-package 14 varied from simple values such as 1:1 and 2:1 to 2520:420 (p. 15). Measurement units for prescribed doses were milligrams or millimoles, and the concentrations of liquid medicines were expressed as fixed volumes of 1, 2, 5, or 50 millilitres. The nurses successfully carried out the calculations using a variety of strategies Hoyles et al. (2001) observed were richer in complexity than was suggested by the researcher s interviews with senior staff and the nurses, or from the existing nursing literature. Nurses used a range of correct proportional reasoning strategies based on the invariant of drug concentration (p. 4). Nurses made no use of the unitary method or the rule of three. The latter finding did not surprise the researchers because, although the rule of three is taught in many countries, it was not taught in UK schools at the time of the study. Mental strategies, with no recourse to pen and paper or use of a calculator, were used for all but one calculation for which the nurse used three separately written calculations. Hoyles et al. (2001) described the four episodes in which nurses employed the formula as being characterised by: the formula, variously used as a written algorithm, a mental strategy and a procedure to use with a calculator (p. 16); an inflexible sequence of computational processes dictated by the format of the formula, first simplifying the quotient, the result by the volume (p. 16 7); and What you want What you've got, then multiplying 14 Referred to also as scalar ratio: mass prescribed to packaged dose (p. 15) and ratio of prescribed-dose to packaged-dose (p. 22). 92

106 Chapter 2: Literature Review a sense of disconnection between the nurse and straightforward arithmetical processes that could potentially have simplified the task, and the meanings of the quantities rooted in the clinical setting of the problem (p. 17 8). The scalar strategies nurses used involved a wide variety of quantities and required nurses to perform as many as five transformations on the quantities involved in the problem. Several of the scalar strategies nurses used were similar to those identified by Vergnaud (1983; see particularly Figure 2.1, and Table 2.2, 2.5.3). Hoyles et al. (2001) noted one technique, which they termed chunking (pp. 21; 22) that seemed particularly meaningful to nurses. This procedure involved identifying a chunk of mass (which was not necessarily one unit) related to a specific volume (or other vehicle such as a tablet or capsule). The chunk of mass was added repeatedly or multiplied by an appropriate number to reach the required dose. Equivalent operations were then performed on the volume (or other vehicle; examples of chunking using multiplicative and additive processes were illustrated in Table 2.2, ) Nurses used other scalar strategies involving partitioning the stock mass by division to obtain a convenient unit, not necessarily one, that was also a factor of the prescribed dose, then, multiplying that unit to obtain the prescribed dose. Parallel transformations were then carried out on the stock volume or vehicle. The finding by Hoyles et al. (2001) that the paediatric nurses made as much use of functional strategies as they did of scalar strategies appears to conflict with the findings of other researchers that point to problem solvers making far greater use of scalar procedures than functional procedures (Karplus et al., 1983; Nunes et al., 1993; Schliemann & Carraher, 1993; Schliemann & Nunes, 1990; Vergnaud, 1983). However, in a twist possibly unique to the nursing context, Hoyles et al. (2001) offered an explanation for this apparent anomaly. They found use of a functional strategy was always characterised by a strong link between the transformation process and the particular medicine. This was evidenced by nurses explanations of their computational processes, such as doubling and halving. Typical explanations included: That s how it is with amakacine (p. 20), and With ondanstron all you need to do is halve the dose (p. 27). Examination of the mathematical processes involved in calculations where nurses used functional strategies in this way shows each shortcut method is the 93

107 Chapter 2: Literature Review embodiment of a functional strategy connecting volume with mass via a particular stock concentration. All episodes in which nurses applied a functional strategy involved particular ratios of mass to volume, defined by the stock concentration. It seems likely, however, in applying functional strategies in this very medicine-specific way, nurses were no longer cognisant of the mathematics of the process. It is also possible nurses never fully understood the mathematical underpinnings of the strategy, but instead applied it in a semi-ritualistic way. Each shortcut thus became part of the fabric and ritual of the practice of nursing, intimately connected to a particular community of practice, clinical setting, medicine and stock concentration. The study by Hoyles et al. (2001) is of immense importance because it is the only study to provide evidence nurses, like the many adults and children studied by other researchers make considerable use of informal proportional reasoning strategies to solve dose calculation problems in the practice environment. Despite the study being limited in its scope, sample size and generalisability, it nevertheless provides clear evidence nurses prefer, in many situations, to use proportional reasoning strategies in preference to the commonly taught formula. The only three studies to investigate nurses dose calculation strategies, those by Wright (2013), Hoyles et al. (2001), and Gillies (2006, 2004) provided evidence of nurses ability to invent algorithms and use informal problem-solving strategies to solve proportional problems in the form of dose calculations. This evidence provides support for Morrow s (1998, p. 2) call for more emphasis to be placed on the fact that men and women invent algorithms. Morrow observed that algorithms are being constructed all the time. She recommended students be encouraged to develop their own algorithms, contending there is no reason everyone should use the same algorithm. Morrow advocated exploring algorithms offered by students, including those from other cultures, suggesting such activity can help students develop number sense by thinking about problems in different ways Summary and purpose of proposed study This literature review described the regulatory environment in which nurses calculate and measure medicine doses, and the strong professional focus on Quality Use of Medicines and patient safety in relation to medicine administration in 94

108 Chapter 2: Literature Review Australia. It reveals an unclear picture of the extent to which nurses calculation and measurement contribute to medicine administration error, thus compromising patient safety. Contemporary approaches to learning mathematics with a particular focus on workplace applications of mathematics, were discussed and related to nurses learning of dose calculation and measurement. Existing research investigating approaches to out-of-school problems of proportionality is presented. This research provides compelling evidence that problem solvers use proportional reasoning methods, especially scalar strategies, to solve problems rather than applying formal school-taught methods such as the rule of three, designed for the purpose. Little evidence was identified of nurses approaches to solving proportionality problems in the form of dose calculations, either posed in narrative test-like forms, or encountered in clinical practice. The few available studies support other research evidence revealing rejection of formal algorithmic methods by problem solvers and a preference for informal invented methods tailored to the particular problem. The literature review identifies several gaps in knowledge relating to nurses dose calculation and measurement practices. Specifically, very little is known about the strategies Australian nurses use to calculate medicine doses and the factors influencing their choices. A knowledge gap exists in relation to nurses skills in measuring medicine doses. With few exceptions, the focus of accuracy relating to the quantity of medicine patients receive has remained firmly fixed on calculation accuracy. Few studies have focused on the dose calculation or measurement strategies nurses use in association with medicine administration, particularly the strategies nurses use in clinical practice. The few studies undertaken have been small in scale and sample size and relate mainly to nursing education and practice in two countries only, the UK and Australia. Further, little comprehensive research has focused on current teaching and assessment practices relating to dose calculation and measurement skills in Australia. The proposed study is aimed at adding new information and filling some of the gaps identified in existing knowledge. 95

109 Chapter 2: Literature Review 2.12 The research questions The research questions for the study were: RQ1 What strategies do registered nurses use to calculate and measure the dose of medicine to administer? RQ2 What factors influence registered nurses choice of strategy for calculating the dose of medicine to administer? RQ3 What strategies are student nurses taught to calculate and measure the dose of medicine to administer? 96

110 3 Methodology Sharing such narratives helps to draw out the practitioner s own expert thinking making it visible to themselves and others and thus open to questioning, critique and reflection an excellent educational opportunity, but one which is only effective for new learners when allied with immersion in the practical experience itself. Sabin (2013, p. e3) Chapter 3 examines the methodological literature. Crotty (1998) suggested that when planning a research study two questions in particular require considerable attention. The researcher must ask firstly: What methodologies and methods will we be employing? and secondly How do we justify this choice and use of methodologies and methods? (p. 2). I attempt to answer these two questions in Chapter 3. The research questions for the study are listed in An appropriate starting point for considering methodological approaches for the study was recognising that the issues of interest cross disciplinary boundaries and encompass nursing practice, nursing education, mathematics education, and applying mathematics in the workplace. My perspective is that of a mathematics educator with a long history of teaching and supporting nursing students to apply mathematics to nursing practice. From this perspective I view the study as a mathematics education study set in the context of nursing practice. In recognition of the cross-disciplinary nature of the issues of interest, the methodological literature I consulted included nursing, healthcare, and education research methodologies as well as general research paradigms. Chapter 3 commences with a description of the philosophical assumptions that guided my approach to the study. Different methodologies considered for the study are described and discussed in terms of their suitability for achieving the goals of the study. The chapter concludes with a rationale for the methodological approaches I decided to use to conduct the study. 3.1 Philosophical assumptions underpinning the study The research process begins with what the researcher brings to the inquiry their personal history, traditions, concepts of self and others, and their stance on the 97

111 Chapter 3: Methodology ethics and politics of research (Denzin & Lincoln, 2011). The researcher s worldview is their theoretical perspective or general philosophical orientation to the research (Creswell & Plano Clark, 2011; Crotty, 1998). Whether realising it or not, researchers approach their study with assumptions and premises about knowledge and how it can be obtained (Creswell, 2012). Worldviews are the broad philosophical assumptions that guide inquiries (Creswell & Plano Clark, 2011). Creswell (2013, p. 16) defines philosophy as the use of abstract ideas and beliefs that inform our research and proposes that philosophical assumptions are typically the first ideas in developing a study. In relation to qualitative research, authors such as Creswell (2013) and Denzin and Lincoln (2011) emphasise the importance of researchers declaring their philosophical assumptions and the interpretive lens or lenses guiding their research. In 1.1, I outlined my personal history and professional background, particularly as they relate to the issues at the heart of this thesis the mathematics needed for medicine administration, with a particular focus on what we should teach students and how we should teach it. The account of my background in the area of nursing mathematics demonstrated reflexivity by providing the reader with an understanding of where I was coming from and what I hoped to achieve by undertaking the study. It explained some of the experiences that have led me to undertake the research study that is the subject of this thesis. It allows glimpses of my views on issues surrounding the topic of interest and provides insights into how those views may have affected my approach to the study. Indeed the observations and findings I made were very much a product of the particular frame of reference I used in the study. My background as a mathematics educator affected every aspect of the study, from its purpose and goals to the research questions and problem statement, design and conduct, the ways in which I selected the data sources, analysed and interpreted the data, and reported the findings (Borbasi, Jackson, & Wilkes, 2005) Interpretive framework for the current study worldview: Mertens (2003) proposed that three defining questions determine one s The ontological question asks: What is the nature of reality, and by extension, truth? 98

112 Chapter 3: Methodology The epistemological question asks: What is the nature of knowledge and the relationship between the knower and the would-be known? The methodological question asks: How can the knower go about obtaining the desired knowledge and understanding? (p. 140) Denzin and Lincoln (2011) added a fourth axiological question: What is the role of values? Authors describe a range of different worldviews or philosophical assumptions which include: positivism, post-positivism, social constructivism, transformative framework, participatory framework, and pragmatism (Creswell, 2013; Creswell & Plano Clark, 2011; Mertens, 2009). According to Crotty (1998, p. 9), epistemology (or ways of knowing and issues of what constitutes knowledge) bears mightily on the way we go about our research (p. 9). Crotty also believed that epistemological stances should not be viewed as watertight compartments (p. 9). Indeed Creswell and Plano Clark (2011) suggested that worldviews may be combined or used individually. My view of how to discover reality with respect to the strategies nurses use to calculate and measure medicine doses is that it will be most completely and truthfully constructed by combining two different viewpoints. The first viewpoint is that of nurses themselves, obtained by asking them to explain and interpret the techniques they use to calculate and measure medicine doses. In the manner of social constructivists, I seek to understand the lived experience of nurses as they prepare and administer medicines in the course of their routine duties. The second viewpoint is my own interpretation of how nurses calculate and measure medicine doses. This viewpoint will be framed by my background as a mathematics educator, and my history of research and inquiry into the ways students are taught to calculate and measure medicine doses. It will be a lens coloured by my efforts to support students who experience difficulty in achieving mastery in this aspect of the nursing curriculum. By combining the two lenses in this way I expect to construct a more truthful picture of nurses medicine administration behaviours than would be achieved by applying either lens alone. Similarly, my view of the reality of the strategies nurse educators teach students to calculate and measure medicine doses is that the truth is most likely to 99

113 Chapter 3: Methodology be found by asking those most closely involved with the curriculum and teaching practices that relate to this aspect of pre-registration nursing education. I expect, too, that with respect to each area of inquiry the strategies nurses use to calculate and measure medicine doses in practice, and the strategies nurse educators teach students for these tasks there will be multiple truths. For example, I expect that different nurses may use different strategies to calculate and measure medicine doses in clinical practice. I anticipate that a nurse s choice of strategy may be largely determined by immediate influences personal and clinical impacting on them at the time. In relation to addressing the research questions for the current study, the philosophical position I adopted in planning the research design was one of pragmatism (Creswell & Plano Clark, 2011; Johnson & Christensen, 2012), overlaid with social constructivism (Creswell & Plano Clark, 2011), and strongly influenced by the transformative paradigm (Mertens, 2009). These worldviews are typically associated with qualitative approaches to research (Creswell & Plano Clark, 2011). I will now describe each of these interpretive frameworks in more detail. Pragmatism Pragmatism embodies a philosophical position that what works is important or valid (Johnson & Christensen, 2012, p. 32). According to Cherryholmes (1992), pragmatists deny foundationalism, the belief that grounded meaning and truth can be determined once and for all (p. 15). They do not pretend to know if their conception or picture is of reality (p. 14). Creswell and Plano Clark (2011) described pragmatism as a paradigm typically associated with mixed methods research, in which the focus is on the consequences of research and the primary importance of the research question, rather than the methods employed. Pragmatists contend that the research design should be planned and conducted based on what will best help you answer your research questions (Johnson & Christensen, 2012, p. 32). The emphasis is on what works in practice and what promotes social justice (p. 32) using diverse approaches, multiple data collection methods, and valuing both objective and subjective knowledge (Creswell & Plano Clark, 2011). Cherryholmes (1992) suggested that pragmatists begin with what he or she thinks is known, look to the consequences they desire and proceed to pick and choose how and what to research and what to do (p. 14). In applying a pragmatic 100

114 Chapter 3: Methodology approach to the current study, I will use those methods I believe will work best to address the research questions. Transformative paradigm Transformative scholars believe that knowledge is not neutral but is influenced by human interests; knowledge reflects the power and social relationships within society (Banks, 1995). According to Mertens (2009), the essence of the transformative paradigm is in the generation of knowledge for social change (p. 4): Transformative-emancipatory scholars recommend the adoption of an explicit goal for research to serve the ends of creating a more just and democratic society that permeates the entire research process, from the problem formulation to the drawing of conclusions and the use of the results (Mertens, 2009, p. 159). Mertens (2009) noted that the transformative paradigm emerged as a means of bringing into the world of research the voices of individuals who have been pushed to the societal margins throughout history (p. 3). Transformative theory is an umbrella term that encompasses paradigmatic perspectives including emancipatory, anti-discriminatory, and participatory. Mertens suggested that the usual application of the transformative paradigm is to address the social inequity, discrimination, and oppression experienced by people on the basis of race or ethnicity, disability, immigrant status, political conflicts, sexual orientation, socioeconomic status or gender. The transformative-emancipatory paradigm addresses the importance of the role of values in research (Mertens, 2003, p. 159). It accompanies increased attention to the need to address the politics of human research and issues of social justice (p. 159). Mertens proposed that the transformative spirit can be applied across disciplines and methods; there is not a single context of social inquiry in which the transformative paradigm would not have the potential to raise issues of social justice and human rights (p. 4). Mertens (2009) illustrated this point with an example of the transformative paradigm applied to a study focusing on inequalities in power relations that existed in the highly male-dominated profession of engineering (Watts, 2006). Kemmis and Wilkinson (1998) described features of the transformative framework in their discussion of participatory action research, at the centre of which is the specific goal of bringing about change in practices. The transformative nature 101

115 Chapter 3: Methodology of participatory action research is evident in the following characteristics of participatory action research described by Kemmis and Wilkinson. Participatory action research aims to change the practice, the way it is understood and the situations in which the practice is conducted (p. 33). At its best, it is a collaborative social process of learning, realised by a group of people who join together in changing the practices through which they interact in a shared social world (p. 22). Participatory action research is emancipatory in that it aims to help people recover, and unshackle themselves from, the constraints of irrational, unproductive, unjust and unsatisfying social structures which limit their selfdevelopment and self-determination (p. 24). The process involves people deliberately setting out to contest and to reconstitute such social structures (p. 24). Constraints people may wish to release themselves from include their modes of work and the social relationships of power (p. 24). Merten s (2003, 2009) description of the transformative paradigm, hinted at by Kemmis and Wilkinson (1998) in their description of participatory action research, echo some of the goals of the current study. The genesis of the study stems from my concern that nursing students may be disadvantaged in their learning in relation to medicine dose calculations because of constraints relating to the calculation methods they are taught, and sometimes permitted to use. These potentially restrictive calculation methods are, in turn, the result of persistent teaching practices that are likely to be socially, historically, politically, and culturally based. The following goals of my study illustrate some of the ways in which the transformative paradigm permeates my investigation: giving voice to experienced nurses, allowing them to explain how they calculate medicine doses in their clinical practice; giving voice to nurses educators, allowing them to explain how and why they teach medicine dose calculations the way they do, and their own personal calculation preferences; making comparisons between how nurses actually perform dose calculations and how nurse educators teach students to perform dose calculations; 102

116 Chapter 3: Methodology drawing conclusions about the appropriateness of current teaching practices; and highlighting issues concerning teaching practices and modes of work (Kemmis & Wilkinson, 1998, p. 24) relating to medicine dose calculation that may impact on the self-determination and self-development of nursing students and nurses. Social constructivism A worldview of social constructivism is typically associated with qualitative approaches (Creswell & Plano Clark, 2011). Social constructivists view reality as multiple, actively seek multiple perspectives from participants, and develop different perspectives through multiple interviews. Meaning is not discovered, but constructed is the belief underlying the epistemology Crotty (1998) described as constructivism. Rather than there being an objective truth waiting for us to discover it, meanings are constructed by human beings as they engage with the world they are interpreting (p. 43). The following goals of the current study demonstrate how a world view of social constructivism is incorporated into the study: constructing meaning about the strategies nurses use to calculate medicine doses by seeking the perspectives of both the nurse participants and the researcher; and constructing meaning about the ways students are taught to calculate medicine doses by seeking the perspectives of the academic staff believed to have the greatest involvement in that aspect of teaching within the nursing curriculum. Table 3.1 provides a summary of the philosophical assumptions and interpretive frameworks that underpin the current study. It is through this multifaceted interpretive prism that I considered different methodological approaches, assessed their suitability, and then selected a research design capable of addressing the three research questions posed. 103

117 Chapter 3: Methodology Table 3.1 Characteristics of interpretive lenses for my study Interpretive framework/ lens Ontological beliefs (Nature of reality) Epistemological beliefs (What counts as knowledge) Axiological beliefs (Values researcher brings to study) Methodological beliefs (Research process) Pragmatism: the umbrella paradigm Reality is both singular and multiple a Reality is what is useful, is practical, and works b Only by acting on our beliefs and observing consequences can we know whether our beliefs described reality c Research occurs in social, historical, political and cultural contexts d,c Reality is known through using many tools of research that reflect both deductive (objective) evidence and inductive (subjective) evidence b Each notion is interpreted by tracing its practical consequences e Values are discussed because of the way that knowledge reflects both the researcher s and participants views b Both objective and subjective knowledge are valued a Focus on consequences of research; primary importance of question asked rather than on methods used a Researcher chooses methods, techniques and procedures that best meet their needs and purposes c,f Pluralistic, uses multiple methods to collect and analyse data d Transformative - emancipatory framework g Researcher provides a voice for marginalised or under-represented group g Knowledge is not neutral; is influenced by human interests; reflects the power and social relationships in society h Purpose is to generate knowledge for social change; create a more just & democratic society g Goal is to change practices by contesting and reconstituting social structures f Action agenda for change should conclude study a,g Focus typically on marginalised or underrepresented people g Use of sensitive data collection techniques that do not further marginalise community under study. a Emancipatory lens threaded throughout project from research questions, data collection techniques to conclusions g 104

118 Chapter 3: Methodology Interpretive framework/ lens Ontological beliefs (Nature of reality) Epistemological beliefs (What counts as knowledge) Axiological beliefs (Values researcher brings to study) Methodological beliefs (Research process) Social constructivism Multiple realities are constructed through our lived experiences and interactions with others a Understanding or meaning of phenomena is formed through subjective views of participants b Reality is multiple a ; is shaped by individual experiences b Focus on multiple perspectives from participants & coconstruction of reality between researcher & the researched a Individual values are honoured, and negotiated among individuals b Uses inductive reasoning: emergent ideas obtained through methods such as interviewing, observing, and analysis of texts b Table 3.1 was adapted from the following sources: a Creswell and Plano Clark (2011); b Lincoln et al. (2011); c Cherryholmes, (1992); d Creswell (2013); e James (1907); f Kemmis & Wilkinson (1998); g Mertens (2003, 2009); h Banks (1995) 105

119 Chapter 3: Methodology 3.2 Research methodologies According to Johnson and Christensen (2012), a research paradigm is a perspective about research held by a community of researchers that is based on a set of shared assumptions, concepts, values, and practices. More simply, it is an approach to thinking about and doing research (p. 31). These authors described the three major paradigms or approaches: quantitative research, qualitative research, and mixed research, the last being variously referred to as mixed methods research (e.g. Creswell & Plano Clark, 2011; Edmonds & Kennedy, 2013) and multi-strategy research (Bryman, 2006). Johnson and Christensen (2012) conceptualised the three major research paradigms as a continuum with qualitative research and quantitative research at the endpoints and mixed methods research somewhere in between. Johnson and Christensen (2012) defined methodology as the identification, study, and justification of research methods (p. 32). In planning research the researcher should match the methodological approach to the research problem (Creswell, 2012). Viewed from the broadest considerations of the three major approaches described earlier, it appeared that neither a quantitative nor a qualitative approach on its own was likely to achieve the complex goals of the study. It seemed that to employ only a quantitative or only a qualitative approach would be limiting and would result in an incomplete picture (Johnson & Christensen, 2012). Employing a mixed methods or multi-strategy approach appeared to offer the best means of understanding how nurses engage in the mathematical aspects of medicine administration and how the requisite skills for this aspect of nursing practice are taught in Australia. A multi-strategy design would allow me to select those features from quantitative and qualitative research paradigms that were most suited to addressing the study aims. Such an approach possesses many of the characteristics of the philosophical paradigm of pragmatism (Cherryholmes, 1992; Creswell & Plano Clark, 2011; Johnson & Christensen, 2012), described earlier in this chapter as the umbrella paradigm for my study the primary interpretive lens. A discussion of the research methodologies considered for the study follows. I have focused on methodological approaches that were of particular interest for 106

120 Chapter 3: Methodology incorporation into the research design because of their potential to achieve the goals of the study Quantitative research Quantitative research involves creating purpose statements, research questions and hypotheses that are specific, narrow, measurable, and observable analyzing trends, comparing groups, or relating variables using statistical analysis, and interpreting results by comparing them with prior predictions and past research (Creswell, 2012, p. 13). Traditional quantitative approaches include experimental, quasi-experimental, causal comparative, correlational, as well as non-experimental research, which may involve ex post facto designs, observational approaches, and survey approaches (Edmonds & Kennedy, 2013; Gay, Mills, & Airasian, 2012; Mertens, 2003). Quantitative research typically results in generalizable findings providing representations of an objective outsider viewpoint of the population of interest (Johnson & Christensen, 2012, p. 34). According to Johnson and Christensen (2012, p. 17), quantitative researchers follow confirmatory scientific method, which they describe as a top down process because the movement is from theory to hypothesis to data. For example, the researcher states an hypothesis, collects data to test the hypothesis empirically, then tentatively accepts or rejects the hypothesis on the basis of the data. Johnson and Christensen (2012) stated that quantitative researchers study behaviours in controlled conditions by holding constant those factors that are not being studied. They use a narrow-angle lens (p. 33), with the focus on one or a few factors. The researcher s intent may be to identify cause-and-effect relationships that enable them to make probabilistic predictions and generalizations (p. 33). A quantitative researcher aims to take an objective, unbiased approach (Creswell, 2012). Data collection is usually based on precise measurement using structured and validated instruments (Johnson & Christensen, 2012, p. 34). It involves collecting numeric or quantifiable data from a large number of people using instruments such as survey questionnaires, standardised tests, observational checklists and inventories (Creswell, 2012). Drew, Clifford, Hardman and Hosp (2008) stated that gathering and analyzing information in the form of numbers distinguishes quantitative research methods from 107

121 Chapter 3: Methodology other types. Investigators using this approach tend to count some aspect of performance or behavior exhibited by those participating in their study (p. 138). Drew et al. offered examples such as the investigator counting the number of correct responses by students to reflect what they have learnt, or counting the number of classroom disruptions to determine how well teachers organise and manage their classes. Applying quantitative approaches to my study The goal of identifying and understanding the strategies nurses use to calculate and measure medicine doses was not consistent with experimental or quasiexperimental design. Allocating participants to experimental and treatment groups, as would occur in experimental or quasi-experimental designs, requires control or manipulation of variables by the investigator (Leedy & Ormrod, 2010). Such techniques were considered unsuitable for the current study where it was sought to collect data in natural contexts. Nor was there a focus on an environmental factor that had occurred prior to the study that might suggest an ex post facto design (Leedy & Ormrod, 2010). Rather, the objective was to describe and explain real-world practice relating to nurses administration of medicines in the settings in which they occur naturally. Quantitative methods such as experimental or quasi-experimental design were considered inappropriate for Research Question 3. Such methods are in no way suited to identifying the strategies nursing students are taught for calculating and measuring medicine doses. Quantitative approaches considered appropriate for the current study were those that might assist in identifying patterns relating to: how Australian nurses calculate and measure medicine doses (Research Question 1); the factors that influence when and why nurses use particular calculation and measurement strategies (Research Question 2); and the dose calculation and measurement strategies Australian nurse educators teach nursing students (Research Question 3). Instruments such as questionnaires, interviews and observations instruments also used in qualitative research (Creswell, 2012) appear to be appropriate data collection methods in the current study. Data collected using these methods might 108

122 Chapter 3: Methodology take a variety of forms, including numerical data and data involving nominal or categorical variables. Anticipated use of quantitative approaches in the analysis of data might include calculating numerical measures such as frequencies and proportions to enumerate particular behaviours nurses were observed using and to enumerate participants responses to survey questions. It is possible that the use of such numerical measures might reveal patterns in the data or interrelationships between variables of interest. While quantitative approaches appear to have a role in the proposed study, the use of statistical procedures commonly associated with quantitative research, such as hypothesis testing, and determining the statistical significance of findings, is expected to be limited. This is because the amount of numerical data collected is expected to be limited Qualitative research Qualitative research is best suited to problems that need to be explored to obtain a deep understanding of a phenomenon (Creswell, 2008). It has its roots in anthropology (Johnson & Christensen, 2012) with the use of thick descriptions that render a clear and accurate picture of the nature of each culture (Drew et al., 2008, p. 185). Johnson and Christensen (2012) stated that qualitative researchers are usually not interested in generalising beyond the particular people who are studied. They follow exploratory scientific method (p. 17) which they described as a bottom up process because the movement is from data to patterns to theory (p. 17). For example, the researcher makes observations, studies them searching for patterns, then makes tentative conclusions, or a generalization about the pattern or how some aspect of the world operates (p. 17). The investigator s intent is to provide a complex and full explanation and to understand multiple perspectives. Johnson and Christensen (2012) suggested that qualitative research uses a wide- and deep-angle lens, examining human choice and behavior as it occurs naturally in all of its detail. Qualitative researchers do not want to intervene in the natural flow of behavior (p. 35). They study behavior naturalistically and holistically and try to understand multiple dimensions and layers of reality (p. 35). 109

123 Chapter 3: Methodology Qualitative data collection methods often involve interviews, observations, questionnaires, examining existing records, videotapes and audiotapes (Drew et al., 2008; Gay et al., 2012). Qualitative approaches do not usually result in data in the form of numbers, but tend to involve nominal or categorical variables that provide information about qualitative differences (Gay et al., 2012; Johnson & Christensen, 2012). Several qualitative research methodologies, such as grounded theory, ethnography, phenomenology and narrative research, possess characteristics suited to the goals of the current study. These qualitative methodologies are now described, before discussing their suitability for the study. Grounded theory Grounded theory is a qualitative research design in which the inquirer generates a general explanation (a theory) of a process, an action, or an interaction shaped by the views of a large number of participants (Creswell 2013, p. 83). Creswell noted that grounded theory was developed in sociology in the 1960s in response to the inadequacies of a priori theoretical orientations prevailing in research methodologies at the time. More recent developments and interpretations concerning grounded theory led to its current popularity in practitioner fields such as education, nursing, business, and social work, as well as among psychologists, architects, communications specialists, and social anthropologists (Creswell, 2013; Strauss & Corbin, 1998). According to Strauss and Corbin (1998), rather than beginning with a preconceived theory or basing a theory on a series of concepts of how one thinks things should work, the researcher begins with an area of study and allows the theory to emerge from the data (p. 12). Because emergence is the foundation of a grounded theorist s approach to theory building, concepts and design must be allowed to emerge from the data (Strauss & Corbin, 1998, p. 34). The researcher uses varying methods to arrive at a theory using the most parsimonious and advantageous means. Edmonds and Kennedy (2013) suggested one reason to use grounded theory is when there is little or no prior information on an area or phenomenon (p. 116). Characteristics of grounded theory (Charmaz, 2014; Edmonds & Kennedy, 2013) include: collecting and analysing data simultaneously; 110

124 Chapter 3: Methodology a focus on analysing actions and processes; coding data an analytical tool for handling masses of raw data, and the pivotal link between collecting data and developing an emergent theory to explain the data; using theoretical sampling (obtaining further selective data to refine and fill out major categories) and saturation (when no new properties of the theoretical category emerge); using comparative methods (emerging theory is constantly being compared to the evidence brought forth from new data); drawing on data to develop new conceptual categories; emphasis on theory construction rather than description or application of current theories; the researcher uses memoing (writing down thoughts, ideas, interpretations and directions for further data collection) as part of theory development ; and searching for variation in the studied categories of process. According to Charmaz (2014), researchers use grounded theory with a variety of data collection methods, the primary tool being intensive interviewing. Strauss and Corbin (1998) suggested that once relevant concepts and hypotheses have emerged from the data, the researcher might turn to quantitative measures and analysis if this will enhance the research process (p. 34) Charmaz (2014) distinguished between objectivist grounded theory and constructivist grounded theory. The former approach, she says, is consistent with positivism. Data are assumed to represent objective facts in a knowable world.... The data exist in the world and the researcher finds them and discovers a theory from them (p. 237). Charmaz noted that this view assumes an external reality and an unbiased observer who records facts about it (p. 237). The constructivist approach sees both data and analysis as created from shared experiences and relationships with participants and other sources of data (Charmaz, 2014, p. 239). Important aspects of the constructivist design are cognisance of the assumptions that the researcher brings to the investigation and awareness that socially constructed meanings occur during data collection. Rather than viewing the researcher as a neutral observer and value-free expert, the researcher and participant 111

125 Chapter 3: Methodology co-construct knowledge (Charmaz, 2014; Edmonds & Kennedy, 2013). The resultant knowledge emerging from the data is not only discovered but also created (Edmonds & Kennedy, 2013, p. 116). Ethnography Leedy and Ormrod (2010) described ethnography as a research tool in which the researcher looks in-depth at an entire group that shares a common culture. Ethnography is a research tool for presenting the perspectives of different group members, allowing the researcher to convey a sense of what it is like to live and work within the group (Leedy & Ormrod, 2010). The object is to study the group in its natural setting for a lengthy period of time, often over several months or several years. Leedy and Ormrod (2010) indicated ethnography was initially used in cultural anthropology and more recently in sociology, psychology, and education. These authors describe the focus of ethnography as being on everyday behaviours of people, for example, interactions, language or rituals, with the intent of identifying cultural norms, beliefs, social structures and other cultural patterns. The methodology enables considerable flexibility in the choice of methods to obtain information about the group. Phenomenology Phenomenology is a qualitative approach in which the researcher attempts to understand people s perceptions, perspectives, and understanding of a particular situation, and describe what it is like to experience that situation (Leedy & Ormrod, 2010). Leedy and Ormrod noted that when phenomenology is used the final result is a general description of the phenomenon seen through the eyes of people who have experienced it first-hand. The researcher s role is to construct a composite picture of the phenomenon as people typically experience it. Narrative research Narrative research is a developing form of qualitative research involving gathering information, in the form of storytelling of the participant, for the purpose of understanding a phenomenon (Edmonds & Kennedy, 2013, p. 129). Edmonds and Kennedy described the narrative approach as most widely used in the disciplines of psychology and psychiatry and is the study of the multitude of ways humans experience the world (p. 129). It is also used in other areas of the social sciences, and is increasingly being applied in the field of education (Creswell, 2012). 112

126 Chapter 3: Methodology Narrative design can be either biographical (the researcher writes and records the experiences of another person s life) or autobiographical (the subject of the study writes the account; Creswell, 2012; Edmonds & Kennedy, 2013). Edmonds and Kennedy described three designs in the narrative approach: descriptive design, explanatory design, and critical design: The descriptive design is used to explore the status of some phenomenon and may involve individual or group narratives of life stories or specific events, or the way certain events impact the participant; the explanatory design is used to explore the causes and reasons of phenomena ; and the critical design uses a critical framework that allows the critiquing of some existing system while maintaining a level of scientific inquiry (2013, p. 130). Qualitative approaches appear appropriate for answering two of the three research questions: RQ1 and RQ2. These questions call for an understanding of the calculation and measurement strategies used by nurses and the factors that influence nurses in their selection of those strategies. These two questions focus on phenomena that occur in natural settings. A qualitative approach would enable me to study the many dimensions and layers of those phenomena in all their complexity and to portray their multifaceted nature (Leedy & Ormrod, 2010). Influences on nurses medicine administration behaviours might include factors in their personal backgrounds such as the calculation methods they learnt as students or the length of their nursing experience. Influences on their behaviours might also include factors and events present in the immediate clinical environment. Such factors might include communications with other nurses and reference to the tools of workplace practice (Hoyles et al., 2001, p. 5), such as patient charts, medicine labels, other reference materials and equipment for measuring doses such as syringes and medicine measures. Environmental factors such as noise, distractions and interruptions may also impact on nurses medicine administration behaviours. Using observation and interview techniques focusing largely on open-ended questions appear appropriate for collecting data aimed at gaining an understanding of the dose calculation and measurement processes nurses use and the circumstances in which they use them. With respect to RQ1 and RQ2, I want to reveal the mathematics associated with medicine administration from two different perspectives: my own perspective and the perspectives of the nurses studied. These perspectives represented just two of the possible perspectives that could have been explored. 113

127 Chapter 3: Methodology With respect to RQ3, survey techniques appeared to be the best data collection method for obtaining information about how members of academic staff in universities teach students to calculate and measure medicine doses. Applying qualitative approaches to my study When I considered the suitability of particular qualitative approaches for my study, no single methodological approach appeared capable of achieving the goals of the study. However, grounded theory, ethnography, phenomenology, and narrative research all offered elements of value in addressing the study aims. Grounded theory appears suited to the study in the sense that the data collected might generate a theory or explanation concerning the determinants of the strategies nurses use for calculating and measuring medicine doses. It was certainly anticipated that if a theory emerged from the study it would be shaped by the views of a large number of participants (Creswell, 2013) through my use of data collection techniques such as interview and observation (Edmonds & Kennedy, 2013). It was also anticipated that any theory emerging from the study would be grounded in data from the field in the manner of grounded theory research. The notion of data saturation is also relevant to the present study. Data saturation could be applied in the sense that data collection continues until a point is reached and passed where no new or different dose calculation or measurement strategies emerge during observation of nurses in clinical practice. Two variants of grounded theory research were of particular interest: the constructivist design and the emerging design. The constructivist design highlights co-construction of knowledge between the researcher and participants. This design confirms that the assumptions I bring to the investigation can contribute to the process of social construction of meanings from the data I collect as it is analysed and interpreted. Use of a grounded theory design for an inquiry where there is little or no prior information concerning the phenomena of interest (Edmonds & Kennedy, 2013) also rang true in respect of the planned inquiry. Indeed, I have found very little empirical evidence concerning the real-life dose calculation and measurement strategies nurses use in clinical practice. Ethnography appeared to offer characteristics that were appropriate for documenting the medicine administration behaviours of registered nurses. Nurses 114

128 Chapter 3: Methodology might, for example, be considered a cultural group sharing the same basic training, a common language of practice, and other common cultural patterns and rituals. In terms of my study, the greatest disadvantage of an ethnographic approach is that it would require the researcher to become embedded in the culture for long periods. Such a requirement is beyond the scope of a PhD study, especially given that one of the goals was to ensure sample sizes in the study were sufficient for findings to be considered generalisable to the populations of interest, or at least transferable to other similar groups. Elements of phenomenology were viewed as appropriate for incorporation into the design, particularly the goal of describing the medicine administration behaviours of registered nurses from their own perspectives. However, the methodology was considered too limiting in that it would have provided only the nurses perspectives and not the perspective of the researcher. Further, like ethnography, phenomenology was considered unsuitable as a sole methodology. Relying solely on nurses descriptions was considered too limiting and unlikely to capture fully the complexity and multifaceted nature of the calculation methods that nurses use. The research hoped to gain insights into the lived experiences of nurses as they engage in medication mathematics and to explore the factors that influence their choice of calculation and measurement strategy in particular circumstances. However, time constraints associated with collecting data in a ward environment rendered phenomenology inappropriate as a single methodology for the study. Time spent interviewing participants would need to be kept to a reasonable and acceptable level from the point of view of nurses and their supervisors. An aspect of narrative research considered appropriate for the study was the notion of storytelling, with nurses being asked to explain the strategies they chose to use to calculate and measure medicine doses, and why they chose to use them Mixed-methods research Mixed-methods research is a relatively new approach aimed at bringing together the strengths of quantitative approaches (large sample size, identification of trends, generalisation) and those of qualitative approaches (small sample, details in-depth) and minimising the effects of the non-overlapping weaknesses of each approach (Creswell & Plano Clark, 2011). 115

129 Chapter 3: Methodology An argument for using mixed methods is that the researcher is able to form a complex picture of the social phenomenon of interest and achieve a better understanding of the issues under investigation than would be possible using either method by itself (Creswell, 2008, 2012). Creswell (2012) offered the following rationale for employing mixed methods designs: Quantitative data, such as scores on instruments, yield specific numbers that can be statistically analysed, can produce results to assess the frequency and magnitude of trends and can provide useful information if you need to describe trends about a large number of people. However, qualitative data, such as open-ended interviews that provide actual words of people in the study, offer many different perspectives on the study topic and provide a complex picture of the situation (p. 535). Creswell and Plano Clark (2011) claimed both forms of data are necessary today because they provide the most complete analysis of problems, with multiple forms of evidence that flow from both forms of data enabling the researcher to situate numbers in the contexts and words of participants, and they frame the words of participants with numbers, trends, and statistical results (p. 21). Using both forms of data generates the multiple forms of evidence demanded by policy makers, practitioners, and people in applied areas. Mason (2006) took the view that mixing methods helps us to think creatively, outside the box (p. 10), and to match social science research methods to the complexity of multi-dimensional experience: Social experience and lived realities are multi-dimensional. Our understandings are impoverished and may be inadequate if we view these phenomena only along a single dimension (p. 10). The lived experience transcends or traverses traditional theoretical divides and, therefore, so should our methods. We need to think creatively and multi-dimensionally about methods, and about our research questions themselves (p. 12). Simple measures will not capture the heart and soul the essence or the multi-dimensional reality of what is taking place (p. 12). Bryman (2006) encouraged researchers to be explicit about the grounds on which multi-strategy research is conducted but to recognize that the outcomes may not be predictable (p. 111). Indeed, if quantitative and qualitative approaches are conducted in tandem, the potential and perhaps the likelihood of unanticipated outcomes is multiplied (p. 111). 116

130 Chapter 3: Methodology Creswell (2012) cautioned that a mixed methods design is very challenging to carry out, is time-consuming, requires skills in both quantitative and qualitative research, involves extensive data collection and analysis, and is best suited to a team of researchers. Mixed-methods designs, such as the typologies outlined by Creswell and Plano Clark (2011) are also demanding because of the planning necessary to determine and execute issues of merging, integrating, linking or embedding the two data strands. Applying a multi-strategy approach to the current study The value of including both quantitative and qualitative elements in the research design has been discussed. A pragmatic, multi-strategy approach combining both approaches appears to be the best design for addressing the aims of the study. Such an approach would draw on the advantages of each approach while minimising the disadvantages inherent in each. The quantitative and qualitative components have the potential to provide different types of information about the same issues. Application of quantitative approaches will assist in discovering patterns in the strategies nurses use to calculate and measure medicine doses. Qualitative approaches will assist in obtaining multiple perspectives, and providing a full understanding of the multidimensional nature of the mathematical processes nurses engage in when they administer medicines. Table 3.2 lists some of the features of multi-strategy or mixed methods research that I viewed as being particularly valuable in achieving the goals of the study. The content of Table 3.2 is adapted from Bryman (2006, p ). 117

131 Chapter 3: Methodology Table 3.2 Features of a multi-strategy approach considered valuable in designing my study Design feature Triangulation Completeness Explanation Credibility Illustration Utility Diversity of views Enhancement Explanation Seeks convergence and corroboration of results from quantitative and qualitative approaches Brings together a more comprehensive account of the area of inquiry by combining quantitative and qualitative approaches One method is used to help explain findings generated by the other Employing both methods can enhance the integrity of the findings Use of qualitative data to illustrate quantitative findings: putting meat on the bones of dry quantitative findings. Combining approaches will result in findings that are more useful to practitioners and others, especially when there is an applied focus Combining researcher s and participants perspectives through quantitative and qualitative research respectively; uncovering relationships between variables through quantitative approaches while also revealing meanings among research participants through qualitative approaches Making more of, or augmenting, quantitative findings by gathering data using a qualitative approach, or vice versa Research design for this study The three research questions suggest that the research be conducted by comparing the results of two separate phases: a Hospital Phase aimed at addressing RQ1 and RQ2, and a University Phase aimed at addressing RQ3. These phases will be discussed in detail in Chapter

132 4 The Research Process Because students have learned to believe that there is one correct method to solving a problem [the teacher-taught algorithm], they often respond to problems inflexibly. Because they have learned to believe that mathematics is foreign to their thinking, they abandon common sense and overlook their own practical knowledge. Baroody and Ginsburg (1990, p. 62) Chapter 4 describes the research process I followed to address the three research questions presented in This chapter commences with an overview of the two separate non-sequential phases of the study. Each phase of the study is then described separately. 4.1 Overview of the study The Hospital Phase addressed Research Question 1 and Research Question 2. Its purpose was to determine the strategies Australian nurses use in clinical practice to calculate and measure medicine doses and the factors that influence their choices. The University Phase addressed Research Question 3. Its purpose was to determine the strategies student nurses are taught to calculate and measure medicine doses in pre-registration nursing programs in Australia. The Hospital Phase was conducted using a qualitatively driven multi-strategy research design involving naturalistic observation supplemented by one-on-one interviews, a questionnaire and focus groups. The research was conducted in three hospitals located in two different states of Australia. The participants were nurses recruited from a broad range of wards. I shadowed the nurses, observing them as they prepared and administered medicines as part of their normal ward routine. At opportune times during observation sessions I sought explanations from the nurses about the dose calculation and measurement strategies they had used. A small number of nurses took part in focus groups at each site. During these, I was able to probe further into nurses dose calculation and measurement strategies and seek clarification concerning other aspects of my observations. 119

133 Chapter 4: The Research Process For the University Phase, an online questionnaire was used to gather information about curriculum content and teaching practices surrounding the calculation and measurement of medicine doses. Each of the 35 universities in Australia known to offer pre-registration nursing education was invited to participate in the study. Two cohorts of academic staff coordinators and teachers of units of study involving calculation and measurement of medicine doses were invited to participate in the questionnaire. The final analysis in the study was to compare the findings from the two phases of the study to determine how closely the calculation and measurement strategies nurses used in clinical practice matched the calculation and measurement strategies students were taught in nursing education programs. 4.2 Hospital Phase The purpose of the Hospital Phase was to address Research Question 1 and Research Question 2. I sought to identify the strategies nurses use in clinical practice to calculate and measure medicine doses and to determine the factors that influence these choices The settings for data collection Hospitals are among a range of healthcare settings that could have been used for data collection. Other healthcare facilities in which nurses administer medicines include residential aged care facilities, day-surgery clinics, and community health facilities. Hospitals were selected because they employ large numbers of nurses on a single, compact site, making them suitable sites for recruiting a sufficiently large and varied sample of nurses to address Research Questions 1 and 2. In selecting the hospital sites, the goal was to achieve a sample of nurses that was representative of registered nurses in hospitals across Australia employed in roles that require them to administer medicines. Three hospitals in two different Australian states were selected: a large metropolitan hospital, Alexander Metropolitan Hospital 15 ; a regional hospital, Murraydale Regional Hospital; and 15 All names of hospitals and nurses are pseudonyms. 120

134 Chapter 4: The Research Process a rural hospital, Gemmaville Rural Hospital. The hospitals were all public hospitals; two were state-operated and one was privately operated. They were selected because, together, they were expected to provide a representative sample of hospitals that crossed state/territory borders and provided a range of care settings and treatments for patients. Such diversity was expected to yield rich variety in the medicines the nurses administered and the type of calculations they would need to perform to administer them. The particular characteristics and locations of the selected hospitals also meant that, together they had the potential to yield a sample of nurses with diverse backgrounds (e.g. city and country), ethnic origins, backgrounds, length and types of professional experience. An important factor in selecting three hospitals that fitted the desired criteria city, regional and rural was the ease of access I had to each. The particular hospitals selected were sufficiently close to my own home, or the home of family members with whom I could stay. This made possible the repeated visits over many weeks to each hospital that was required for data collection. Ease of access was also important in reducing travel and accommodation difficulties and costs associated with the project. Description of hospitals Alexander Metropolitan Hospital is a tertiary referral hospital to which patients may be referred from other referral centres. Located in a metropolitan area, it has in excess of 500 beds and is a multi-specialty facility. Murraydale Regional Hospital is a secondary referral hospital. It is a major regional hospital with several hundred beds and services a region that includes many surrounding satellite communities. Patients needing specialist treatment in areas such as paediatrics and neurosurgery may be transferred to the nearest capital city several hundred kilometres away. Gemmaville Rural Hospital has in excess of 130 beds and serves the local rural community and a small number of immediately surrounding areas. Many categories of patient, such as major trauma and neurosurgery patients, are transferred to a capital city, the closest being 400 km away. Gaining consent to undertake the research Having selected the hospital sites, I contacted the Director of Nursing (DON) at each hospital to gain in principle approval to conduct the research at the site. 121

135 Chapter 4: The Research Process The next step was to make formal application to the relevant ethics committee/s. The ethics issues relevant to the research included effects on nurse participants, the colleagues who checked their medicine administrations, and their patients. The issues identified, and the provisions I negotiated with the ethics committees to accommodate them, are described later in Recruitment strategy Following the initial face-to-face meeting with the DON, a meeting was held with senior nursing staff at each hospital as a prelude to recruiting nurse participants. I met with staff such as Nurse Unit Managers (NUMs), Nurse Educators, and Clinical Nurse Educators to outline the project and its aims and explain what participation would require of nurses and their managers. These meetings were faceto-face, except for the meeting held with Murraydale Regional Hospital staff, where the DON arranged a teleconference with NUMs prior to my arrival on site. The senior staff members attending these meetings were a valuable source of information that helped me determine the wards and nurses to target to begin the recruitment process. The orientation session and hospital tour that I requested at each site helped me find my way around the hospital. The NUMs and other senior staff I met during the tours were vital in facilitating access to specific ward areas for recruitment of nurses. The wards and nurses targeted In the National Ethics Application Form I anticipated a total number of forty nurses might be recruited at the three hospital sites. Recruitment of participants at each hospital commenced with information and recruitment sessions attended by small groups of nurses and senior nursing staff. The sessions were arranged in consultation with senior staff, or, in the case of Murraydale Regional Hospital, by the DON. Purposeful sampling, in particular the maximum variation (heterogeneity) sampling version of it (Patton, 2000, pp ), guided the recruitment process. The goal was to recruit nurses working in as many wards or units of the hospitals as possible, selecting wards that would provide maximum diversity in terms of nurses, clinical contexts, and the medicines administered. The logic of using this sampling strategy was that any common patterns that emerge from great variation are of 122

136 Chapter 4: The Research Process particular interest and value in capturing the core experiences and central, shared dimensions of a setting or phenomenon (Patton, 2000, p. 235). The nature of the patients cared for in a particular ward, and the types of treatment they receive, are the primary determinants of the medicines prescribed for them. The wards targeted for recruitment of participants were identified in consultation with senior nursing staff as being those in which nurses were most likely to administer a high volume of medicines in the course of a single medicine round. Other criteria applied in selecting wards included achieving variety in the medicines administered, and a high proportion of medicines requiring nurses to calculate the dose to administer 16. Paediatric wards were of particular interest because of the high likelihood of patients requiring medicines. Paediatric doses are also likely to require calculation because frequently the dose is tailored to the small size and increased sensitivity of the child receiving it. Further, when dose calculations are performed, they are often based on the weight of the child. Doctors therefore frequently prescribe paediatric doses as a milligram per kilogram value, rather than a mass (mg) of the medicine to be administered. It is the nurse who then calculates the actual mass (mg) to be administered, based on the weight of the child (kg). One of the very few ward areas not actively targeted for recruitment was maternity because few medicines are prescribed for pregnant women and new mothers. Those that are prescribed (for example, for pain relief) are often administered at unpredictable times when I could not easily be present to observe the administration. Apart from targeting potentially high data yield ward areas, purposeful sampling was conducted with several other goals in mind. Within the three hospital sites and the wards selected, maximum variation sampling a specific application of purposeful sampling was applied to the recruitment of individual participants. The goal was to achieve a broad range of ages, cultural and nursing backgrounds, number of years of nursing experience, and a representative gender balance. While nurses were recruited primarily because of their willingness to participate, it was hoped to achieve a gender balance similar to that occurring in the nursing profession in 2011, 90% female and 10% male (Australian Bureau of 16 The dose to administer is the quantity of medicine required, using the stock form selected, to administer the medicine to the patient; further explanation of the term can be found in

137 Chapter 4: The Research Process Statistics, 2013). Another goal was to achieve a representative balance in the level of nursing experience of the volunteers. I hoped to recruit a representative mix of new graduates, nurses with just a few years of experience, and nurses who had many years of experience. Information and recruitment sessions Information and recruitment sessions were conducted on a ward by ward basis in each hospital and took different forms. Where possible and facilities were available I used a PowerPoint presentation so that all prospective participants received the same information, and information was not likely to be inadvertently omitted. Some of the addresses to large groups of nurses and supervisors were scheduled as research presentations. These sessions formed part of the unit s formal staff development program, attendance was recorded, and nurses were awarded points for attending. Some nurses volunteered at the conclusion of the session, while others were recruited later. For nurses who had not yet committed or who had missed the session, reminders in the form of A4 posters were posted in strategic places frequented by nurses usually the tea room. The posters provided a summary of information about the research project and invited participation (see Appendix 1 for a sample poster). I gave each nurse who volunteered a Plain Language Statement (PLS) which included a consent form and a withdrawal of consent form. This occurred either at the conclusion of the information session or when I visited them in their ward shortly after. At the same time, I scheduled the first one or two observation sessions in consultation with the nurse. Progressive recruitment At each site, recruitment of participants continued after data collection commenced. An ongoing recruitment process proved necessary to accommodate the shift-based systems used to staff hospital wards and the resultant difficulties these systems posed for me in terms of being able to reach potential participants. The progressive sampling that occurred took the form of opportunistic sampling typical of the sometimes emergent nature of qualitative research (Creswell, 2012). I used the time between scheduled observation sessions to progressively seek out senior staff in wards not yet visited so that I could continue the recruitment process. I also returned to wards previously visited to seek out nurses who had 124

138 Chapter 4: The Research Process missed earlier information sessions and who were now available. So some information and recruitment sessions were simply a strategically timed informal chat in a tea room with a small group of nurses. These were nurses to whom I had been directed by a supervisor because they were on a break and were therefore available for me to approach Data collection methods The primary data collection method for the Hospital Phase was naturalistic observation of nurse participants as they went about their routine duties of preparing and administering medicines to patients. Data recorded during observation sessions were supplemented by data collected through a questionnaire and focus groups. Data collection instruments The data collection instruments were: an observation schedule I created for recording details of the medicine administrations I observed during observation sessions (an example of a completed observation schedule is included in Appendix 2); the questions I asked participants concerning the methods they used to calculate and measure medicine doses during observation sessions; a questionnaire completed by participants at the conclusion of observation sessions (see sample page in Appendix 3); and the semi-structured interview schedule I used during focus groups (see sample in Appendix 4). I now describe in more detail the data collection methods, the instruments employed, and how I used them. Naturalistic observation of participants I shadowed participants as unobtrusively as possible while they undertook their routine activities on the ward. During the medicine round my goal was to document and understand the mathematical aspects of each medicine administration I observed, and the context in which it occurred. During observation sessions, nurses first introduced me to their patients in accordance with a written format I handed to each nurse. I used an observation 125

139 Chapter 4: The Research Process schedule to record data relating to: (a) the medicine administrations I observed; and (b) the nurse s explanation of the calculation and measurement strategies they used. Handwritten records were supplemented by occasional use of the digital audio recorder which I carried relatively unobtrusively on a lanyard around my neck. I activated it, as required yet sparingly, to capture the most significant of nurses explanations of their calculation and measurement techniques. Occasionally, with the knowledge of both nurses, I activated the device to record a significant communication between the nurse participant and the colleague who was checking the medicine administration. The observation schedule The observation schedule was a multi-page, printed, A4 proforma. The compact design of each page was intended to assist me in rapid note-taking and organisation of data relating to nurses calculation, measurement, and administration of medicine doses, and any environmental factors that may have impacted on those processes. These factors included resources the nurse accessed, distractions, interruptions, etc. At the start of the session, I used a small coversheet on the first page to record administrative details, such as hospital, participant, ward, date, observation session number, starting and finishing times. The code A written on the coversheet signified that an audio file existed for the session. The remainder of the page, reverse side, and subsequent pages were used to record information about every medicine I observed the nurse administering during the session. There was a dedicated space on the page to record each piece of information, including: administration event number; patient number (circled); prescribed dose (generic name of medicine and dose ordered) ; administration route; formulation of stock used; whether a calculation was performed to determine the dose to administer; whether a calculator was used for that calculation; the nurse s explanation of the calculation method used, if obtained; and 126

140 Chapter 4: The Research Process the measuring instrument/s used to measure the dose. Three small spaces at the bottom of each page were intended for use with any of the medicine administrations recorded on that page. The spaces enabled me to record notes relating to particular aspects of an administration event: the nurse s calculation process; measurement process; and clinical or environmental factors of note. I trialed the observation schedule during the first two observation sessions I held and made minor refinements to the layout of the schedule to improve its functionality. One-on-one interviews With few exceptions, one-on-one interviews were conducted with the participant during, or immediately following, the observation session. The purpose of the unstructured interview was to clarify what I had observed and to record the nurse s explanation of the calculation and measurement processes they had used. In most cases interviews with a participant took the form of a series of short, intermittent and informal discussions with the nurse during the course of the observation session where it was likely to yield immediate and relevant data, rather than a sustained single interview. The duration of interviews and the topics of discussion were to some extent determined by where the nurse was located when preparing the medicine in the treatment room or at the patient s bedside. Many of the interviews took place in the privacy of the treatment where the nurse was preparing the medicine before administering it at the bedside. At all times the over-riding consideration that governed the timing and duration of discussion, and whether it was appropriate to record it on the audio recorder, was minimisation of the impact of my presence on the conduct of normal nursing functions and the nurse-patient relationship. I used the observation schedule to note important aspects of the discussion, sometimes supplementing the written record with an audio recording. Preliminary observation sessions The first observation session with each participant was a preliminary session that provided an opportunity for the nurse to become accustomed to my presence and use of data collection tools. Immediately prior to the first observation session, I received the completed consent form and briefed the nurse about what I would be hoping to achieve, and what they might expect to occur. 127

141 Chapter 4: The Research Process The preliminary session provided an opportunity for me to become familiar with the nurse s clinical environment and identify any issues that needed to be resolved before the formal data collection period commenced. The preliminary session also allowed time for a sense of trust to develop between me and the nurse. Scheduling of observation sessions Observation sessions were scheduled so that I could observe each nurse administering as many medicines as possible within the available timeframe. This gaol was achieved by scheduling observation sessions to coincide with medicine rounds, particularly key medicine rounds which were nominally 8 am and 8 pm. Key medicine rounds were those rounds identified as being likely to yield the greatest number of medicine administrations, number of calculations performed, and variety in the medicines administered. At each hospital, key medicine rounds were identified in consultation with senior nurses and/or participants. Collection of workplace artefacts In the course of observing participants I collected a small number of workplace artefacts, tools of trade, and reference items. The purpose of collecting these items was to expand my understanding of the mathematical processes involved in the medicine administrations I observed, and the clinical environments in which they took place. Examples of such items included: medicine packaging; syringes; nurses written explanations or examples of calculation processes; and other printed materials nurses consulted to guide their medicine administration. The latter materials included copies of relevant pages from pharmaceutical guides, and hospital protocols relating to the administration of particular medicines. Questionnaire During their last observation session I gave each participant a questionnaire to complete and return to me, either in person or in the reply-paid envelope provided. The questionnaire was structured in two parts. Appendix 3 provides an excerpt from Part 2 showing a sample medicine administration task. Part 1: Background information The first part of the questionnaire sought demographic data, including the number of years of nursing experience, and information about the nurse s 128

142 Chapter 4: The Research Process mathematics background. Nurses were asked to give their perspective about issues such as: their beliefs and feelings about calculating medicine doses; their level of confidence and how they rated their ability level with respect to calculating and measuring medicine doses; the extent of their use of calculators; their use of estimation and checking techniques; and their experiences relating to medication error and their advice to beginning nurses for reducing the risk of medication error. Part 2: Sample medicine administration tasks The second part of the questionnaire comprised eight sample medicine administration tasks posed as word problems. Most of the problems were similar to the questions posed in tests for student nurses and the annual competency tests many hospitals require nurses to sit. The purpose of the written medicine administration tasks was to determine whether nurses used the same calculation methods for penand-paper test problems as they used in the real-life problem-solving context of the ward. The items also sought to assess the accuracy of nurses dose measurement processes. Each scenario described a clinical situation, the dose of medicine prescribed, and the available stock. Participants were asked to calculate the dose to administer showing their working in full. For solid medicines participants were asked to illustrate the dose they would administer by shading the appropriate number of tablets. For liquid medicines they were asked to select an appropriate syringe from several illustrated and shade it appropriately to indicate the volume they would administer. I was concerned that the questionnaire was quite long and, as a result, some participants might not complete it. To minimise this risk, two versions were created, identical in all respects except for the order of the eight sample administration tasks. I distributed equal numbers of each version. The purpose of reversing the order of questions was to ensure that all questions would be attempted by at least some participants, even if not all participants completed the questionnaire. 129

143 Chapter 4: The Research Process Validating and piloting the questionnaire The questionnaire underwent a rigorous process of review and refinement before nurses completed it. In the early stages of development members of academic staff at Deakin University and a hospital pharmacist reviewed it. The penultimate version was reviewed by an expert panel comprising seven senior staff members from four different universities and similar professional organisations and including several nurses. The final version of the questionnaire was trialed by several nurses from the target cohort nurses working in clinical practice in Australian hospitals. The last group gave their feedback by completing a proforma feedback package I provided. The feedback I sought from the expert review panels focused on: general layout and readability; face validity (Does the questionnaire appear to measure what it sets out to measure in terms of the project goals?); content validity: (Does the content cover all issues that should be included? Are there questions or items that should be deleted? Are there questions or items that should be added?); length of questionnaire and the time it would take to complete; clarity of instructions; and clinical efficacy of the sample medication administration tasks. As a result of the feedback provided by the expert review panel I made a number of changes to improve the questionnaire, including changes to the medicine administration scenarios so they more accurately reflected real-world clinical scenarios. Focus groups Participants at each site were invited to attend a focus group conducted after completion of all observation sessions. The purpose of the focus groups was to further explore and clarify what I had observed during the observation sessions and to discuss any issues arising from my observations. 130

144 Chapter 4: The Research Process Data collection during focus groups I used a semi-structured interview schedule as a prompt to guide discussion during focus groups. The schedule varied slightly from site to site, reflecting what I had observed on site and the issues for which I sought further clarification or expansion from participants. Topics listed for discussion included: comparison between the calculation methods nurses used in their clinical practice and those they learnt as students; the extent to which nurses used the formula; nurses choice of calculation method for particular types of medicine administration, and the factors that determined the method they used; the extent of nurses use of calculators in medicine administration, and the checks they performed when using a calculator; issues surrounding the volume of fluid contained in ampoules; the likelihood of having to calculate an intravenous flow rate in drops per minute; and factors operating in the clinical environment that impact on the nurse s ability to administer the correct dose of medicine. An audio recorder was used to record proceedings; acceptance of its use was a condition of participation in the focus group. A backup tape recording was made of each focus group session. The recordings were supplemented by my occasional hand-written notes recording points of particular significance, and those made by an assistant. Focus groups were scheduled in consultation with participants and nurse managers. At least one was held at each site, attended by small numbers of participants who were available and willing to attend. At Alexander Metropolitan Hospital, the vast size of the hospital and the difficulties I experienced in gathering nurses together in one place at a pre-determined time meant that four focus groups were conducted, attended by two, three or four nurses Data management and analysis procedures I applied different data reduction, management, and analysis procedures to the different types of data collected during the observation sessions on observation 131

145 Chapter 4: The Research Process schedules and through recordings of one-on-one interviews in focus groups, and through the questionnaire. An Excel spreadsheet was the primary data management and reduction tool for data collected during the Hospital Phase of the study. It contained data collected during observation sessions and from participants questionnaires. The data recorded in the spreadsheet were numerical, textual, or a combination of both. An extract from the spreadsheet showing some of the entries for Gemmaville Rural Hospital is included as Appendix 5. Management and analysis of data collected during observation sessions Data were collected during observation sessions on observation schedules; some one-on-one interviews were recorded on the digital audio recorder. Data recorded on observation schedules were transcribed to Columns A to AL of the spreadsheet. Data transcribed from observation schedules included: administrative details of medicine administrations; details concerning the medicines administered; details concerning the calculations nurses performed; and details concerning the measuring instruments used, and other information concerning the medicines and the clinical environments in which they were administered. included: Administrative details, recorded in Columns A to O of the spreadsheet, the identification number for the medicine administration (Column A); observation session identification number (Column B); total administration events for the session (Column C); the name of the hospital (Column D); the name of the nurse participant (Column E); the name of the ward (Column F); the date (Column G); the starting time of the session (Column H); the finishing time of the session (Column I); 132

146 Chapter 4: The Research Process the duration of the session (Column J); a description of the session (e.g. P1: preliminary session 1; O1: observation session 1) (Column K); whether an audio file (Column L) or scanned image (Column M) exist for the medicine administration; the patient number for the medicine administration (Column N); and the total number of patients who received medicines during the session (Column O). Figure 4.1 provides a facsimile of this part of the spreadsheet. Figure 4.1. Administrative details of observed medicine administrations Details concerning the medicines administered, recorded in Columns P to AB of the spreadsheet, are illustrated in Figure

147 Chapter 4: The Research Process Figure 4.2. Details concerning the medicines administered Details included: the generic name 17 of the medicine administered (Column P); the administration route (Column Q); the prescribed dose (Columns R to T); the stock used (Columns U to Y); and the quantity of medicine the nurse gave to the patient (Column AB). The drop-down menu from which the generic name of the administered medicine was selected was developed progressively from the Australian Pharmaceutical Benefits Scheme A-Z medicine listing (Australian Government Department of Health). The list was expanded progressively as data were recorded until it contained all the generic names of medicines administered during observation sessions. I consulted MIMS (2008) (originally the Monthly Index of Medical 17 Generic names were recorded because prescribers use generic names to order medicines on patient charts 134

148 Chapter 4: The Research Process Specialties), MIMS Online, and several other similar pharmaceutical manuals to assist finding the correct generic name for brand-name medicines listed on the patient chart by the doctor (contrary to accepted practice). Nurses calculations associated with administering medicines A calculation was sometimes required for nurses to determine the dose to administer the quantity they should give the patient. Throughout the thesis I use the term calculation of the dose to administer, or more simply, a dose calculation, to mean a calculation performed to determine the quantity of medicine required, using the stock form selected, to administer the prescribed dose to the patient. This quantity is typically expressed as a number of tablets or capsules if the medicine is in solid form, or a number of millilitres if the medicine is in liquid form. Nurses calculated the dose to administer based on the dose prescribed and the formulation of the medicine stock used to administer the medicine. Figure 4.3 shows the progression from the prescribed dose to the dose to administer via the stock formulation. The first row shows the process and the second row gives an example. Figure 4.3. Progression from prescribed dose to dose to administer via stock formulation Other calculations were sometimes needed to correctly administer medicines, some performed prior to determining the dose to administer and some subsequently. Details concerning all calculation processes nurses engaged in when preparing and administering medicines were recorded in Columns AC to AG in the spreadsheet (see Figure 4.4). 135

149 Chapter 4: The Research Process Figure 4.4. Details concerning the calculations nurses performed Details included: whether or not the nurse performed a calculation to determine the dose to administer (Column AC); whether or not a calculator was used to calculate the dose to administer (Column AD); a description of the nurse s strategy for calculating the dose to administer (Column AE); any other calculations the nurse performed (Column AF); and the nurse s explanation of the calculations performed, if obtained (Column AG). Determining whether the nurse needed to calculate the dose to administer For each medicine administered during the observation sessions, a key goal was to determine whether the nurse needed to calculate the dose to administer, and if so, to identify the calculation strategy used. Identifying the strategies nurses used to calculate medicine doses was a two-step process. 136

150 Chapter 4: The Research Process Deciding whether the nurse needed to calculate the dose to administer was achieved by comparing two key quantities in the administration process the quantity of medicine prescribed and the first-mentioned quantity in the stock formulation of the stock (i.e. the stock mass) used to administer the medicine. If these two quantities were identical, it was deemed that no calculation had been performed, and the nurse had simply administered the stock volume or a single tablet or capsule, if the medicine was in solid form. Conversely, if these two quantities were not identical, it was deemed that a calculation had been performed. Nurses measurement of doses Data concerning the instruments and processes nurses used to measure medicine doses were recorded in Columns AH, AI, and AL (administration notes) (see Figure 4.5). Figure 4.5. Details concerning the measurement instrument/s used Column AH shows the measuring instrument used. If more than one instrument was used the primary measuring instrument was recorded in Column AH and the secondary instrument in Column AI. Information written in the small dedicated spaces at the bottom of the observation schedule relating to the clinical or environmental factors and the measurement process were recorded in Column AJ and Column AL respectively 137

151 Chapter 4: The Research Process (see Figure 4.6). Miscellaneous information relating to the medicine or the administration process was recorded in Column AK. Column AM was where I recorded my later reflections and comments as I performed the first analysis of the medicine administration during the transcription process. I recorded notes I made as I listened to audio recordings in Column AN. Figure 4.6. Additional information concerning the medicine administration Analysis of data collected during observation sessions There were several goals in analysing the data collected during the observation sessions. One goal was to paint an overall picture of the participants and settings in which naturalistic observation had been conducted. However, the primary goal was to identify and describe the different calculation and measurement strategies nurses used as they prepared and administered medicines. All calculations nurses performed as part of the process of administering medicines were identified and described, with a particular focus on calculation of the dose to administer. Descriptive statistics were used to summarise many aspects of what took place during the observation sessions, such as the nurses who participated, the wards visited, the time spent observing, and the medicine administrations observed. Comparisons between hospitals, wards and administration routes were made on the basis of the frequencies and proportions calculated. Notable differences between variables of interest were described on the basis of the numerical values calculated. 138

152 Chapter 4: The Research Process Descriptive statistics, such as frequencies and proportions, were used to report the results of classifying the strategies nurses used to calculate the dose to administer. Calculation of the dose to administer The proportion of medicine administrations requiring calculation of the dose to administer was calculated, and a comparison made between the proportions observed at the three hospitals. Being able to identify the calculation strategy a nurse used was contingent upon whether or not I had sought an explanation of the strategy. This, in turn, depended on factors such as: the circumstances prevailing in the ward at the time (e.g. how busy the ward was and the level of stress the nurse was subjected to at the time); whether an explanation had been sought previously from the nurse for a similar medicine administration; and the judgement I made at the time about the likely impact of the intrusion and interruption associated with obtaining the information, and whether seeking an explanation was warranted and appropriate. Where the nurse was not asked to explain the strategy used to calculate the dose to administer, I recorded not advised in Column AG (CalcsExplained), and unknown in Column AE (CalcMethod: DTA) Classifying and labelling nurses dose calculation strategies The first step in classifying nurses calculation strategies occurred during transcription of data from observation schedule to spreadsheet. For each medicine administration for which I had sought an explanation of the nurse s calculation strategy, I drew on all the data I had gathered during the observation session to classify that strategy. I consulted data transcribed from the observation schedule, transcriptions of audio recordings, and my own memory of the event to formulate a descriptor for the nurse s calculation strategy, recording it in Column AE. The process of classifying and labelling each known calculation strategy was repeated as I progressively transcribed the data from observation schedule to spreadsheet. A drop-down menu of descriptors for Column AE (CalcMethod: DTA) was progressively created and refined as the transcription process proceeded. Newly 139

153 Chapter 4: The Research Process created labels were added and existing labels revised until the final drop-down menu provided a suitable description for every calculation strategy described by a nurse. A later step in the analysis process was aimed at forming categories of related calculation strategies. I analysed the characteristics of each calculation strategy I had recorded in Column AE and grouped strategies together on the basis of shared characteristics. The final step in the classification process was to ascribe a label to each category so formed, thus setting that category apart from others. I created a drop-down menu for Column AF (OtherCalcsPerf) in the spreadsheet to classify and record all other calculations the nurses performed in order to administer the correct dose of medicine. These calculations including those calculated prior to, and following calculation of the dose to administer. The menu was progressively expanded and refined until it contained descriptors for all such other calculations, or combinations of calculations, I had observed. Investigating possible associations between variables Investigation of possible associations between variables of interest was undertaken by cross-tabulation matrices. For example, the question of whether the administration route was linked to the need for the nurse to calculate the dose to administer was explored by cross-tabulating calculation of dose performed with administration route and comparing the frequencies in the matrix. Many such cross-tabulations were performed using the Pivot Table and Chart, and filter functions of Excel to explore possible associations between variables. Chi-squared tests of goodness of fit or independence were used to test the significance of associations between variables. Investigation of error-prone mathematical calculations The analysis of the calculations nurses performed during the observation sessions included investigation of two particular types of calculation, known to be associated with medication errors, namely metric conversions and manipulation of decimal numbers. Instances of these mathematical operations occurring were identified and the frequency of each operation was recorded. Describing nurses measurement strategies Descriptive statistics were used to summarise the frequency of use of different instruments and devices the nurses used to measure and administer medicine doses. Possible associations between the measuring instrument used and other factors were 140

154 Chapter 4: The Research Process investigated using cross-tabulation matrices, facilitated by the use of the pivot table function of Excel. Factors investigated in relation to the measuring instrument used included the administration route and the ward in which the medicine was administered. Several measurement issues that became apparent as I observed nurses were further investigated, assisted by the use of Excel functions such as sorting and filtering. These issues related to (a) how nurses responded to the phenomenon of excess fluid in ampoules, and (b) the type and capacity of the syringe nurses selected to measure and administer liquid medicines. Analysis of interview data Data collected during the discussions I had with participants, or that occurred between nurse participants and checking nurses, formed part of the data I recorded on the observation schedules and later transcribed to the Excel spreadsheet. This data was sometimes supplemented by an audio recording of the discussion. Audio recordings Data collected on the audio recorder related almost exclusively to nurses dose calculation strategies. In instances where the topic of the discussion related to measurement of the dose, or some other topic associated with medicine administration, the transcription was appropriately coded and set aside so that data relating to another topic could be included in analyses concerning that topic. Data in the form of an audio recording For recorded discussions, the process of analysis was to: listen, in some cases many times, to the discussion; allocate a code of little interest, of minor interest, or of major interest to indicate its significance in terms of addressing the research questions; transcribe significant parts of the discussion; and note the existence of the recording on the Excel spreadsheet. I returned, sometimes several times, to recordings and transcriptions of discussions. I used information from recordings of these events to extend my understanding of nurses calculation and measurement processes and to fill gaps in my written record of the medicine administrations I observed. Being able to report a 141

155 Chapter 4: The Research Process direct quote from a nurse explaining her thinking and her calculation method was viewed as important to achieving the goal of giving voice to nurse participants. Analysis of questionnaire data Different processes were used to analyse the two sections of the questionnaire that nurse participants completed. Part 1: Background information Part 1 of the questionnaire sought demographic data which were recorded in the Excel spreadsheet. Part 2: Sample medicine administration tasks Eight sample medicine administration tasks in the questionnaire allowed me to compare the test and ward problem-solving practices of participants and to determine whether there were discernible differences between nurses error rates in the two different settings. Five of the items were analysed, selected because they most closely resembled the dose calculations the nurses performed during the observation sessions. The purpose of the analysis was to: identify the calculation strategies nurses used to calculate the dose to administer; identify and classify any calculation or measurement errors nurses made; investigate nurses use of calculators, including possible links between nurses use of calculators and specific calculation strategies; and identify any noteworthy patterns of behavior when nurses calculated and measured medicine administration tasks posed as word problems. Analysis of focus group data I listened to the recordings of focus group discussions numerous times. Applying thematic content analysis, I transcribed significant segments of discussion from the focus groups and coded these according to the topic of discussion. Segments of discussion were aggregated by topic and each topic area was reviewed in its entirety and reported. For each topic of interest, a summary document was prepared in which common themes and striking differences in the ideas and responses nurses expressed across locations and between individuals were identified. 142

156 Chapter 4: The Research Process Ethical issues relating to the Hospital Phase There were considerable ethical issues relating to the Hospital Phase, which were integral to many aspects of the research design, and fundamental to the smooth conduct of the investigation. The risks identified in the National Ethics Application Form (NEAF), and the provisions implemented to accommodate or minimise them, related not only to nurse participants, but also to their patients and the colleagues they called upon to perform mandatory checks of their medicine administrations. I gained approval from a number of ethics committees and bodies before I commenced the research at the selected hospitals. The process of gaining approval was relatively straight forward for one hospital and extremely long and difficult in respect of one other. Approvals gained included the following. Approval by Deakin University Human Research Ethics Committee; Approval by area health service Human Research Ethics Committee (a lead ethics committee whose approval extended to all hospitals in that state including Murraydale Regional Hospital and Alexander Metropolitan Hospital); Site specific approvals for Murraydale Regional Hospital and Alexander Metropolitan Hospital; and Approval by Gemmaville Rural Hospital Human Research and Ethics Committee. A protocol was prepared, outlining the background and rationale for the research, its purpose, the research questions to be addressed, and the research team. Acceptance of the protocol formed part of the approval process in respect of the over-arching state approval authority covering two of the three hospitals. The Protocol included a summary of the project. All nurse participants and checking nurses who participated in the Hospital Phase were required to give their written consent. Nurses were advised of the procedures that I would implement should a medication error occur. Obtaining consent from checking nurses for me to observe that part of the administration process by completing a Checking Nurse Consent Form was a provision put in place in acknowledgement that in certain circumstances nurses are required to call on a fellow nurse to conduct a mandatory check of a medicine 143

157 Chapter 4: The Research Process administration. In such circumstances, the checking nurse completed a Checking Nurse Consent Form, indicating their consent for me to observe that part of the administration process. Patient consent and privacy A key aspect of the protocol concerned potential risks to patients and the provisions in place to minimise such risks. The protocol outlined the provision negotiated with the relevant ethics committee to protect patient privacy and minimise the effect of my presence on the nurse-patient relationship. Most medicines were prepared away from the bedside in a treatment room and it was there that the nurse calculated and measured the quantity to be administered. For those medicines for which there was a perceived benefit in my being at the patient s bedside to observe the medicine being administered, the nurse was required to introduce me and obtain the patient s verbal consent to my being present. I gave each nurse participant a short, printed statement suggesting the wording they might use to introduce me and obtain the patient s consent. 4.3 University Phase The purpose of the University Phase was to identify the strategies nurse educators teach students in pre-registration nursing programs to calculate and measure medicine doses The settings for data collection Information concerning teaching practices surrounding medicine dose calculation and measurement could potentially have been obtained from sources such as School or Faculty curriculum documents and unit outlines. Such sources were considered likely to be less productive than approaching the members of academic staff who were directly involved in the teaching of such skills. Medicine dose calculation and measurement is rarely, if ever, taught as a discrete unit of study, or even as a discrete topic within a unit of study. Rather, such skills are typically embedded in many units of study, and are introduced across a variety of contexts as they become relevant. For example, dose calculations relating to medicines used to treat diabetes might be introduced in a unit relating to endocrinology; calculation of paediatric doses might be introduced in a unit on 144

158 Chapter 4: The Research Process paediatric nursing. Consequently, to seek the information from sources such as institutional documents was unlikely to be productive. The information sought was unlikely to be held by a single group of academic staff. In the spirit of purposeful sampling (Patton, 2002, p. 230) in which information-rich samples are identified, two groups of academic staff of universities were targeted for data collection. They were staff members involved in teaching and coordinating units of study involving calculation and measurement of medicine doses were considered the best source of the desired information. A second source of data was the reference books and other learning resources nominated by the university staff as resources students used to support their learning. The first task in conducting the University Phase was to select the universities from which to collect data. Purposeful sampling (Patton, 2002; Creswell, 2012) was used to select the universities for the study and the participants within them who were targeted for recruitment to complete the online questionnaire. The universities were selected with a view to them yielding a representative sample from the population of interest academic staff involved in teaching medicine dose calculation and measurement strategies to students in Australian pre-registration nursing programs. It was hoped that the universities selected and the nurses recruited from within them would be as varied as possible, in the spirit of maximum variation (heterogeneous) sampling (Patton, 2002, pp ), described earlier in Initially twenty-five Australian universities offering pre-registration nursing education programs were selected. These universities were selected because they represented all states and territories in Australia, and included universities located in cities and regional areas. The number of universities invited to participate was later extended to include all known universities in Australia offering pre-registration nursing programs. The decision to broaden the number invited to participate was made when it appeared that the acceptance rate from Heads of School may be low and the size of the sample of academic staff participating would fail to reach the desired number nominally between sixty and ninety participants. Ultimately a total of 38 s were sent, in two batches approximately five weeks apart, to different campuses of 35 Australian universities. The first approach to each university was an to the Head of School or Faculty or closest 145

159 Chapter 4: The Research Process equivalent person 18, as determined from information on the university s website. In the case of multi-campus universities, where it appeared that the School of Nursing operated independently on each campus, the Head of School at each campus was contacted Recruitment strategy for the questionnaire Participants targeted for the questionnaire were members of academic staff involved in teaching calculation and measurement of medicine doses to students in pre-registration nursing programs. The target sample for the questionnaire was thirty to forty participants recruited from between ten and fourteen university sites. As soon as the HOS consented to staff participating in the questionnaire, I sent the Invitation to participate as an attachment for distribution to the targeted staff. The invitation targeted two groups of staff for recruitment. They were members of academic staff who, in the previous twelve months had either (a) coordinated a unit of study involving calculation and measurement of medicine doses, or (b) taught a unit of study involving calculation and measurement of medicine doses 19, or both. Members of staff of academic and learning support units who supported student learning in this aspect of the nursing curriculum were also sought. Some Heads of School referred me to another person, and in some cases the HOS responded by asking me to make formal application to the relevant ethics committee within the School or university. The requirements for approval varied between universities and in each case I provided the information requested. Reminder s Heads of School were asked to respond to the initial contact within two weeks. If no response was received after three weeks, a reminder was sent to the HOS. If the HOS had agreed to distribute the Invitation to participate but no participants were forthcoming, I followed up by sending a second attachment for the HOS to distribute to staff to remind them of the invitation The Head of School or Faculty, or equivalent person, or their nominee will be referred to hereafter as the Head of School or HOS. It was expected that some members of staff who coordinated such a unit might also teach it. 146

160 Chapter 4: The Research Process Data collection methods The target population from whom information was sought was scattered across the Australian continent, so use of web-based technology appeared to be the most efficient way to collect data. The online questionnaire was created and administered using SurveyMonkey, which allowed access to two target groups through one questionnaire by using navigation tools. Members of academic staff targeted for the questionnaire received the Invitation to participate as an attachment distributed by the Head of School. They were invited to click on a link taking them to the online questionnaire (see sample pages in Appendix 6. Participants were asked to provide information about: the university, campus and unit of study they were reporting on; their employment status and role in the unit (coordinator, teacher or both); entry-level mathematics requirements for students studying the unit; the modes of delivery of instruction, who taught medicine dose calculations and how they were selected, and the resources used to support learning; who determined the dose calculation strategies taught to students; the calculation strategies staff taught students to calculate and measure medicine doses; the staff member s personally preferred dose calculation strategy; the strategies used to assess dose calculation and measurement skills; whether it was possible to fail the medicine dose calculation component of the unit, but still pass the unit; staff perceptions about the difficulties students experienced learning medicine dose calculations and the difficulties experienced by staff in teaching medicine dose calculations; and staff perceptions about their role in the teaching of medicine dose calculations and their personal professional development needs. Many questions were common to both groups, however, some were specific to unit coordinators and others were specific to teachers of units. For each of the two 147

161 Chapter 4: The Research Process groups of respondents, the skip-logic function of SurveyMonkey facilitated navigation along the intended pathway according to the respondent s role that of coordinator, or teacher, or both. Skip logic was also used to direct the respondent to the next relevant question, depending on their response to a question. Validating and piloting the online questionnaire An extensive process of validation and piloting was undertaken before the questionnaire went live for participants to complete. The process used to validate and pilot the questionnaire was similar to that followed in relation to the questionnaire completed by nurse participants in the Hospital Phase of the study (see 4.2.3). An expert panel was created comprising three senior members of academic staff from two universities two of them from the nursing discipline and one from the mathematics education discipline who reviewed the questionnaire at critical stages of its development. During the initial development phase two panel members reviewed the two paper-based questionnaires, providing comprehensive feedback on issues of content and face validity. As a result of their comments major changes were made to the design to improve aspects such as the sequencing of questions, clarity of instructions, and design elements relating to Likert scales. The sample medicine dose calculation problem used to obtain information about how nurse educators teach dose calculation and measurement skills to student nurses was identical to one of the dose calculation tasks used in Part 2 of the questionnaire for nurse participants. This meant that the sample problem had already been validated as part of the review process for that questionnaire. A highly qualified independent consultant with extensive experience in areas such as IT software, online survey and analysis, epidemiology, health statistics and public health surveys was consulted after amalgamating the two questionnaires into one in the final SurveyMonkey design. The consultant advised on techniques to maximise the participant response rate, and provided technical advice to optimise navigation using the skip logic function of SurveyMonkey. She also advised on conducting trials to confirm all aspects of the technology were functioning as expected. These trials included a trial release to a pilot panel of respondents, setting up a test collector, and testing the data export and reporting options. Prior to the last step in piloting the questionnaire, a final expert review was conducted by one of the university panel members. The reviewer accessed the 148

162 Chapter 4: The Research Process questionnaire online and tested the functionality of all aspects including the links from the Invitation to participate to the questionnaire in the SurveyMonkey website, and from the questionnaire to the PLS. She also tested the functionality of the skip logic aspect of the questionnaire, designed to direct respondents to appropriate questions, in some situations based on their role coordinator, teacher, or both and in others, based on how they had answered the previous question. The reviewer commented on the suitability of the PLS, the clarity of the questions, and the time it took to complete the questionnaire (25 minutes taking my time ). The reviewer also provided feedback on the attractiveness of presentation, confirmed that the questionnaire flowed smoothly and that headings were helpful in flagging the start of new topic areas. Some minor refinements were made to the wording of the questionnaire following her review in which she commented that the questionnaire was designed in a way that would motivate the target group to participate. She concluded that: This is an easy questionnaire and I think it is one that participants should be easily able to complete. The final stage in piloting the questionnaire was to set up a test collector in SurveyMonkey and to send the Invitation to participate attachment to a questionnaire pilot team. Nine volunteers took the roles of coordinator, teacher, or both coordinator and teacher, and tested all aspects of the questionnaire in a live trial before it was released. Team members submitted up to three completed questionnaires each and recorded the time it took them to complete them (between 15 and 20 minutes). The live trial also allowed me to confirm that responses generated in the trial were accessible, a set of results had been created in the SurveyMonkey test collector site, and that a report had been generated and was able to be exported in the desired format Data management and analysis procedures The SurveyMonkey report was exported into an Excel spreadsheet. Many of the same data reduction, management, and analysis procedures used in relation to Hospital Phase data were used for the questionnaire. The frequencies and proportions of variables of interest were calculated. These variables included the dose calculation strategies taught, the modes used to deliver instruction, the staff involved in delivering instruction, the types of resources used to 149

163 Chapter 4: The Research Process support student learning, and the modes used to assess dose calculation and measurement competence. Investigation of possible associations between variables of interest was undertaken by cross-tabulation matrices. An example was the question of whether the level of agreement that students experienced difficulties in learning dose calculations was linked to the calculation strategy taught. Thematic content analysis was used to organise and report qualitative data in response to open-ended questions relating to topics such as the difficulties experienced by student and staff in learning and teaching dose calculations. Participants responses were aggregated and reported on the basis of common themes. For example, in relation to factors contributing to student difficulties, themes included poor mathematical preparation at school, and affective factors. I examined learning resources nominated by academic staff who participated in the online questionnaire to see what information they provided relating to dose calculation and measurement processes. A specific goal was to identify the type or types of strategies modelled in the resources to calculate medicine doses. Skills in measuring doses were also identified and described. A small sample of additional reference books nurses were likely to use as learning resources was examined in a similar way. These were sourced from libraries and were current editions at the time of examination Ethical provisions relating to the University Phase Participants accessed the PLS from a link on the first page of the questionnaire. Participants were able to proceed to the questions in the questionnaire only after confirming they had read the information in the PLS and agreed to the conditions of participation. The PLS outlined the means to be used to protect the identities of the universities named in participants responses. Although participants themselves remained anonymous, they were asked to identify their university, campus, and the unit of study they were reporting on in their responses to questions. Knowing the identity of each participant s university, campus and the unit of study was considered necessary to determine the breadth of representation of respondents by state, university, campus, and unit of study. It also allowed me to determine whether there was duplication of information, such as more than one 150

164 Chapter 4: The Research Process person providing information about a particular unit at a university. It also allowed the possibility, if warranted, of cross-checking information, such as whether there were differences between universities, campuses, or units of study in policies that related to how dose calculation and measurement skills were taught. 4.4 Summary of the research process Table 4.1 provides a summary of the research process followed for each phase of the study. 151

165 University Phase Hospital Phase Chapter 4: The Research Process Table 4.1 Summary of the research process Study phase Research questions addressed Settings for data collection Ethics approvals Recruitment strategy Sample Data collection methods Data analysis methods RQ1 and RQ2 Three Australian hospitals in two different states/ territories: metropolitan regional rural Director of Nursing (each hospital) State Health ethics body (two hospitals) Site specific approval (two hospitals) Hospital ethics committee (one hospital) Ward-specific research committee (one hospital) Information and recruitment sessions; posters inviting participation Plain Language Statement (PLS) and consent forms distributed 73 nurse participants Naturalistic observation of participants One-on-one unstructured interviews Focus groups using semistructured schedule Questionnaire Descriptive statistics Thematic content analysis Cross-tabulation matrices to investigate possible associations between variables Chi-squared tests of goodness of fit, or independence, between variables RQ3 Schools/ Faculties of Nursing offering preregistration education programs at Australian universities Agreement from Head of School (HOS) to distribute Invitation to participate Approval from individual School or Faculty ethics or research committee, as required Invitation to participate distributed by HOS to two target groups First page of questionnaire included: link to PLS consent statement 65 academic staff from 43 campuses of 28 universities, involved as coordinator and/or teacher in relevant units of study Online questionnaire, administered using SurveyMonkey, accessing both target groups using skip logic Descriptive statistics Thematic content analysis Cross-tabulation matrices to investigate possible associations between variables 152

166 Chapter 4: The Research Process The findings from the Hospital Phase are described in Chapter 5 The strategies nurses use to calculate medicine doses, and Chapter 6 Measuring medicine doses. The findings from the University Phase are described in Chapter 7 The teaching of medicine dose calculation and measurement skills. The final step in the research was to compare the findings of the two investigations. This comparison allowed me to draw conclusions about whether the strategies nurses were observed using in clinical practice to calculate and measure medicine doses were the same strategies nurse educators involved in pre-registration education programs reported teaching students to use for similar calculation and measurement tasks. The results of this comparison are described and discussed in Chapter 8 Discussion and Chapter 9 Conclusion. 153

167 5 The Strategies Nurses Use to Calculate Medicine Doses I m not using anything more difficult than if I was grocery shopping. Marion (N40), Alexander Metropolitan Hospital One of the goals of the Hospital Phase of the study was to identify the calculation strategies nurses employ in their clinical practice to determine the dose of medicine to administer and to investigate the factors that influence their choice of calculation strategy. This goal addresses research questions RQ1 and RQ2. It was achieved through observing nurses as they administered medicines in the wards of three hospitals; interviewing nurses to elicit their own explanations of the dose calculation strategies they had used; and conducting focus groups at each hospital site. The dose calculation strategies nurses used in clinical practice were compared to the strategies they used to solve a series of medicine administration tasks in the questionnaire they had completed. This chapter presents the findings from these processes. 5.1 Observation of nurses as they administered medicines A total of 73 nurse participants, employed at the three hospitals selected for the Hospital Phase, volunteered to be observed as they administered medicines to their patients in the normal course of their duties. Observations were undertaken in a total of 35 different wards including medical, surgical, combined medical/surgical, paediatric, neonatal, renal, coronary care, medical high dependency, cardiothoracic surgery, stroke, catheter laboratory, recovery, neurosurgery, rehabilitation, hospital in the home (HITH), and the emergency department and intensive care unit (ICU) of each hospital. Over a total of 57 observation days during the period November 2010 to June 2011, I observed 1571 individual medicine administrations. Total observation time was 100 hours, spanning 181 observation sessions and 444 interactions between nurse participants and their patients. 154

168 Chapter 5 The Strategies Nurses Use to Calculate Medicine Doses Table 5.1 provides a summary of the research conducted at the three participating hospitals. Table 5.1 Details of the Hospital Phase of the study Study feature Gemmaville Rural Murraydale Regional Hospital Alexander Metropolitan All hospitals Total nurse participants No. of male participants No. of female participants No. of wards observed 8 a Total observation time (hours) No. of observation sessions Average no. of observation sessions per participant No. of nurse-patient interactions No. of medicine administrations No. of distinct generic medicines administered b a b The paediatric ward at Gemmaville Rural Hospital was part of a medical/surgical ward There was considerable overlap between the medicines administered at the three hospitals Most nurse participants worked in just one ward over the course of the observation sessions, so their observations took place in their home ward. Several nurses were observed in two ward areas, five at Gemmaville Rural Hospital and one at Alexander Metropolitan Hospital, who was the only agency nurse to volunteer for the study. The overall ratio of 12% male participants to 88% female participants roughly reflected the gender ratio that exists in the nursing profession. The proportion 155

169 Chapter 5 The Strategies Nurses Use to Calculate Medicine Doses of males was greatest at Alexander Metropolitan Hospital 20 (20%) and least at Murraydale Regional Hospital (5%). In this thesis I will refer to all products that were prescribed by a doctor and appeared on a patient chart as medicines. These products included generic medicines, combination medicines, and vitamin and mineral supplements. Patients receiving medicines during the study were not individually identified. So rather than describing the total number of patients receiving medicines, the summary refers to the total number of nurse-patient interactions. A nurse-patient interaction was defined as a nurse interacting with a patient to administer one or more medicines during a medicine round. When nurses moved to the next patient to administer medicines, a new nurse-patient interaction began. It was possible that the same nurse returned on a later occasion to a patient to whom they had previously administered medicine, in which case the subsequent interaction was regarded as a new nurse-patient interaction. Nurses administered as many as twelve medicines to a patient, with the average number per patient being as high as seven at one hospital and eight at another. The number of patients receiving medicines during a single medicine round varied from one (for example, in intensive care, medical high dependency, and neonatal wards) to eleven. Two occurrences of a nurse administering medicines to eleven patients took place in the rehabilitation ward of Murraydale Regional Hospital. On one occasion, a nurse administered a total of 73 medicines to 11 patients over a period of one-and-ahalf hours. An average of 33 hours was spent at each hospital observing participants. As Table 5.1 illustrates, the greatest amount of observation time was spent at Murraydale Regional Hospital where medicine rounds tended to be longer, with a larger number of medicines administered per round to a larger number of patients. At Alexander Metropolitan Hospital, observation sessions tended to be shorter, with fewer medicines administered per round to fewer patients. A possible reason for the differences between hospitals is that the patients cared for at Murraydale Regional Hospital were older and in need of more complex care, whereas patients at Alexander Metropolitan Hospital tended to be younger with more acute needs. 20 All names of hospitals are pseudonyms 156

170 Chapter 5 The Strategies Nurses Use to Calculate Medicine Doses The duration of observation sessions ranged from five minutes to one hour and fifty minutes, the average duration being 33 minutes. With one exception, a period of 30 minutes spent in the emergency department of Murraydale Regional Hospital, every observation session yielded at least one medicine administration. The longest observation session occurred in the renal ward of Murraydale Regional Hospital where between eight and ten day-visit patients waited for their dialysis treatment at 8 am. I was present with the nurse for one hour and fifty minutes. However, this unusually long observation session was atypical in that it took place in extraordinary circumstances and was characterised by a major equipment failure, many interruptions, distractions and delays, and high levels of stress among the nurses present, particularly the nurse participant I was observing who was in charge of the unit at the time. I left after almost two hours in the ward, feeling that my presence may have been adding to the confusion and stress, but before the nurse had administered all the prescribed medicines. The way medicines are named and packaged can impact on safety, with medicine names that look alike or sound alike having been identified as causes of medication error (Australian Commission on Safety and Quality in Health Care, 2011); (Deans, 2005). During observation sessions, examples of look-alike and sound-alike medicine names included: valaciclovir and valganciclovir, prednisolone and prednisone, cefotaxime and ceftriaxone, cephalexin and cefazolin, budesonide and bumetanide. The risk of error was highlighted when two medicines, valaciclovir and valganciclovir, were administered orally, minutes apart, to two different patients in the same ward by the same nurse during a single medicine round. Used to treat vastly different conditions, the nurse correctly administered 500 mg of valaciclovir by giving one 500 mg tablet, and 900 mg of valganciclovir by giving two 450 mg tablets. 5.2 Calculations associated with medicine administration Although it is frequently possible to administer medicines without the need for calculation, nurses often must perform at least one calculation, and sometimes several, to correctly administer medicines. Calculation of the quantity of medicine to give the patient, also referred to in this thesis as the dose to administer, is one type of 157

171 Chapter 5 The Strategies Nurses Use to Calculate Medicine Doses calculation nurses may need to perform and is a central focus of this study. Nurses may also need to perform some calculations prior, or subsequent, to determining the dose to administer. During observation sessions, the calculations nurses performed prior to determining the dose to administer included: calculation of the prescribed dose, (for example, a number of milligrams, micrograms, or millimoles) based on the weight of the patient (often a child), using a stated milligram per kilogram (or similar) value; calculation of the concentration (for example, a number of milligrams per millilitre) of a solution reconstituted from a powdered medicine; and metric conversions. Seventeen medicine administrations were recorded for which nurses calculated or confirmed the prescribed dose, based on a milligram per kilogram value. All such calculations were performed in relation to medicines administered to paediatric patients. Metric conversions were sometimes needed so that nurses could decide whether they needed to perform a dose calculation. The calculation most commonly performed after determining the dose to administer was calculation of the flow rate (millilitres per hour) needed to deliver the medicine at a constant rate over a fixed period of time. Forty-six such calculations were recorded. All calculations nurses performed in the course of administering medicines during observation sessions were documented. However, little further examination of calculations performed prior, and subsequent, to determining the dose to administer took place. Some of the calculations nurses performed in association with medicine administration during the observation sessions are shown in Table

172 Chapter 5 The Strategies Nurses Use to Calculate Medicine Doses Table 5.2 Examples of medicine administrations and the types of calculation they required Medicine Administration route Prescribed dose Stock used Dose-tostock ratio Administered dose Calculation of dose to administer performed? Other calculateions performed Sertraline Oral 50 mg 50 mg per tablet 1:1 1 tablet No None Sodium valproate Oral 200 mg 200 mg per 5 ml 1:1 5 ml No None Atorvastatin Oral 40 mg 20 mg per tablet 2:1 2 tablets Yes None Salbutamol Nebuliser 2.5 mg 5 mg per 2.5 ml 1: ml Yes None Colchicine Oral 0.5 mg 500 micrograms per tablet 1:1 1 tablet No Metric conversion Lincomycin IV a infusion 200 mg b 600 mg per 2 ml 1: ml Yes mg per kg (paediatric) dose Amikacin IV infusion 1.5 g 500 mg per 2 ml 3:1 6 ml Yes Metric conversion & infusion rate c a b c IV = intravenous The prescribed dose was calculated by the nurse on the basis of a mg/kg value Amikacin was added to 100 ml bag of normal saline and infused over half an hour 159

173 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses The examples reveal the mathematical and other characteristics of the medicine administrations that determined the need to perform a dose calculation (Column 7) and/or other calculations (Column 8) prior, or subsequent, to determining the dose to administer. Column 5 shows the dose-to-stock ratio for the medicine administration, the ratio of the prescribed mass to the stock mass the first-named quantity in the stock formulation used to administer the medicine. Prior calculation of the prescribed dose was required for the lincomycin administration. The nurse performed the calculation using the recommended dose range for the medicine (15 20 mg/kg) indicated on the patient chart. Using this information and the child s weight of 13 kg, the nurse determined an appropriate dose range for the administration ( mg per dose), adopting 200 mg as the prescribed dose. Having determined the prescribed dose, the nurse then calculated the dose to administer (0.66 ml). A prior metric conversion was needed before the nurse could calculate the dose of amikacin to administer (6 ml). The nurse performed a subsequent calculation to determine the infusion rate in ml per hour, entering the appropriate values into the digital settings of the electronic infusion pump. Calculation of the dose to administer was not necessary for the colchicine dose. After first performing a metric conversion so the prescribed mass (0.5 mg) and the stock mass (500 micrograms) were expressed in the same unit, it was clear that the two quantities were identical and the dose to administer was therefore one tablet. 5.3 Nurses calculation of the dose to administer The central focus of data collection during observation sessions was the calculations nurses perform to determine the dose of medicine to administer, typically a number of tablets or a volume of liquid measured in millilitres. Calculation of the dose to administer, or more simply, a dose calculation, was previously defined in as a calculation performed to determine the quantity of medicine required to administer the prescribed dose to the patient, using the stock form 21 selected. 21 In a small number of cases, two stock forms were selected. 160

174 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses Figure 5.1 illustrates the decision process nurses are assumed to use, consciously or unconsciously, to determine whether they need to perform a dose calculation. Figure 5.1. Nurses assumed decision process for determining the need for a dose calculation The majority of medicines were administered using one pharmaceutical product. Two products of different strength or size were used for 18 medicine administrations. The majority of these involved proportionality, the only exceptions being eight medicine administrations for which only simple addition was needed to add the masses of the two products administered. Although it was not possible to confirm the accuracy of each calculation at the time of observation, nurses accuracy was confirmed subsequently by checking the recorded data to verify that the dose administered corresponded to the prescribed dose. The number and proportion of medicine administrations that required calculation of the dose to administer at each hospital is shown in Table

175 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses Table 5.3 Frequency of medicine administrations requiring calculation of the dose to administer Dose calculation required? Gemmaville Rural n = 538 Murraydale Regional n = 659 Hospital Alexander Metropolitan n = 374 All hospitals n = 1571 Yes 126 (23%) 199 (30%) 106 a, (28%) 431 (27%) No 412 (77%) 460 (70%) 267 (71%) 1140 (73%) a Yes was assumed for an administration involving three medicines administered together by subcutaneous infusion As Table 5.3 shows, just over a quarter of the 1571 observed medicine administrations required a calculation to determine the quantity of medicine to be given to the patient. No calculation errors were detected among the 431 medicine administrations requiring a dose calculation. Identifying nurses dose calculation strategies Throughout the hospital observation sessions, I recorded details of each medicine administration and, for over half the administrations, nurses own explanations of how they calculated the dose. Whether I was able to elicit an explanation from nurses depended on many factors. Ultimately my decision whether to seek nurses explanations of their calculation strategies was based on weighing up the likely benefit of this information against the intrusion and interruption I might cause by seeking it. My decision was also influenced by the number of similar administrations I had recorded for which nurses had given an explanation. I employed the concept of data saturation, in the sense that when a pattern of similar explanations for the same or similar medicine administrations became evident, I refrained from seeking further explanations. For all dose calculations performed, I used the nurse s explanation and my own observation and interpretation of events to identify the nurse s calculation strategy. My understanding of the calculation strategies nurses used was amplified by information I obtained from participants during focus groups conducted at each hospital. 162

176 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses Nurses explained their calculation strategy for 240 of the 431 medicine administrations for which they performed a dose calculation. Thus, it was possible to identify nurses calculation strategies for 56% of dose calculations performed. Table 5.4 shows the frequency of the medicine administrations and dose calculations performed at each hospital and frequency of dose calculations for which the nurse s dose calculation strategy was elicited. Table 5.4 Frequency of medicine administrations and dose calculations Hospital Gemmaville Rural Murraydale Regional Alexander Metropolitan No. (%) of medicine administrations n = 1571 No. (%) of dose calculations performed n = 431 No. (%) of calculation strategies elicited n = (34%) 126 (29%) 82 (34%) 659 (42%) 199 (46%) 97 (40%) 374 (24%) 106 (25%) 61 (25%) During observation sessions, nurses use of the formula often required only cursory confirmation from nurses. Observing nurses picking up a calculator and keying in the three relevant values in the sequence dictated by the structure of the formula stock required stock strength volume was a strong indicator of formula use. By contrast, when nurses used non-formula-related mathematical processes, their calculation processes were usually invisible because nurses tended to use mental arithmetic. When nurses used strategies other than the formula, I was only able to understand their calculation strategies if they gave detailed explanations of how they calculated the dose. When the formula was used to calculate doses involving tablets or capsules, in keying in the values on the calculator nurses usually omitted the third value, volume or vehicle, which, in the case of solid medicines is one tablet or one capsule. This omission is justified by the fact that the relevant value is 1 and multiplying a quantity by one leaves the quantity unchanged. 163

177 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses 5.4 Classifying nurses dose calculation strategies Medicine administration events were first classified as known calculation strategy or unknown calculation strategy on the basis of whether nurses had given an explanation of their dose calculation strategy. All known calculation strategies were then classified using the process described in A descriptor for each strategy was chosen on the basis of nurses descriptions, supported by my recorded observations and interpretation of events, audio recordings if they existed, and my memory of the event, but never solely on my own observations, understandings or assumptions. For both one product and two product medicine administrations, nurses used either the formula or non-formula-related strategies to calculate the dose. Table 5.5 shows the number and percentage of nurses dose calculations that were carried out using the Nursing Formula compared to those that were carried out using a nonformula-related strategy. As can be seen in Table 5.4, the ratio of non-formularelated strategies to the Nursing Formula was approximately 7:1. Table 5.5 Frequency of use of the Nursing Formula Calculation strategy No. (%) of medicine administrations n = 240 Nursing Formula 28 (12%) Non-formula-related strategy 212 (88%) The non-formula-related strategies nurses used for all dose calculations, whether related to one- or two-product administrations, were based solely on proportional reasoning. Consequently, henceforth I will use the umbrella term proportional reasoning strategy or simply proportional reasoning to describe all calculation strategies that did not involve use of the formula. 164

178 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses 5.5 The proportional reasoning strategies nurses used For the majority of dose calculations involving proportionality, nurses used one of four scaling strategies: multiplicative reasoning; repeated addition; fraction operation; and division process. Nurses used these simple processes to scale up or down from the stock mass to the prescribed mass by multiplying or dividing respectively by an integer (2, 3, 4, etc.). These processes corresponded to techniques nurses described as doubling and halving, which they sometimes applied twice. A small number of dose calculations involved non-integer scalar factors, with nurse using strategies described here as halving combined with addition, and complex proportional reasoning. During the classification process, it was not clear for a small number of events which of two closely related scaling-up or scaling-down processes nurses had used. Consequently these events were classified as either multiplicative reasoning or repeated addition and either fraction operation or division process respectively. In one such event the nurse explained her strategy as follows. I want eight milligrams. I've got four milligrams. I need 2 [of the tablets] to make eight milligrams (Event #106). In this example it was not clear whether the nurse was thinking multiplicatively (2 4 mg) or using repeated addition (4 mg + 4 mg). This lack of clarity led to the decision to combine these two scaling up processes to form a single category labelled multiplicative reasoning or repeated addition Scaling processes Nurses used integer scalar factors and non-integer scalar processes to scale up or down from the stock mass to the prescribed mass. Multiplicative reasoning or repeated addition was the integer scalar strategy used to scale up. Fraction operation or division process was the strategy used to scale down using integer scalar factors. 165

179 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses Halving combined with addition, and complex proportional reasoning were the noninteger scalar processes nurses used to scale up or down from the stock mass to the prescribed mass. A striking feature of nurses use of proportional reasoning strategies was that, without exception, they used mental arithmetic to perform all computations. Nurses did not use calculators or pen and paper to assist their calculations for any of the medicine administrations for which they used proportional reasoning. Multiplicative reasoning or repeated addition Two mathematically distinct processes, multiplicative reasoning and repeated addition, were used to achieve the same result of scaling up from the stock mass to the prescribed mass. Multiplicative reasoning or repeated addition was the most frequently used calculation strategy. Nurses used it for 120 (50%) of the 240 dose calculations for which the calculation strategy was known. Fraction operation or division process Nurses used the two closely related processes, described here as fraction operation and division process, to scale down from the stock mass to the prescribed mass. Although both scaling-down processes relied on dividing by an integer (2, 3, 4, etc.), I drew a distinction between them, as I had between the two scaling-up processes, on the basis of the terminology nurses used to describe their calculation processes. If nurses said: Two hundred divided by two is one hundred, I classified the strategy as a division process. If nurses said: Half of eighty is forty, I classified the strategy as a fraction operation. Because of the similarity between the two strategies, they were combined and described as fraction operation or division process. Nurses used these scaling down techniques for 58 (24%) of the 240 dose calculations for which the calculation strategy was known. The final step in each scaling procedure, whether used to scale up or down, was to apply the same process to the stock volume or vehicle. By correspondingly scaling that quantity up or down the dose to administer was obtained. The frequency of nurses use of each type of scaling procedure is shown in Table

180 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses Table 5.6 Frequency of integer scalar strategies used to scale up and down from stock mass Calculation strategy No. (%) of medicine administrations Scaling up process 120 (50%) Multiplicative reasoning 72 Repeated addition 45 Either multiplicative reasoning or repeated addition Scaling down process 58 (24%) Fraction operation 45 Division process 11 Either fraction operation or division process 3 2 Halving combined with addition Nurses used halving combined with addition to scale the stock mass up to x-and-a-half times its value. Nurses applied this strategy to 13 dose calculations. The process involved nurses halving the stock mass, then adding that quantity to the stock mass or a multiple of the stock mass. The final step in the procedure was to apply the transformation to the stock volume or vehicle to scale it up correspondingly to obtain the dose to administer. Complex proportional reasoning Complex proportional reasoning was the descriptor for calculation strategies involving either a multi-step scaling process and/or using the scale on a syringe to assist in calculating the dose to administer. In the twelve medicine administrations for which nurses used such processes, the prescribed mass was always a number of milligrams or micrograms and the stock used was in liquid form. Complex proportional reasoning typically involved expressing the stock concentration as a series of equivalent concentrations until they reached the form of the concentration that included the prescribed mass. For example, if the prescribed mass of medicine was 20 mg and the stock concentration was 80 mg in 10mL, equivalent expressions for the stock concentration include: 40 mg in 5 ml and 20 mg 167

181 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses in 2.5 ml. The latter concentration includes the prescribed mass, 20 mg, resulting in 2.5 ml being the dose to administer. This procedure results in scaling down, and possibly scaling up again, both the stock mass and the stock volume in the same calculation process until the prescribed mass is reached. The stock volume that corresponds to the prescribed mass in that formulation is the volume to be administered. Two complex proportional reasoning calculations involved nurses using the scale on a syringe to calculate the volume needed to administer a given number of milligrams. As nurses drew liquid into the syringe, they used the syringe scale not only to measure millilitres, but also as a scale for the number of milligrams or vials of the medicine to be administered. The nurse also used the technique of expressing the stock as a series of equivalent concentrations for one of these calculations. Proportional reasoning strategies for two-product medicine administrations Proportionality was also involved in the majority of two-product medicine administrations. Typically nurses needed to find the mass of several tablets or part tablets of different strength, summing them to calculate the total mass to be administered. An example of such a two-product medicine administration involving proportional reasoning was the administration of a 4.5 mg oral dose of warfarin (Event #1054). The nurse administered the dose by giving tablets of different strengths: one-and-a-half 1 mg tablets and one 3 mg tablet. Nurses made no use of the formula for two-product dose calculations involving proportionality. Instead they used the same informal proportional reasoning strategies they used for single-product administrations. 5.6 Overview of nurses dose calculation strategies The dose calculation strategies nurses used are summarised in Table 5.7 and Figure 5.2. Table 5.7 shows the frequency of different strategies nurses used to calculate medicine doses for all single- and two-product medicine administrations. For the major categories, the table also shows the percentage of all medicine administrations in that category. 168

182 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses Table 5.7 Frequency of dose calculation strategy Calculation strategy No. (%) of medicine administrations Single-product administration n = 413 Two-product administration n = 18 Total n = 431 Unknown strategy 187 (45%) 4 (22%) 191 (44%) Known strategy 226 (55%) 14 (78%) 240 (56%) Nursing Formula 28 (7%) 0 (0%) 28 (6%) Proportional reasoning 198 (48%) 6 (33%) 203 (47%) Multiplicative reasoning or repeated addition Fraction operation or division process Halving combined with addition Complex proportional reasoning Simple addition NA 8 (44%) 9 (2%) Figure 5.2 shows the final classification structure of nurses dose calculation strategies. It draws together the results of the iterative process of aggregating nurses dose calculation strategies on the basis of shared characteristics and assigning descriptors to the categories so formed. 169

183 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses Figure 5.2. Final classification of nurses observed dose calculation strategies 170

184 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses Examples of nurses use of proportional reasoning strategies and the formula (see Table 5.7 and the final column in Figure 5.2) appear later in this chapter (see 5.9 and 5.16, respectively). An example of nurses use of simple addition to calculate the dose for a two-product medicine administration appeared earlier in The dose-to-stock ratio for a medicine administration During the analysis of the data to identify the calculation strategies nurses used to determine the dose to administer, the nature of nurses calculation strategies appeared to be linked to the relationship that existed between two of the key quantities that defined the medicine administration: the prescribed mass 22 and the stock mass (the first-named quantity in the stock formulation of the pharmaceutical product used to administer the medicine). For the purpose of this thesis, I have defined the ratio of the prescribed mass to the stock mass as the dose-to-stock ratio (DSR). For example, if a nurse needed to administer 50 mg of a medicine from liquid stock containing 25 mg per 2 ml, the prescribed mass is 50 mg, the stock mass is 25 mg, and the DSR is 2:1. The fact that the relationship between these two quantities appeared to influence nurses choice of dose calculation strategy led me to increasingly focus my analyses on the DSR. Accordingly, for each of the 1571 medicine administration to which it applied, the DSR was recorded in the form n:m, where n and m are integers. (Column 5 of Table 5.2 shows the DSRs for the listed medicine administrations.) A category of DSR, labelled as varied, was created to accommodate the 18 medicine administrations for which nurses combined two pharmaceutical products of different strength or quantity to administer the dose. These medicine administrations therefore involved more than one dose-to-stock ratio. For more than three hundred medicine administrations, the DSR was recorded as not applicable or unknown. These administrations included those where either the prescribed dose or the stock used was not expressed as a mass in measurement units such as grams, milligrams, or micrograms, or as the amount of a substance in units such as millimoles or international units. Such medicine administrations included those for which the prescribed dose written on the patient chart was 22 In this thesis the term mass is used to include forms such as millimole and international unit that can be used to express the amount of a substance. 171

185 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses expressed as a number of tablets, capsules, puffs, drops, teaspoons, sachets, patches, or similar. The unknown category also included a small number of medicine administrations for which the formulation of stock used had not been recorded, so no DSR could be calculated. The stimulus for examining the relationship between the prescribed mass and the stock mass initially came from the work of Hoyles et al. (2001). In reporting their study, involving twelve nurses administering medicines to paediatric patients in a specialist paediatric hospital in the UK, Hoyles et al. listed 18 distinct scalar ratios, and 26 different combinations of the prescribed mass and the formulation of the stock used to administer the dose (p. 15). Hoyles et al. (2001) referred to these scalar ratios variously as the scalar ratio of mass-of-drug-prescribed to mass-in-package (p. 15), the scalar ratio, mass prescribed: packaged dose (p. 15, Table 3), and again later, more simply as the ratio of prescribed-dose to packaged-dose (p. 22). In this thesis, I use the term DSR for the ratio Hoyles et al. referred to in these different ways. Hoyles et al. (2001) recorded scalar ratios ranging from 1:1 to 83:1000. These ratios had emerged from 30 episodes of medicine administration observed in their study, 24 of which required calculation of the dose to administer. Hoyles et al. attributed no further relevance to these ratios, which was understandable given the relatively small number of dose calculations observed and the limited number of DSRs that had resulted from the medicine administrations witnessed. As can be seen in Table 5.2, a DSR of 1:1 corresponds to medicine administrations where no dose calculation was required. Hoyles et al. (2001) referred to this as a one-one situation in which the prescription was identical to the dose concentration (p. 16). All ratios other than 1:1 correspond to medicine administrations where a dose calculation was required. The DSR for a medicine administration can also indicate the degree of difficulty for a nurse to perform the necessary dose calculation using mental arithmetic strategies alone. For example, a medicine administration with a DSR of 2:1 could be regarded as easier than one for which the DSR was 2:25. In the first example, to calculate the dose to administer, nurses simply need to double the stock volume or vehicle, such as one tablet, a task that should be easy to execute mentally. In the second example, the calculation process is bound to be far more complex and therefore more difficult to carry out mentally. 172

186 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses Thirty-five distinct DSRs were recorded for the 240 medicine administrations for which nurses calculation strategies were known. Table 5.8 provides a summary of the frequencies of the DSRs for all medicine administrations that occurred during observation sessions. For each DSR, the table shows the number of medicine administrations associated with the DSR and provides an illustrative example drawn from the data showing the prescribed mass and the formulation of the stock used by nurses to administer the medicine. The frequencies of DSRs are arranged in classes of DSR, n:1, 1:n, and n:2, with n increasing in magnitude. 173

187 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses Table 5.8 Frequency of DSR Dose-tostock ratio No. (%) of occurrences n = 1571 Prescribed mass Example Stock formulation 1:1 724 (46%) 75 mg 75 mg per tablet 2:1 229 (15%) 1.2 g 600 mg per vial 3:1 22 (1%) 450 mg 150 mg per capsule 4:1 13 (0.8%) 320 mg 80 mg per 2 ml 28:1 5 (0.3%) 140 mg 5 mg per ml 1:2 84 (5%) 2.5 mg 5 mg per 2.5 ml 1:3 2 (0.1%) 50 microg 150 microg per ml 1:4 a 20 (1%) 12.5 mg 50 mg per tablet 1:25 a 11 (0.7%) 4 IU 100 IU per ml 1:50 a 6 (0.4%) 2 IU 100 IU per ml 3:2 15 (1%) 7.5 mg 5 mg per tablet Other b 67 (4%) NA NA Varied 18 (1%) 15 mg Two tablets, each of different strength (10 mg and 5 mg) Unknown 35 (2%) NA NA Not applicable 322 (20%) 1.5 tablets NA a b Many administrations in the group 1:n involved a prescribed volume (rather than a mass) that was administered from a bottle, e.g. many 1:4 DSRs involved administering a 50 ml dose from a 200 ml bottle of medicine. Other includes 32 administrations that occurred once, 9 that occurred twice, and 5 that occurred three times. 174

188 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses Further details regarding the way in which the DSR was used in answering the research questions relating to nurses choices of dose calculation strategy follow later in this chapter. 5.8 Factors influencing choice of calculation strategy Nurses calculation strategies were investigated to determine whether there were identifiable factors with which they may be linked. Factors examined included characteristics of the clinical contexts in which the medicine administrations occurred, for example, the hospital, ward, and administration route. The numerical characteristics of the medicine administration and factors in the personal backgrounds of nurses, such as the length of their nursing experience and the country in which they were educated, were also examined Relationships between DSR and calculation strategy used The only factor that proved to be strongly related to nurses choice of calculation strategy was the dose-to-stock ratio. The decision to investigate possible links between particular DSRs and the calculation strategies nurses used to calculate doses was triggered by the patterns that emerged in nurses explanations of their dose calculation strategies. For example, as the data were analysed, it gradually became clear that doubling and halving strategies were very commonly used and that these strategies were linked to the relationship between two of the key values that defined the medicine administration, namely the prescribed mass and the stock mass. My growing awareness of the importance of the DSR was further strengthened by the realisation that the DSR served as an informal measure of difficulty if nurses were to calculate the dose by applying scalar approaches using only mental computational processes. When nurses known calculation strategies were examined, a very small number of DSRs accounted for the vast majority of the dose calculations. The discussion that follows relates to nurses dose calculations for these medicine administrations. Excluding medicine administrations for which nurses used two products to administer the medicine (and for which no single DSR applied), five DSRs accounted for 185 (81%) of the 240 dose calculations for which the nurse s calculation strategy was known. These DSRs were: 2:1, 3:1, 4:1, 1:2, and 3:2. The 175

189 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses order of the frequency of occurrence of the DSRs for medicine administrations for which the nurse s calculation strategy was elicited differed, however, from the order in Table 5.8 that applies to all medicine administrations observed. When calculation strategy was viewed against the DSR, several distinct patterns of association emerged that linked certain calculation strategies to particular DSRs. Three distinct calculation strategies emerged as being particularly prominent among nurses dose calculation strategies: multiplicative reasoning or repeated addition; fraction operation or division process; and halving combined with addition. These strategies appeared to be triggered by a particular DSR, or group of DSRs, from among those identified earlier as n:1, 1:n, and n:2. These dose calculations and the DSRs they are associated will be discussed in these groups of DSR. Examples of medicine administrations from the group of DSRs n:1 follow, namely 2:1, 3:1 and 4:1. DSR 2:1 By far the most frequently observed medicine administrations were those with a DSR of 2:1. Such medicine administrations accounted for 228 (53%) of the 431 medicine administrations for which a dose calculation was required, and 101 (42%) of the 240 medicine administrations for which the calculation strategy was known. Table 5.9 shows the frequency of the dose calculation strategies nurses used for medicine administrations whose DSR was 2:1. 176

190 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses Table 5.9 Frequency of dose calculation strategies DSR 2:1 Calculation strategy No. (%) of medicine administrations n = 101 Formula 3 (3%) Proportional reasoning 98 (97%) Multiplicative reasoning or repeated addition Fraction operation or division process 95 3 Table 5.9 shows the strong dominance of multiplicative reasoning and repeated addition methods, reflected in nurses doubling techniques. The formula was used for only 3 (3%) of such medicine administrations. Examples 1 and 2 below illustrate two different approaches nurses used to solve dose calculation problems for medicine administration with a DSR of 2:1. Example 1 Multiplicative reasoning Prescribed dose and route Stock used Paracetamol 1 g; oral 500 mg per tablet Dose-to-stock ratio 2:1 Administered dose 2 tablets John 23, a new graduate, explained his strategy as he pushed each tablet out of the packaging and into a measuring cup. Five hundred milligrams [pushes one tablet out], times two [pushes another tablet out]. That s one gram. (John, N35, AH 24, Event #926) All names of nurses are pseudonyms N35 is the identification code for nurse participant 35; AH = Alexander Metropolitan Hospital; GH = Gemmaville Rural Hospital; MH = Murraydale Regional Hospital 177

191 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses Example 2 Fraction operation Prescribed dose and route Stock used Abacavir 600 mg; oral 300 mg per tablet Dose-to-stock ratio 2:1 Administered dose 2 tablets Half [the required dose] is three hundred. Three hundred is half of what I need, so I'll give two of these [tablets]. (Susie, N66, AH, Event #797) Susie s explanation suggested a departure from the more usual direction of calculation nurses followed, namely, working from stock mass to prescribed mass. Consequently, her use of a fraction operation, the inverse of multiplicative reasoning, corresponded with her working from prescribed mass to stock mass. DSR 3:1 Medicine administrations with a dose-to-stock ratio of 3:1 accounted for 22 (5%) of the 431 medicine administrations requiring a dose calculation and 11 (5%) of the 240 calculations for which nurses explained their strategy. Table 5.10 shows the frequency of dose calculation strategies nurses used for medicine administrations whose DSR was 3:1. Table 5.10 Frequency of dose calculation strategies DSR 3:1 Calculation strategy No. (%) of medicine administrations n = 11 Formula 0 (0%) Proportional reasoning 11 (100%) Multiplicative reasoning or repeated addition Fraction operation or division process

192 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses Table 5.10 shows the dominance of multiplicative reasoning and repeated addition methods, reflected in nurses tripling techniques. The formula was not used for any medicine administration involving a DSR of 3:1. Examples 5 and 6 illustrate how two nurses calculated the same dose of amikacin on separate occasions for administration to the same patient in a small Hospital in the Home treatment room at Gemmaville Rural Hospital. The calculations required nurses to perform metric conversions that also involved manipulation of decimals. In Example 5, the nurse, Anne, calculated the dose by working in millilitres using a multiplicative process. In Example 6, the nurse, Robyn, worked in vials using an additive process. Example 5 Multiplicative reasoning Prescribed dose and route Stock used Amikacin 1.5 g; IV infusion Vial labelled 500 mg per 2 ml Dose-to-stock ratio 3:1 Administered dose 6 ml Three times five hundred milligrams gives the one point five grams, which equals six mils of liquid. (Anne, N67, GH, Event #1160) Anne then prepared three vials of amikacin, each containing 2 ml of liquid. Example 6 (Identical to Example 5) Three vials. Five hundred milligrams plus five hundred milligrams is one gram and I need one and a half grams. (Robyn, GH, Event #1200, repeated addition.) Robyn inserted the liquid contents she had withdrawn from the three vials into a 100 ml bag of normal saline, ready for infusion. 179

193 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses DSR 4:1 Medicine administrations with a dose-to-stock ratio of 4:1 accounted for 13 (3%) of the 431 medicine administrations requiring a dose calculation and 12 (5%) of the 240 calculations for which nurses explained their strategy. Table 5.11 shows the frequency of dose calculation strategies nurses used for medicine administrations whose DSR was 4:1. Table 5.11 Frequency of dose calculation strategies DSR 4:1 Calculation strategy No. (%) of medicine administrations n = 12 Formula 2 (17%) Proportional reasoning 10 (83%) Multiplicative reasoning or repeated addition Fraction operation or division process 8 2 Table 5.11 shows the dominance of multiplicative reasoning and repeated addition methods, reflected in nurses quadrupling techniques. The pattern of calculation strategies for DSR 4:1 is mixed, however. Nurses made greater use of the formula and division processes, each being used for 2 (17%) of calculations. Examples 7 to 9 illustrate the different ways nurses approached dose calculations for medicine administrations with a DSR of 4:1. Example 7 Repeated addition Prescribed dose and route Stock used Metformin 2000 mg; oral 500 mg per tablet Dose-to-stock ratio 4:1 Administered dose 4 tablets 180

194 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses As the nurse took the tablets one by one, and put them into a container, she counted out loud: Five, ten, fifteen, twenty. (Sherobhi, N26, AH, Event #768) Sherobhi counted in hundreds using repeated addition. Thus, the final amount, twenty hundreds, was equivalent to the required dose of 2000 mg. Example 8 Multiplicative reasoning Prescribed dose and route Stock used Bisoprolol 10 mg; oral 2.5 mg per tablet Dose-to-stock ratio 4:1 Administered dose 4 tablets Two-point-five times two is five, times two is ten. (John, N35, AH, audio, Event #925) John used doubling, then doubling again, a process that involved decimal manipulation. Example 9 Division process Prescribed dose and route Stock used Spironolactone 100 mg; oral 25 mg per tablet Dose-to-stock ratio 4:1 Administered dose 4 tablets A hundred divided by twenty five is four. (Trisha, N53, GH, Event #1112) 181

195 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses Trisha s explanation suggested she had worked in the reverse direction to that nurses most commonly follow. She had worked from the prescribed dose to the stock formulation, using a division process. This operation was the inverse of multiplicative reasoning, the process that one might have expected her to use, had she had worked from stock mass to prescribed mass. Examples of medicine administrations from the group of DSRs 1:n follow, namely 1:2, 1:3 and 1:4. DSR 1:2 The second most numerous group of medicine administrations observed was that with a DSR of 1:2. These medicine administrations accounted for 78 (18%) of the 431 medicine administrations for which a dose calculation was required, and 47 (20%) of the 240 for which the calculation strategy was known. Table 5.12 shows the frequency of the dose calculation strategies nurses used for medicine administrations whose DSR was 1:2. Table 5.12 Frequency of dose calculation strategies DSR 1:2 Calculation strategy No. (%) of medicine administrations n = 47 Formula 1 (2%) Proportional reasoning 46 (98%) Multiplicative reasoning 1 Fraction operation or division process Complex proportional reasoning 44 1 Table 5.12 shows the dominance of fraction operations and division processes, reflected in nurses halving strategies. The two closely allied strategies of fraction operation and division process accounted for 44 (94%) of the administrations for which the DSR was 1:2. The formula was used for only one administration (2%). Example 3 illustrates the use of a fraction operation to solve the dose calculation problem for which the medicine administration had a DSR of 1:2. 182

196 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses Example 3 Fraction operation Prescribed dose and route Stock used Dexamethasone 2 mg; IV infusion 4 mg per 1 ml Dose-to-stock ratio 1:2 Administered dose 0.5 ml So two milligrams is half the dose of four milligrams [in the ampoule]. So half of one [mil] is point-five of a mil. (Deidre, N33, AH, audio, Event #869) Deidre used a 1 ml syringe to draw up 0.5 ml from the glass ampoule, ready for administration. DSR 1:3 Examples 10 to 12 illustrate the different ways nurses approached dose calculations for medicine administrations with a DSR of 1:3. Example 10 illustrates how one nurse, Tom, approached calculation of a liquid dose. He used a strategy involving diluting the stock solution, then applied a proportional reasoning approach involving a fraction operation to calculate the dose to administer. Example 10 Fraction operation Prescribed dose and route Stock used Clonidine 50 micrograms; IV infusion 150 micrograms per 1 ml Dose-to-stock ratio 1:3 Administered dose One third of the solution created Using a 5 ml syringe, Tom took a vial of clonidine, withdrew 1 ml of liquid from it and added it to 2 ml of normal saline. Thus, he had created a solution containing 150 micrograms of clonidine in a volume of 3 ml. 183

197 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses I need to give fifty micrograms which is one third of the one hundred and fifty micrograms [in the syringe]. So I give one third of the three mils. (Tom, N43, AH, Event #785) DSR 1:4 Examples 11 to 14 illustrate nurses application of different proportional reasoning strategies for medicine administrations with a DSR of 1:4. Example 11 illustrates how one nurse, Lee, started with the stock mass and performed a series of halvings until she reached the prescribed mass. The calculation required manipulation of decimal numbers. Example 11 Fraction operation Prescribed dose and route Stock used Metoprolol 12.5 mg; oral 50 mg per tablet Dose-to-stock ratio 1:4 Administered dose ¼ tablet Twenty five is half; twelve-point-five is a quarter. (Lee, N18, MH, Event #405) A pharmacy note on the patient chart stated: ¼ 50 mg, confirming that quarter of a 50 mg tablet was the correct quantity to give. In Example 12, Adelina started with the stock concentration and, through a series of halvings, found equivalent concentrations until she reached the concentration that referred to the prescribed dose. Example 12 Complex proportional reasoning Prescribed dose and route Stock used Digoxin 125 micrograms; IV infusion 500 micrograms per 2 ml Dose-to-stock ratio 1:4 Administered dose 0.5 ml So as it s five hundred micrograms in two mils, it will be two fifty micrograms in one mil just half. And one-twenty-five will be in point-five mil. So we ll take 184

198 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses point-five mil of this medication and mix up with fifty mils of normal saline and infuse over thirty minutes. (Adelina, N36, AH, audio, Event #986) The administration described in Example 13 took place in the paediatric ward where the patient was a three-year-old child. Lothlorian dissolved one 20 mg tablet in 10 ml of water for injections, illustrated in Figure 5.3. Figure 5.3. Water for injections: contents of ampoule used to dissolve tablet Lothlorian explained the concentration of the solution she had created as a series of equivalent concentrations, repeatedly halving both quantities in the concentration of the solution until she reached the concentration that contained the five milligrams mass she needed to administer. Example 13 Complex proportional reasoning Prescribed dose and route Stock used Omeprazole 5 mg; oral gastric PEG feed 20 mg per tablet Dose-to-stock ratio 1:4 Administered dose 2.5 ml of solution created by the nurse Twenty milligrams in ten mils; ten milligrams in five mils; five milligrams in two point five mils. (Lothlorian, N62, GH, Event #1513) Lothlorian then discarded all but the 2.5 ml needed to deliver the 5 mg dose. 185

199 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses DSR 3:2 Medicine administrations with a DSR of 3:2 accounted for 15 (3%) of the 431 medicine administrations for which a dose calculation was required, and 14 (6%) of the 240 administrations for which the calculation strategy was known. Interestingly, no medicine administrations with a DSR of 3:2 were observed at Alexander Metropolitan Hospital. Table 5.13 shows the frequency of the dose calculation strategies nurses used for medicine administrations whose DSR was 3:2. Table 5.13 Frequency of dose calculation strategies DSR 3:2 Calculation strategy No. (%) of medicine administrations n = 14 Formula 0 (0%) Proportional reasoning 14 (100%) Halving combined with addition Complex proportional reasoning 13 1 The dominant calculation strategy used for administrations with a DSR of 3:2 was halving combined with addition, a process used to obtain one-and-a-half times the stock mass. The formula was not used for any medicine administration with a DSR of 3:2. Example 4 illustrates a medicine administration with DSR 3:2 for which the nurse used halving combined with addition to calculate the dose to administer. The calculation involved a decimal manipulation. 186

200 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses Example 4 Halving combined with addition Prescribed dose and route Stock used Prednisalone 37.5 mg; oral 25 mg per tablet Dose-to-stock ratio 3:2 Administered dose 1½ tablets One tablet is twenty five [mg], so half a tablet is twelve-point-five [mg]. Twenty five plus twelve-point-five is thirty-seven-point-five. (Sky, N65, GH, Event #1514) Of the 240 medicine administrations for which nurses calculation strategies were known, 185 (77%) involved the five DSRs 2:1, 1:2, 3:2, 3:1, and 4:1. The dominant calculation strategies that were used for these five DSRs are shown in Table Table 5.14 Dominant calculation strategies for commonly occurring DSRs DSR No. (%) of medicine administrations n = 240 Dominant calculation strategy 2:1 102 (43%) Multiplicative reasoning or repeated addition 1:2 46 (19%) Fraction operation or division process 3:2 14 (6%) Halving combined with addition 3:1 11 (5%) Multiplicative reasoning or repeated addition 4:1 12 (5%) Multiplicative reasoning or repeated addition Number (%) of occurrences Number (%) of occurrences of formula use 94 (92%) 3 (3%) 43 (93%) 1 (2%) 13 (93%) 0 (0%) 10 (91%) 0 (0%) 8 (67%) 2 (17%) Other DSRs 55 (23%) Various (40%) 187

201 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses As Table 5.14 shows, a single dominant calculation strategy was used by over 90% of nurses for four of the five listed DSRs. Nurses made almost no use of the formula for three of these DSRs (2:1, 1:2, and 4:1), and never used the formula for the other two (3:2 and 3:1). The five ratios that were the focus of these analyses may appear to be just five of a very large number of ratios that defined the dose calculations nurses performed during the study. However, the significance of the strong links between each of these DSRs and nurses use of a particular calculation strategy lies in the fact that these five DSRs together accounted for (77%) of the 240 dose calculations performed for which the calculation strategy was known, and 83% of the 431 medicine administrations that required calculation of the dose to administer. The concept of grouping medicine administrations into broader classes on the basis of their DSRs was triggered by the realisation that the same pattern of associations identified between nurses dose calculation strategies and the three most commonly occurring DSRs, 2:1, 1:2, and 3:2, may carry over to the broader classes of DSR to which these individual DSRs belong. The classes of DSR of interest are respectively as follows: n:1 (n 1) (for example, 2:1, 3:1, 4:1); 1:n (n 1) (for example, 1:2, 1:3, 1:4); and n:2 where n is odd (n 1) (for example, 3:2, 5:2, 7:2). The pattern of nurses use of multiplicative reasoning or repeated addition, identified first in relation to medicine administrations with a DSR of 2:1, was also apparent among medicine administrations with a DSR of 3:1 and 4:1 (see Table 5.14). However, it was not possible to determine whether this pattern of association applied when n > 5 because there were too few medicine administrations to consider. Nor were there sufficient examples of medicine administrations with DSRs of the form 1:n or n:2 to investigate patterns of association beyond those previously reported for n 4. Only a small proportion of medicine administrations in my study 11% fell outside these three classes of DSR. These DSRs will be referred to as complex DSRs. 188

202 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses Varied DSRs: Two-product dose calculations DSRs for two-product medicine administrations involving proportionality were classified as varied, reflecting the fact that no single DSR could be used to describe the numerical relationship between the prescribed mass and stock mass. Medicines administered using two products were, with two exceptions, tablets administered orally. The two exceptions were intravenous infusions, one using liquid stock and the other involving reconstitution of a powdered medicine to liquid form. For two-product calculations involving proportionality, nurses used proportional reasoning strategies similar to those used for single-product administrations. The strategy of halving combined with addition was not observed. Nurses made no use of the formula, pen and paper, or calculators for dose calculations involving two pharmaceutical products. Examples 14 and 15 illustrate nurses use of proportional reasoning to calculate doses for two-product administrations. Example 14 Repeated addition Prescribed dose and route Stock used Dose-to-stock ratio Administered dose Gabapentin 800 mg; oral Tablets of different strength: 300 mg and 100 mg Varied Four tablets of two different strengths Olivia administered four tablets: two of 300 mg strength and two of 100 mg strength. She explained: Three plus three is six. One plus one gives eight hundred. (Olivia, N25, AH, Event #735) Working in hundreds, Olivia s explanation meant = 600 and = 200. She then added the two quantities to give 800 mg. 189

203 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses Example 15 Multiplicative reasoning Prescribed dose and route Stock used Dose-to-stock ratio Administered dose Prednisone 60 mg; oral Tablets of different strength: 25 mg and 5 mg Varied: Two products administered Four tablets of two different strengths Susie explained her decision to give two 25 mg tablets and two 5 mg tablets: Two of this [takes two 25 mg tablets from pack] will give me fifty and I need to find a five milligram [pack of tablets]. After finding a pack of 5 mg tablets, Susie continued: Two times twenty five gives fifty milligrams. Two times five gives ten milligrams. Total: sixty milligrams. (Susie, N66, AH, Event #801) 5.9 Factors influencing nurses use of the formula Nurses used the formula for only 28 (12%) of the 240 medicine doses for which the calculation strategy was known. Several factors were examined to see whether they were associated with nurses use of the formula. These factors included the hospital and ward in which the medicine was administered, and the numerical characteristics of the medicine administration, including whether nurses needed to manipulate decimal numbers to calculate the dose. Two factors emerged as being related to nurses use of the formula: the DSR of the medicine administration and the ward in which the medicine was administered. The pattern of formula use between nurses and across hospitals and wards is shown in Table

204 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses Table 5.15 Pattern of formula use across hospitals, nurses, and wards Hospital Gemmaville Rural Murraydale Regional Alexander Metropolitan All hospitals No. (%) of dose calculations performed No. (%) of dose calculations for which formula was used No. (%) of nurses observed Study Feature No. (%) of nurses using formula No. (%) of wards visited No. (%) of wards in which the formula was used n = 431 n = 240 n = 73 n = 73 n = 35 n = (29%) 13 (10%) 21 (29%) 7 (33%) 8 (23%) 5 (63%) 199 (46%) 6 (3%) 22 (30%) 3 (14%) 12 (34%) 2 (17%) 106 (25%) 9 (8%) 30 (41%) 4 (13%) 15 (43%) 2 (13%) 431 (100%) 28 (12%) 73(100%) 14 (9%) 35 (100%) 9 (26%) There was not a great deal of variation between hospitals in the proportion of dose calculations for which nurses used the formula. As Table 5.15 shows, use of the formula by nurses at Gemmaville Rural Hospital was more widely dispersed between nurses and wards than it was in the other two hospitals. Of note, however, was that Gemmaville Rural Hospital was the only hospital that did not have a dedicated paediatric ward where the majority of formula use was concentrated. At the other two hospitals the concentration of formula use among fewer nurses and fewer wards may be explained in part by the fact that these two hospitals had a paediatric or neonatal ward (but not both) which is where the formula use was likely to have been concentrated Relationship between formula use and other factors In examining whether nurses use of the formula might be linked to the hospital in which the medicine was administered, the possible influence of annual 191

205 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses testing of medication calculations arose. Alexander Metropolitan Hospital was the only hospital that did not have a policy requiring RNs to sit for an annual medication calculation test to confirm their competency in the calculations associated with medicine administration. At hospitals where this requirement applied, nurses were required to pass this test each year to be able to continue to administer medicines. In such tests, it is common practice for the formula to be provided. Thus annual testing might predispose nurses at those hospitals to use the formula. If nurses are regularly exposed to the formula by providing it to assist nurses in tests, particularly if they are also required to show their working, this might act as an annual reminder of the merits of the formula and apply subtle pressure on nurses to use it. At Alexander Metropolitan Hospital, annual testing of nurses had been discontinued more than a decade earlier. Discontinuation of the practice was apparently a decision of the Director of Nursing who believed that dose calculation skills were a core requirement of all registered nurses. The director also believed that annual testing was costly, both in terms of the staff resources required to administer and mark the tests and provide feedback to nurses, and in terms of the time away from their normal duties for nurses undertaking tests. Because nurses at Alexander Metropolitan Hospital did not have to sit an annual test, it was thought that they might make less use of the formula than nurses at the other two hospitals. No evidence was found, however, to support a link between formula use and annual testing of medication calculation competence. Another hypothesis tested concerned the possibility that the need to manipulate decimals might also influence nurses to use the formula. This hypothesis was tested by examining the rate of formula use for medicine administrations involving decimal numbers. Of the 240 doses for which the calculation strategy was known, 42 (18%) involved decimal numbers. Nurses used the formula to calculate only 4 (10%) of these doses, two of which also had a complex DSR, one of them being a paediatric dose. The remaining 38 (90%) of the calculations involving decimal numbers were solved using a variety of proportional reasoning strategies. The conclusion reached from this analysis was that there was no support for the hypothesis that the need to manipulate decimal numbers in a dose calculation influences nurses to use the formula. On the contrary, the data showed that even when decimal manipulation was required within a dose calculation, the DSR for the 192

206 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses medicine administration remained the primary factor influencing nurses choice of calculation strategy. Use of the formula was concentrated in medicine administrations for which the dose-to-stock ratio was classified as complex DSR. This was a relatively small group of 49 (13%) of the 431 medicine administrations requiring a dose calculation whose DSRs fell outside the n:1, 1: n, and n:2 classes of DSR that accounted for the majority (382 or 87%) of medicine administration requiring a dose calculation Relationship between formula use and calculation of doses for paediatric patients An association was identified between nurses use of the formula and calculation of doses administered in paediatric and neonatal wards. Of the 28 doses calculated using the formula 19 (68%) were administered to paediatric patients. Yet only 41 (3%) of the 431 medicines requiring a dose calculation were administered to paediatric patients The strength of the relationship between formula use and paediatric medicines was further illustrated by the fact that nurses used the formula for 19 (58%) of the 33 doses calculated for medicines administered in paediatric and neonatal wards for which the calculation strategy was known. By contrast, just 9 (4%) of the 207 dose calculations in other wards were performed using the formula. The relationship between DSR and formula use for paediatric doses The strong association between formula use and calculation of doses for paediatric patients did not stem from the fact that the dose was intended for a paediatric patient per se. Rather, the association could be attributed to the fact that the heaviest concentration of medicine administrations with a complex DSR occurred in paediatric and neonatal wards. In children s wards, of the 41 medicine administrations that required a dose calculation, 25 (61%) had a complex DSR. This heavy concentration in children s wards of medicine administrations for which nurses were not easily able to calculate the dose to administer using proportional reasoning contrasted starkly with the corresponding proportion occurring in adult wards, where only 14 (4%) of the 388 medicine administrations had a complex DSR. Among medicine administrations for which nurses calculation strategies were known, 21 (64%) of the 33 medicine administrations in children s wards had a 193

207 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses complex DSR. This proportion can be compared to just 8 (4%) of the 207 medicine administrations in adult wards having a complex DSR. The large proportion of complex DSRs in paediatric and neonatal wards was, in part, the result of nurses frequently needing to perform a prior calculation of the prescribed dose, based on the patient s body weight. In children s wards, for 14 (42%) of the 33 medicines that required calculation of the dose to administer, nurses had performed a prior mg/kg calculation to determine the prescribed dose. Twelve of these calculations resulted in a complex DSR, making mental computation difficult for nurses. A prescribed dose determined on the basis of a mg/kg value or dose range rarely resulted in a simple scalar relationship between the stock mass and the prescribed mass. An example taken from the neonatal unit at Alexander Metropolitan Hospital (Event #806) was a prescribed dose of 10.7 mg of ursodeoxycholic acid calculated by the nurse on the basis of the infant s weight of 2.13 kg and an order for 5 mg/kg/dose. Calculation of the dose to administer resulted in a volume of 0.43 ml being administered orally from liquid stock whose concentration was 25 mg/ml. An awkward prescribed dose of 10.7 mg was the result of the nurse having to multiply 5 mg by This awkward value meant that the numerical relationship between the prescribed mass (10.7 mg) and the stock mass (25 mg) made the nurse s use of proportional reasoning and mental arithmetic in calculating the dose to administer virtually impossible. The obvious alternative was for the nurse to use the formula, which she did. The evidence suggests the strong link between formula use and calculation of paediatric doses stems from the fact that among paediatric medicine administrations, there is a heavy concentration of medicine administrations with complex DSRs and nurses faced with complex DSRs are more likely to use the formula than they are for simple DSRs. An additional factor likely to have contributed to the high formula use by nurses in the calculation of paediatric doses relates to the high use of calculators in paediatric wards. Nurses often have to perform a greater number of calculations in paediatric wards, including calculation of the prescribed dose, based on the patient s weight, and calculation of the intravenous infusion rate. Prior calculation of the prescribed dose usually involves the use of a calculator which remains in the nurse s hand, making calculation of the dose to administer using the formula a process usually performed using a calculator the logical next step. 194

208 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses For paediatric nurses performing such calculations on a daily basis, it seems that a calculator is generally regarded as an essential tool for quick and accurate calculation of the prescribed dose. If nurses need to calculate the prescribed dose, the need to use a calculator arises because of the awkward nature of the numbers involved when the child s weight is multiplied by the relevant mg/kg value. For example the child s weight is frequently expressed as a decimal number, correct to two decimal places, particularly if the patient is a neonate. Such a decimal value results in a multiplication that is difficult and possibly error prone to perform were mental arithmetic to be used. Rather, nurses most often use calculators for such calculations. Because nurses have calculators still in their hands from previous calculations, it seems logical and natural that they would continue to use the calculators as they progress from calculation to calculation, even if in some cases, the use of proportional reasoning and mental arithmetic may be possible. Cognitive load may also have been a factor of greater relevance when nurses perform calculations in order to administer medicines to paediatric patients. This factor may predispose nurses to use the formula and a calculator. Factors that may add to nurses cognitive load include the need to perform a metric conversion (likely because a child s dose is often a fraction of the adult dose and may be expressed in a smaller unit of measure than the available stock), and other calculations prior, or subsequent, to calculation of the dose to administer. The likelihood of having to calculate intravenous infusion rates in association with medicines administered to paediatric patients is likely to be higher, compared to adult wards, because medicines are more likely to be administered intravenously than orally or by injection, as occurs more frequently in adult wards. This fact was confirmed by comparing the stock forms used by nurses in the two types of ward area during observations sessions. The impact of stock form on calculation strategy for paediatric doses The high incidence of formula use in paediatric wards could be traced to the high proportion of difficult calculations in paediatric wards. However the impact of prior calculation of a mg/kg quantity adopted as the prescribed dose only partially explained the heavy concentration of difficult calculations in paediatric wards. Another factor examined to assess whether it contributed to the high concentration of difficult calculations in paediatric and neonatal wards was the stock 195

209 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses form. Three main stock forms were identified among the pharmaceutical products administered during the study: solid form (tablets and capsules); liquid form (volumes of liquid measured in millilitres); and powder for reconstitution as a liquid, typically antibiotics. The trigger for investigating stock form as a possible influence on calculation strategy was the realisation that in paediatric and neonatal wards few medicines were administered in tablet or capsule form a stock form associated with simple DSRs such as 2:1, 1:2, and 3:2 and proportional reasoning strategies. Rather in paediatric wards medicine administrations were more typically associated with complex DSRs, and consequently, a reduced likelihood of nurses using proportional reasoning strategies to calculate doses. Administration of tablets for which mental computation of the dose to administer was usually possible, accounted for just three (9%) of the medicines administered in children s wards. This stood in direct contrast to the dominant stock form used in other wards where tablets and capsules that allowed mental computation of the dose to administer accounted for 163 (79%) of the 206 medicines administered. By contrast, in paediatric wards, the primary forms of stock used were liquids and powdered antibiotics, both associated with a high proportion of complex DSRs. Liquid medicines accounted for 19 (56%) of the medicines administered, of which 13 had a DSR rated as complex. For 12 of these, nurses used the formula to calculate the dose to administer. Liquids reconstituted from powdered stock accounted for 11 (33%) of the medicines administered, of which 8 had a DSR rated as complex. For 5 of these nurses used the formula to calculate the dose. In summary, paediatric doses were strongly associated with complex DSRs that made mental computation of the dose to administer difficult for nurses. As a result, use of the formula dominated the calculation strategies of paediatric nurses. The complex DSRs were in turn the result of two factors. The first factor was prior calculation by nurses of the prescribed dose on the basis of a constant number of milligrams per kilogram of the child s weight. Such calculations invariably resulted in awkward doses that precluded the use of proportional reasoning in the dose calculation. 196

210 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses The second factor was the high proportion of complex DSRs resulting from the dominant stock forms used in the treatment of paediatric patients liquid formulations and stock in the form of a powder that needed to be reconstituted as a solution. These two stock forms were strongly associated with complex DSRs which, in turn, influenced nurses to use the formula to calculate the dose to administer Summary: Frequency of dose calculation strategy by DSR Table 5.16 provides a summary of the distribution of dose calculation strategies nurses used to calculate medicine doses according to the DSR for the medicine administration. 197

211 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses Table 5.16 Distribution of medicine administrations requiring dose calculation by calculation strategy used and dose-to-stock ratio Calculation strategy used DSR class n:1 DSR class 1:n DSR class n:2, where n is odd 2:1 3:1 4:1 n 5 1:2 1:3 1:4 n 5 3:2 n 5 Complex DSR Two products (varied DSRs) Formula Multiplicative reasoning or repeated addition Fraction operation or division process Halving combined with addition Complex proportional reasoning Total Simple addition Total administrations with known calculation strategy Total administrations with unknown calculation strategy Total dose calculations performed

212 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses 5.11 Nurses innovative dose calculation strategies Nurses were able to perform many of the more difficult calculations using proportional reasoning strategies and mental arithmetic, without the need for a calculator or pen and paper. These more difficult calculations were associated with medicine administrations for which the DSR did not fall within the three classes of DSR, n:1, 1:n, and n:2, discussed previously. How nurses performed some of the more difficult calculations will now be explored Creating mathematically convenient liquid solutions when reconstituting medicines Nurses use of proportional reasoning extended beyond calculating the number of tablets or a volume to be administered from a liquid pharmaceutical product. Nurses created liquid solutions from powdered pharmaceutical products and diluted available stock ampoules. In each case, nurses used their proportional reasoning skills with the aim of achieving a solution concentration that enabled them to use simple proportional reasoning strategies and mental computation to calculate the dose to administer. They achieved this goal through careful and deliberate mathematical manipulation of the concentration of the solution they created, often creating what I call a mathematically convenient solution. The two medicine administrations shown in Examples 16 and 17 required a complex series of calculations prior to the nurse, Cate, administering each medicine by intravenous infusion to a paediatric patient. In both examples, Cate calculated the prescribed dose for the child based on a mg/kg value, then reconstituted a vial of powder. Cate followed a process of creating a solution whose strength was carefully designed to allow her to then use proportional reasoning strategies to determine the dose to administer. Both medicine administrations required a metric conversion. Cate s explanations describe the complex calculation processes she used in each case. 199

213 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses Example 16 Complex proportional reasoning Prescribed dose and route Stock used Flucloxacillin 650 mg; IV infusion 1 g per vial of powder for reconstitution Dose-to-stock ratio 13:20 Administered dose 6.5 ml of the reconstituted solution created The medicine was prescribed for a two-year-old boy weighing 13 kg. Before calculating the dose to administer, Cate performed a calculation to confirm that the prescribed dose of 650 mg the doctor had recorded on the patient chart accorded with the recommended dose of 50 mg/kg of the child s body weight. Cate stated that she had done this calculation in her head. Cate then proceeded to create a solution from the vial of antibiotic powder. She prepared the solution according to a carefully planned strategy. She used a 10 ml syringe to draw up 9.4 ml of water for injection to reconstitute the flucloxacillin powder. She already knew this volume would result in a final solution volume of 10 ml, allowing for the displacement of the powder. Cate explained each step as she went. Cate: With fluclox you have to take in the volume that the powder takes up. So I ll add about nine point four mils of water sterile water that should be enough. So the displacement is probably it has to be point six. Cos you re going to end up with a gram in ten mils. That s what your end volume will be. RG: So you expect that to be ten mils with what you ve done? Cate: Yeah, and if it s a fraction less, I ll make it up to ten mils. [She mixes the water for injection and powder.] I might need a tiny bit more I ll need a tiny bit more water. [Adds more water] That s fine that s ten! And I m going to give six point five. Because it s a gram one gram in ten mils and the dose is 650 [mg]. Therefore I m going to give 6.5 [ml]. RG: You re too quick for me! One gram in ten mils? There was laughter, then Cate explained again, almost as quickly: Cate: Yep. One hundred milligrams per mil. Six hundred and fifty milligrams equals six-point-five mils. That OK? (Cate, N5, MH, audio, Event #655) 200

214 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses Cate checked the flucloxacyllin dose with a colleague who observed her pushing it into the burette with 50 ml of water and setting the IV pump to deliver the infusion over one hour. Example 17 Complex proportional reasoning Prescribed dose and route Stock used Cefotaxime 190 mg; IV infusion 500 mg per vial Dose-to-stock ratio 19:50 Administered dose 1.9 ml of the reconstituted solution created Before Cate could administer this dose she went through similar calculations, first establishing that the prescribed dose for the baby was 190 mg, a quantity she calculated on the basis of the baby s weight. She then explained how she had calculated the concentration of the reconstituted solution she had created using the 500 mg vial of cefotaxime powder and then the dose to administer. If you put in four-point-eight mils you should end up with a volume of five mils, which equals a hundred milligrams per mil. And then we re going to give a hundred and ninety [mg], so now we ve got to give one-point-nine mils. Cate used a 5 ml syringe to draw up the solution created by mixing the 4.8 ml of water with the powder in the vial. She discarded most of the liquid leaving the 1.9 ml she needed to administer. She explained how she would administer it in a tiny volume about 10 ml cos he s only a tiny baby before setting the infusion to run over an hour. (Cate, N5, MH, audio, Event #155) In these two calculations, the key relationship that made use of proportional reasoning strategy and mental calculation possible was not the DSR (13:20 and 19:50 respectively). Indeed, in each case the DSR suggested that mental calculation would be difficult. Rather, mental calculation was made possible because nurses created a mathematically convenient solution such that the volume of the solution and the mass of the powder contained within it were numerically related in a way that made easy calculation possible. 201

215 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses When the stock mass was 1 g (or 1000 mg), a 10 ml solution was created. This solution was equivalent to 100 mg per ml, making calculation of the volume to deliver 650 mg a matter of multiplying both terms in the solution concentration by 6.5. When the stock mass was 500 mg, a 5 ml solution was created, again resulting in a solution equivalent to 100 mg per ml. Calculation of the volume to deliver 190 mg was then achieved by multiplying both terms in the solution concentration by 1.9. On some occasions when nurses created mathematically convenient solutions that allowed them to easily calculate the dose to administer, they followed a reconstitution procedure provided in printed information that came as part of the product packaging. An example of such a reconstitution guide 25 (for the same medicine administered in Example 14) is shown in Figure 5.4. Figure 5.4. The manufacturer s instructions for reconstituting flucloxacillin powder The manufacturer s guide removes the need for nurses to use a trial and error approach of gradually adding water to create a solution of fixed concentration that takes into account the displacement of the powder. Instead, the guide gives a recipe for how much water nurses should add to the 1 g of powder, depending on the final 25 Note that the suggested 9.3 ml of water to be added to create a 100 mg per ml solution differs slightly from the 9.4 ml suggested by Cate 202

216 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses solution volume they wish to obtain. It may also prevent nurses from making errors by assuming there is a linear relationship between the volume of water to add and the concentration of the solution they wish to create. Further, when nurses calculate the dose to administer, they can confidently use the clear statement in the guide of the concentration of the solution they have created to assist their calculation. By following the illustrated flucloxacillin guide to reconstitution which allows for displacement, nurses have a choice of four final solution volumes: 10 ml, 5 ml, 4 ml, and 2 ml respectively. These four final volumes result in solutions whose concentrations are shown below. For each solution concentration, a final division process converts the concentration to the equivalent per ml form that appears on the top line of the table in Figure 5.4. On other occasions, rather than consulting a guide, nurses determined the volume of the solution themselves, selecting it so that it was carefully matched to the stock mass that would be contained within it. Always the goal was to create a solution whose concentration allowed easy subsequent mental calculation of the dose to administer. Example 18 illustrates how a nurse in the dialysis ward, Joan, approached a medicine administration with a complex DSR. She diluted a medicine already in liquid form to create a mathematically convenient solution, carefully crafting the concentration of the solution to facilitate application of proportional reasoning to calculate the dose to administer. Example 18 Complex proportional reasoning Prescribed dose and route Stock used Heparin 2000 international units; IV infusion with dialysis Ampoule labelled IU per 5 ml Dose-to-stock ratio 2:25 Administered dose 2 ml of the solution created Joan referred to the label on the stock ampoule: it contained international units per 5 ml. She mentally converted this solution to a series of equivalent solutions: 203

217 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses Five thousand units in one mil; fifteen thousand units in three mils. (Joan, N20, MH, Event #336) Joan then proceeded to work with the concept that by diluting 3 ml of the fluid from the ampoule to create a 15 ml solution she would have a solution with a concentration of IU in 15 ml. This concentration would facilitate calculation of the dose to administer by proportional reasoning using mental arithmetic. Using a 20 ml syringe, Joan withdrew 3 ml from the ampoule then added 12 ml of normal saline. The solution created contained IU in 15 ml, and was thus equivalent to 1000 IU in 1 ml. It was an easy final step for Joan to use proportional reasoning, mentally doubling both terms in the concentration, to calculate that she would need 2 ml of the solution she had created to deliver the prescribed dose of 2000 IU of heparin. She administered this dose by intravenous infusion with dialysis. The medicine administration in Example 16 differed from the previous two examples involving reconstitution of a powder in that the stock was already in liquid form. The example illustrates how, by careful manipulation of the volume of solution created to match it appropriately to the mass contained in the solution, a nurse can reduce a medicine administration with a complex DSR to one where proportional reasoning involving easy mental manipulation is possible. The sequence of steps in the calculation process was, in essence, identical to the steps in the previous two examples. The inventiveness of nurses in their clinical practice and their preference for calculation methods based on proportional reasoning was also evident in the information nurses provided in focus groups. One such focus group, held in the recovery ward of Alexander Metropolitan Hospital, revealed additional techniques that nurses in that ward regularly used to simplify the calculation and administration of intravenous medicines. With just two recovery ward nurses in attendance, Florence and Renata, the focus group provided an opportunity to obtain information from nurses about medicine administration practices that related specifically to the recovery ward. Dilution of a stock ampoule to create a solution for which the concentration was carefully crafted to facilitate proportional reasoning and mental calculation of the dose to administer was one of the practices that nurses highlighted. 204

218 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses Renata, assisted by Florence, gave a number of examples of how she might create a diluted solution for intravenous 26 administration, with the intention of avoiding (a) use of the formula, and (b) the need to calculate and measure a dose that was extremely small. Renata used the example of the medicine droperadol, available in ampoules of strength 2.5 mg in 1 ml, to explain why creating such solutions simplified medicine administration in their work. And they give us weird doses, like point-fives or point-seven-fives or pointeights. I had a point-eight yesterday. Renata explained how she and her colleagues in the recovery ward frequently used a technique that involved creating a diluted solution from a stock ampoule, tailoring the concentration to enable mental calculation of the volume they needed to administer. Say they [the doctor] want to give point-eight of a milligram. We ve just learnt Well I, for myself, and I know for a few of the other girls I m not sure about Florence all we do now is we don t even worry about trying to work out break it up And we just put the whole drug [ampoule] we make it up to two-and-a-half [ml] so that the concentration is a milligram per mil. So it s one for one. So then you give point-eight of a mil without having to worry about, like, trying to break this [contents of the ampoule] up into something tiny. (Renata, N68, AH) Table 5.17 lists the droperadol example and several others that Renata and Florence provided to illustrate this practice, one they suggested I was unlikely to see in other wards of the hospital, except possibly in the intensive care unit. In relation to the first medicine listed, dropederol, the same dilution process (Column 4) is used for all three sample prescribed doses (Column 2). In relation to the last medicine listed, clonidine, a different dilution process is used for each of the three sample prescribed doses. 26 Intramuscular drugs are not usually diluted because administration of a large volume may cause pain 205

219 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses Table 5.17 Examples of dose calculations simplified by the creation of a mathematically convenient solution Medicine Example of prescribed dose Stock available (ampoule) Dilution process a Concentration of diluted solution Equivalent concentration Volume to be administered Droperadol 0.5 mg 0.75 mg 0.8 mg 2.5 mg in 1 ml Make volume up to 2.5 ml: Put an extra 1.5 ml of Normal Saline in the syringe. Total volume = 2.5 ml 2.5 mg per 2.5 ml 1 mg per 1 ml 0.5 ml 0.75 ml 0.8 ml Morphine 2 mg 10 mg in 1 ml Mix morphine ampoule with 9 ml of Normal Saline. Total volume = 10 ml 10 mg per 10 ml 1 mg per 1 ml 2 ml Fentanyl 30 microg b 100 microg in 2 ml Mix contents of ampoule with 8 ml Normal Saline Total volume = 10 ml 100 microg per 10 ml 10 microg per 1 ml 3 ml Clonidine 15 microg 30 microg 150 microg in 1 ml Make volume up to 10 ml Make volume up to 5 ml 150 microg per 10 ml 150 microg per 5 ml 15 microg per 1 ml 30 microg per 1 ml 1 ml 1 ml 75 microg Make volume up to 2 ml 150 microg per 2 ml 75 microg per 1 ml 1 ml a b A label attached to the solution indicating the composition and concentration of the liquid is vital to avoid medication error. The abbreviation microg is recommended to reduce medication error through misinterpretation (Australian Commission on Safety and Quality in Health Care, 2016). 206

220 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses Not all the examples of dilution processes listed in Table 5.17 resulted in onefor-one solutions, however in every case the concentration of the diluted solution allowed easy mental calculation of the volume to be administered. Naloxone, ephedrine, hydralazine and Arranon (nelarabine) were among the other medicines Renata and Florence said nurses in the recovery ward regularly diluted in this way prior to administering them intravenously Proportional reasoning using body parts Nurses inventiveness in the strategies they used to calculate medicine doses included the use of body parts to assist in their use of proportional reasoning. Examples 19 and 20 describe the calculation strategies of two nurses as they prepared an identical dose of a liquid medicine, ibuprofen, for oral administration on consecutive days in the paediatric ward of Gemmaville Rural Hospital, possibly to the same child. The first nurse, Verity, used her fingers to aid her in her calculation. By contrast, Roberta used the formula and a calculator to determine the dose to administer. Example 19 Fraction operation combined with repeated addition Prescribed dose and route Stock used Ibuprofen 350 mg; oral 100 mg per 5 ml Dose-to-stock ratio 7:2 Administered dose 17.5 ml Verity s patient was a child. She decided not to use the usual form of the medicine given to adults 200 mg tablets because she could not sensibly break a tablet to get the 1¾ tablets she would need to administer. The alternative formulation of ibuprofen available to her was a liquid labelled 100 mg/5 ml. Under pressure from her fellow nurse to calculate the dose using her calculator (presumably in tandem with the formula), Verity resisted, explaining: I m using my brain, because you don t always have a calculator that s what I got taught in Adelaide! 207

221 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses Verity proceeded with her calculation of the volume to give, using her fingers as an aid. One by one, Verity held up three of her fingers and then, finally, an additional crooked, or half finger. As she did this she explained: Five [ml], ten [ml] so that s two hundred [mg] fifteen [ml] three hundred [mg] and then half of five [ml] which would give us fifty [mg]. That s right, isn t it? Two-point-five [ml]. (Verity (N69, GH) Verity s method was both visual and, to an extent, kinaesthetic. She utilised a proportional reasoning process involving repeated addition combined with a fraction operation. Verity used each finger to represent 100 mg or 5 ml of liquid, so three fingers equated to 300 mg or 15 ml of liquid. Half a finger equated to half of 100 mg, that is, 50 mg or 2.5 ml of liquid. After carrying out the initial calculation, her procedure also incorporated not one, but two checks. With three-and-a-half fingers raised, Verity counted out across them again, finger by finger to check the calculation. So that s five, ten, fifteen, seventeen and a half [ml]. In respect of the half finger she raised, Verity explained how she was able to use her finger method to deal with a simple fraction such as half. And then the half then we just need the fifty out of the hundred [mg], so it s half of whatever. Otherwise if it [the fraction] was something else [other than an easy half] then I d really need a calculator! On completing the calculation, Verity reflected on the answer she had obtained, questioning whether the quantity was too large: Seventeen-point-five mils seems a lot! She stressed that she always double-checks with a calculator, then proceeded to key the relevant values into the calculator in the order consistent with using the formula. Verity explained each value as she keyed it into the calculator. What we want divided by what we ve got.three hundred and fifty divided by one hundred times five equals seventeen-point-five. 208

222 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses Verity gave the following explanation of why she followed her initial calculation using her invented finger method with a double-check using the formula and a calculator. But I love double-checking. I always do [check], because I m such a sceptical person when it comes to medication. (Verity, N69, GH, audio, Event #1274) Example 20 In a total contrast to Verity s method, to perform the same calculation (see Example 17) Roberta followed the standard sequence of numbers in the formula as she keyed the values into the calculator. Three hundred and fifty divided by a hundred times five equals seventeen point five. (Roberta, N60, GH, Event #1284, formula method) Using a 20 ml oral (pink) syringe, Roberta drew up 17.5 ml of the liquid and squirted it into the child s mouth Using a syringe scale as an aid to proportional reasoning Several examples follow (see Examples 21 24) illustrating nurses innovative use of the scales on syringes to assist in calculating or confirming the volume of liquid to administer. In these examples, nurses extended the intended function of the millilitre scale printed on the syringe as a measure of volume by using the graduations on the scale as a scale for mass (milligrams in Example 21, 23, and 24), or vials and part-vials as well as mass (Example 22). 209

223 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses Example 21 Complex proportional reasoning using a syringe scale (ml) to measure mass (mg) Prescribed dose and route Stock used Ketorolac 15 mg; intramuscular injection Ampoule labelled 30 mg per 1 ml Dose-to-stock ratio 1:2 Administered dose 0.5 ml Susan broke open the 1 ml ampoule of ketorolac. As she drew up the contents into a 3 ml syringe, she explained her method for calculating and preparing the dose to administer. Thirty milligrams is at the one mil level [points to 1 ml]. So fifteen milligrams is at the half mil mark [points to ½ ml]. (Susan, N4, MH, Event #104) Susan s calculation method is illustrated in Figure 5.5, which is a reproduction of the sketch I drew on the observation schedule as I observed Susan s technique and listened to her explanation. Figure 5.5. Thinking in milligrams on a millilitre scale Susan discarded fluid from the syringe, retaining the ½ ml needed to administer 15 mg of ketorolac to the patient, a practice consistent with nurses usually being required to discard unused medicine. 210

224 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses Example 22 Complex proportional reasoning using a syringe scale (ml) to measure mass (mg) Prescribed dose and route Stock used Vitamin K 15 mg; IV dose Ampoule labelled 10 mg per ml Dose-to-stock ratio 3:2 Administered dose 1.5 ml Using proportional reasoning, Susan determined that she would need 1½ vials to deliver 15 mg of Vitamin K to the patient. As she used a 3 ml syringe to draw liquid from two ampoules, Susan described how she had three different scales in mind as the liquid moved along the millilitre scale (see Figure 5.5). As the liquid reached the 1 ml mark she registered the volume as 1 vial. Then she noted that at the 2 ml mark she would have two vials more than the 1½ vials she needed. So by drawing liquid up to a point halfway between 1 ml and 2 ml on the syringe scale i.e. the 1½ ml mark she would have the required 1½ vials of Vitamin K. As the liquid reached the 1 ml mark, then the 2 ml mark, Susan called out the number of vials along the millilitre scale: One vial, two vials etc. She explained she was also measuring the corresponding number of milligrams along an imaginary scale on the other side of the syringe: Ten milligrams [corresponding to one vial], twenty milligrams [corresponding to two vials], etc. Susan s technique of using the syringe scale to measure quantities expressed in three different units vials, millilitres and milligrams is illustrated in Figure 5.6. Figure 5.6. Thinking in vials as well as milligrams on a millilitre scale 211

225 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses Susan: Two vials makes two mils and to get because we just need half of one of them. RG: So one vial equates with ten milligrams. That s two vials [points to the 2 ml mark]. So that s your one and a half vials [points to the 1½ ml mark]? Susan: So two vials [points to 2 ml mark] and there s your fifteen milligrams [points to 1½ ml mark] or one-and-a-half vials? Susan then went on to explain how she would measure a different dose, one such as 7.5 mg. Susan: If I didn t want ten milligrams Sometimes I only want seven- point-five milligrams. Susan pointed to the 0.75 ml mark on the syringe corresponding to a mass of 7.5 mg. (Susan, N4, MH, audio, Event #135) Example 23 Complex proportional reasoning Prescribed dose and route Stock used Cefotaxime 190 mg; IV infusion 500 mg per vial Dose-to-stock ratio 19:50 Administered dose 1.9 ml Example 3 in described how Cate reconstituted a vial of cefotaxime powder to create a solution to deliver a 190 mg dose to a baby in the paediatric ward of Murraydale Regional Hospital. Cate discarded most of the liquid leaving the 1.9 ml she needed to administer. Cate used the millilitre scale on a 5 ml syringe a similar way as a scale for the dose expressed in milligrams. After Cate had administered the dose to the baby, she drew a sketch for me (see Figure 5.7) to illustrate how, as she was drawing the solution into a 5 ml syringe, she was also using the millilitre scale on the syringe to confirm the number of milligrams represented in each whole millilitre of liquid that she drew up. 212

226 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses Figure 5.7. Confirming a dose in milligrams on a millilitre scale Cate pointed to the graduations along the syringe scale on her sketch as she read out the equivalences, based on proportional reasoning: A hundred milligrams in one mil, two hundred milligrams in two mils, three hundred milligrams in three mils, etcetera. (Cate, N5, MH, audio, Event #155) Using this method, Cate was able to confirm that 100 mg of cefotaxime would correspond to 1 ml of liquid, 200 mg would correspond to 2 ml, etc. It was evident that 190 mg would correspond to a volume of liquid just less than 2 ml, so she was able to confirm that the 1.9 ml she had calculated independently was indeed the volume she would need to give the baby to deliver 190 mg. Example 24 Complex proportional reasoning Prescribed dose and route Stock used Cefazolin 200 mg; IV infusion 1 g per vial Dose-to-stock ratio 1:5 Administered dose 2 ml Another nurse observed in the paediatric ward of Murraydale Regional Hospital used the same technique to confirm the dose she had calculated was correct as she prepared it for administration. Jude had reconstituted a 1 gram vial of cefazolin powder, creating a 100 mg in 1 ml solution. To give the prescribed dose of 200 mg she then calculated she would need to administer 2 ml of the solution. Jude 213

227 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses began to draw up the required 2 ml into the syringe. As the liquid reached the 1 ml mark, then the 2 ml mark she counted out: One hundred milligrams, two hundred milligrams. (Jude, N19, MH, Event #245) Not only was Jude measuring the medicine but the procedure she used to draw up the liquid also acted as a check on her calculation Nurses use of functional strategies During observation sessions, nurses explanations of their calculation methods indicated little to suggest nurses use functional strategies in their dose calculations. However, there were five administrations that took place at Alexander Metropolitan Hospital for which use of a functional strategy was possible. Table 5.18 gives a summary of these five administrations. Table 5.18 Medicine administrations for which a functional strategy may have been used Event no. Ward Prescribed dose Stock used DSR Amount administered 660 a Neonatal 6.25 mg b 1 mg/1 ml 25: ml 665 a Neonatal 6.3 mg b 1 mg/1 ml 63: ml 905 a Neonatal 2.4 mg b 1 mmol/1 ml 12:5 2.4 ml 906 a Neonatal 0.4 mg b 1 mmol/1 ml 2:5 0.4 ml 867 ICU 24 mg 1 mg/1 ml 24:1 24 ml a b Four doses were incorrectly recorded in the spreadsheet as not requiring a calculation. Calculated by the nurse on the basis of the infant s weight using a mg/kg value stated by the doctor The fact that the stock used to administer these doses was 1 mg/1 ml or 1 mmol/1 ml suggests the nurse may have applied the simplest of functional strategies, a function rule recognising the volume has the same numerical value as 214

228 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses the mass. Following Vergnaud s model of a functional strategy, the dose for Event # 665 could have been calculated as follows (see Table 2.2, 2.5.3): Figure 5.8. Function rule: The number of millilitres is the same as the number of milligrams. It is equally plausible that in each case the nurse applied the unitary method. For example, the stock used for administration Event #665 was 1 mg/1 ml, so application of the unitary method might have proceeded as follows (see Table 2.2, 2.5.3): 1 ml delivers 1 mg of the medicine. So ml delivers mg of the medicine. Give 6.3 ml. Nurses calculation strategies for these medicine administrations went unrecorded at the time. The reasons for this were (a) the focus was on nurses prior calculations of the prescribed dose, and (b) the simplicity of the dose calculation resulting from the equivalence of the number of millilitres administered and the number of milligrams or millimoles prescribed (i.e. ml = mg/mmol) effectively disguised the fact that a dose calculation was being performed. The result was that four of the five such dose calculations went unnoticed and the administrations were incorrectly recorded in the spreadsheet as not requiring a dose calculation. One nurse in the neurology ward at Alexander Metropolitan Hospital used what appeared to be a functional strategy to check her calculation, having calculated the dose using a scalar method. The nurse was administering 6 mg of noradrenaline 215

229 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses acid tartrate by intravenous infusion from stock labelled 2 mg/2 ml in the neurology ward. The nurse explained her scalar calculation strategy. Need six milligrams. Two plus two is four, plus two is six. Then without any explanation of what she was doing or why, she articulated what seemed to be a check on the calculation. One milligram in one mil, or one-to-one. So I need to draw up six mils. (Deidre, N33, AH, Event #985) The only other indication of nurses use of functional strategies emerged in a focus group at Alexander Metropolitan Hospital. Lindie, a very experienced nurse in the neonatal ward, described a shortcut transformation involving doubling and moving the decimal point one place to the left. This method was an example of the medicine-specific transformation methods described by Hoyles et al. (2001) as functional strategies. Lindie illustrated her shortcut method using the example of an order for 4 mg of caffeine citrate, administered from stock labelled 50 mg in 10 ml, a concentration she broke down to 5 mg in 1 ml. Lindie explained that she had learnt this method from other nurses, remarking it was convenient to use if she was asked to quickly check a colleague s medicine administration. When questioned about how and why the shortcut method worked, Lindie was unable to give a clear answer. I know that it works because if you do it the long way [using the formula] you get the same answer. (Lindie, N23, AH) 5.13 Calculator use in clinical practice Nurses made very little use of calculators to calculate the dose to administer during observation sessions. A range of factors were investigated to see if they were associated with nurses use of calculators. These factors included hospital, ward, calculation strategy, administration route, and dose-to-stock ratio. In fact the data suggested a complex inter-relationship between several of these factors. Calculator 216

230 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses use was found to be associated with calculation strategy, ward, administration route, and dose-to-stock ratio. A calculator was used for only 26 (6%) of the 431 medicines administrations requiring a dose calculation, and for 23 of these, the calculator was used in conjunction with application of the formula. For the remaining 3 medicine administrations, although the calculation strategy was unknown, because they all occurred in the neonatal unit of Alexander Metropolitan Hospital and followed nurses mg/kg calculations of the prescribed dose resulting in an awkward value and a complex DSR, it seems likely that for these dose calculations too, nurses were most likely to have applied the formula. Nurses did not use calculators in association with proportional reasoning calculation strategies, instead performing all such computations mentally. Thus, the data suggests a very strong association between nurses use of calculators and formula use. The association extends beyond these two factors, however, to include calculation of medicine administrations for paediatric and neonatal patients. Twenty-two (88%) of the 26 medicine administrations for which nurses used a calculator occurred in a paediatric or neonatal ward. The remaining 4 medicine administrations for which nurses used a calculator took place in an intensive care unit, an emergency unit, a rehabilitation ward, and a medical/palliative ward in two different hospitals. Just two administration routes were involved in the use of calculators for dose calculation, intravenous (14 instances) and oral (10 instances). For a further two dose calculations for which a calculator was used, the route of administration had not been recorded. This finding is perhaps not surprising given that overall, 91% of medicines requiring a calculation were administered by these two routes. The 54% proportion of dose calculations for which a calculator was used in association with the intravenous administration route was higher than expected, given that only 64 (15%) of the 431 medicine administrations requiring a dose calculation were administered intravenously. The explanation for this lies in the fact that 12 of the 14 intravenous dose calculations supported by a calculator were administered in paediatric or neonatal wards. In relation to the DSR for medicine administrations calculations where a calculator was used, 23 of the 26 had a DSR that did not lend itself to mental calculation, with the DSR rated as complex. In summary, the data revealed a strong inter-relationship between application of the formula, supported by calculator use, 217

231 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses for medicines with a complex DSR that were administered by intravenous infusion in children s wards The impact of medicine packaging on dose calculation Two particular products administered by nurses suggested that certain pharmaceutical products were packaged in ways that made available to the nurse a quantity that exactly matched the prescribed dose. These products were prefilled syringes of enoxaparin (brand name Clexane), administered predominantly at Gemmaville Rural Hospital, and sealed glass ampoules of heparin, administered only at Murraydale Regional Hospital and Alexander Metropolitan Hospital. The packaging in unit-dose form of these two medicines highlighted how the practice of manufacturers tailoring medicines exactly to commonly prescribed doses meant that nurses had no need to perform a dose calculation. Olivia explained how both heparin and Clexane are anticoagulants used to prevent clots during bedrest. All surgical patients are on either heparin, which is administered two or three times a day, or Clexane which has a different structure. (Olivia, N25, AH) Table 5.19 shows the breakdown of doses of enoxaparin and heparin, administered. Table 5.19 Frequency of enoxaparin and heparin doses administered by hospital Hospital Gemmaville Rural Murraydale Regional Alexander Metropolitan No (%) of observed medicine administrations (n = 1571) No. (%) of doses administered Enoxaparin (n = 46) Heparin (n = 33) 538 (34%) 23 (50%) 0 (0%) 659 (42%) 15 (33%) 18 (55%) 374 (24%) 8 (17%) 15 (45%) 218

232 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses Enoxaparin accounted for 46 (3%) of the 1571 medicines administered, and 35 (36%) of the 98 medicines administered subcutaneously. The remaining 11 doses of enoxaparin were administered intravenously, with dialysis, in the renal unit of Murraydale Regional Hospital. All doses of enoxaparin were administered from prefilled, single-dose syringes. The strengths printed on the labels of the syringes nurses selected to administer enoxaparin during the study included 20 mg in 0.2 ml, 40 mg in 0.4 ml, 60 mg in 0.6 ml, 80 mg in 0.8 ml, and 100 mg in 1 ml. In all but one case, nurses simply selected the syringe for which the stock mass coincided with the prescribed dose. This procedure greatly simplified the medicine administration because nurses did not need to perform a dose calculation. Nor did nurses need to measure the dose to be administered, instead simply expelling the contents of the prefilled syringe. The exception was an in-between 50 mg dose of enoxaparin, which required the nurse to both calculate and measure the dose to be administered subcutaneously. The nurse calculated she would need to administer 0.5 ml of the 0.6 ml of liquid in a prefilled syringe labelled 60 mg/0.6 ml, and withdrew it using a 1 ml syringe. Heparin, which was not used at all at Gemmaville Rural Hospital, accounted for 33 (2%) of the 1571 medicines administered and 29 (36%) of the 98 medicines administered subcutaneously. The remaining four doses of heparin were administered intravenously. All prescribed doses of heparin were 5000 international units and all were administered using single-dose ampoules containing 5000 international units in 0.2 ml. So for 78 of the 79 prescribed doses of enoxaparin and heparin nurses had no need to perform a dose calculation, a fact confirmed by the 1:1 DSR for each of these medicine administrations. Together, the use of single-dose enoxaparin and heparin products administered without the need for dose calculation accounted for 78 (5%) of the 1571 medicines administered, resulting in a considerable saving in terms of the dose calculations that nurses might otherwise have needed to perform Nurses performance on pen-and-paper medicine administration tasks After completing observation sessions with each nurse, I gave them a questionnaire, a copy of which is included as Appendix 3. Part 1 of the questionnaire, 219

233 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses comprised demographic data and sought information about nurses mathematical backgrounds and their perspectives about dose calculation issues and medication error very little of this is reported in this thesis. Part 2 comprised eight sample medication administration tasks similar to those used to test students dose calculation in university nursing programs. Part 2 was completed by 44 (60%) of the nurse participants. Nurses were asked to complete the tasks showing their working to indicate the techniques you use to work out your answers, showing enough detail that I could do the calculation the same way that you do. Nurses were free to use a calculator whenever they wished but were instructed to indicate their calculator use by marking the relevant part of the calculation with a highlighter pen or by circling it. Then for each item they were instructed to show the quantity of medicine they would administer by shading it on the diagram provided. I analysed nurses performance on five of these tasks, Items 1 5, selected because of their similarities to the dose calculation and measurement tasks nurses performed during their ward medicine administration rounds 27. In this chapter I report briefly on nurses performance on both the calculation and measurement aspects of these five items, and then focus in more detail on those aspects relating to calculation of the dose to administer. In Chapter 6, I report more fully on the dose measurement aspects of nurses responses to the items. For each of Items 1 5, Table 5.20 summarises the features of the medicine administration task, including the DSR and the mathematical demands of the task associated with determining the dose to administer. 27 Items 6-8 required nurses to calculate quantities unrelated to the dose to administer, such as the time required for an infusion to run. 220

234 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses Table 5.20 Features of questionnaire medicine administration Items 1 5 Feature Item 1 (solid form) Item 2 (liquid form) Item 3 (solid form) Item 4 (liquid form) Item 5 (liquid form) Prescribed dose Diazepam 12.5 mg Gentamicin 300 mg Digoxin mg Heparin Digoxin 2500 IU a 0.75 mg Administration route Oral IV infusion Oral Subcutaneous injection IV injection Stock used 5 mg per tablet 80 mg in 2 ml 62.5 microg b per tablet 5000 IU in 0.2 ml 500 microg in 2 ml DSR 5:2 15:4 2:1 1:2 3:2 Dose administered 2.5 tablets 7.5 ml 2 tablets 0.1 ml 3 ml Mathematical demands Decimal manipulation Decimal answer Metric conv. & decimal manipulation Large nos. & decimal manipulation Metric conv. & decimal manipulation a IU = international units b Microg is a recommended abbreviation for microgram, aimed at minimising 1000-times overdosing errors resulting from mcg and µg being misread as mg (Australian Commission on Safety and Quality in Health Care, 2016) (p. 10 ) to: The purpose of the analyses I performed on nurses responses to the items was identify the calculation strategies nurses used to calculate the dose to administer; identify and classify the calculation and measurement errors nurses made (if any); investigate nurses use of calculators, including possible links between calculator use and calculation strategy; and identify any discernable patterns in nurses responses to dose calculation tasks posed as written word problems. 221

235 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses Nurses dose calculation strategies and calculator use Table 5.21 summarises nurses calculation strategies for the five questionnaire items and their use of calculators. The strategies were classified as formula, proportional reasoning, strategy unclear, and item not answered, with proportional reasoning further classified into four sub-categories. The dominant proportional reasoning calculation strategy for each task is indicated by a frame around the number of nurses using that strategy. The final row shows the total number and percentage of nurses who used a calculator for the item/s. 222

236 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses Table 5.21 Nurses dose calculation strategies and calculator use on pen-and-paper medicine administration tasks Calculation strategy Number (%) of nurses using different calculation strategies and calculators by item Item 1 (DSR 5:2) Item 2 (DSR 15:4) Item 3 (DSR 2:1) Item 4 (DSR 1:2) Item 5 (DSR 3:2) All items Strategy used Calculator used Strategy used Calculator used Strategy used Calculator used Strategy used Calculator used Strategy used Calculator used Strategy used Calculator used n = 44 n = 44 n = 44 n = 44 n = 44 n = 220 Formula 23 (52%) (77%) (50%) (59%) (68%) (61%) 75 Proportional reasoning 19 (43%) 0 10 (23%) 1 20 (45%) 0 15 (34%) 2 13 (30%) 0 77 (35%) 3 Multiplicative reasoning/repeated addition Fraction operation/division process Halving combined with addition Complex proportional reasoning Rule of three Unspecified Unclear 2 (5%) 0 (0%) 2 (5%) 2 (5%) 0 (0%) 6 (3%) Not answered 0 (0%) 0 (0%) 0 (0%) 1 (2%) 1 (2%) 2 (1%) Total calculator use 11 (25%) 22 (50%) 12 (27%) 15 (34%) 18 (41%) 78 (35%) a The working of three nurses conveyed this process as being multiplicative rather than involving repeated addition. 223

237 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses The most striking finding concerning the calculation strategies nurses used for the pen-and-paper dose calculation tasks was that the formula was the dominant strategy for all five tasks. This finding contrasts strongly with the very limited use nurses made of the formula during the observation sessions. On the questionnaire tasks, nurses used the formula for 135 (61%) of the 220 items compared to just 28 (12%) of the 240 dose calculation performed during observation sessions for which nurses calculations strategies were known. Further, on the questionnaire tasks, 14 (32%) of the 44 nurses used the formula for all dose calculations performed, compared to none of the 73 nurses using the formula for all calculations in clinical practice. Conversely, on the questionnaire tasks, 18% of nurses made no use of the formula, compared to 25% of nurses during observation sessions. Further, the high rate of formula use was not associated with medicines intended for paediatric patients, a factor which, in clinical practice, led to more complex calculations and a greater likelihood of nurses using the formula. Rather, the high rate of formula use occurred despite all medicines being prescribed for adult patients. Formula use was greatest for Item 2 (DSR 15:4) and Item 5 (DSR 3:2), and least for Item 3 (DSR 2:1). Nurses as Gemmaville Rural Hospital made greatest use of the formula with the 11 nurses who completed the sample medicine administration tasks using the formula, on average, for 4.4 of the 5 tasks. There was little difference in formula use between the 19 nurses at Alexander Metropolitan Hospital and the 14 at Murraydale Regional Hospital where, on average, nurses used the formula for 2.8 and 2.4 of the 5 tasks respectively. Of particular interest was the fact that nurses made greater use of the formula in relation to Item 4, for which the DSR was 1:2, than in relation to Item 1, for which the DSR was 5:2. A possible explanation for the high rate of formula use for Item 4 was that both the prescribed mass and stock mass involved large numbers (2500 international units and 5000 international units, respectively) and a decimal number for the stock volume (0.2 ml). These values may have made mental computation seem more daunting to nurses than if the numbers had been smaller and integers. By contrast, the numerical relationship between the stock mass and prescribed mass in Item 1 was relatively evident, the former being 5 mg and the latter being 12.5 mg, thus making mental calculation easier than for the apparently easier Item 4, 224

238 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses with a DSR of 1:2. Further, the magnitude of the vehicle was an integer, an easy one tablet, making the overall calculation a relatively simple one, able to be performed mentally. Because of the differences between hospitals in their requirements for nurses to sit annual medication calculation tests, it was thought that this might affect nurses tendency to use the formula for the questionnaire tasks. These tests typically include written dose calculation tasks similar to those in the questionnaire. At both Gemmaville Rural Hospital and Murraydale Regional Hospital testing policy is that the formula is provided, nurses are required to show their working, and nurses must achieve 100% competency. At Gemmaville Rural Hospital nurses are advised that their working should reflect use of the formula; at Murraydale Regional Hospital nurses are instructed to use a calculator only to check their answers. Unlike nurses at Gemmaville Rural Hospital and Murraydale Regional Hospital, those at Alexander Metropolitan Hospital were not required to sit for such tests. Consequently, it was thought possible that they might be less familiar with the formula, and less inclined to use it than nurses at the other two hospitals. However, analysis of the formula use at the three hospitals provided no support for this hypothesis. Nurses preference for the formula for Items 1 and 2 was not surprising. With DSRs of 5:2 and 15:4, respectively, both were relatively complex calculations that did not lend themselves to proportional reasoning or mental computation. However, for Items 3, 4, and 5, it was surprising that the majority of nurses chose to use the formula, given that these three items had DSRs of 2:1, 1:2, and 3:2 respectively, thus making the use of proportional reasoning strategies and mental computation viable. During observation sessions, the same sample of nurses had shown their strong preference for proportional reasoning strategies, and their proficiency in using them, for medicine administrations with the same DSRs. A hypothesis tested in relation to nurses dose calculation strategies in clinical practice was that the presence of decimal numbers in the calculation may influence nurses to use the formula. This hypothesis was not supported by the evidence from observation sessions. The same hypothesis was proposed in relation to the questionnaire tasks. However, because decimal numbers or a decimal answer were present in every one of the five tasks, it was not possible to draw any conclusions about whether the decimal numbers had increased the likelihood of nurses using the formula. 225

239 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses Nurses calculator use Analysis of nurses use of calculators on questionnaire tasks relied on nurses shading or circling the relevant part of the calculation to indicate they had used a calculator for all or part of the calculation. Nurses used calculators for 78 (35%) of the 220 items analysed, with 75 (96%) of these instances of calculator use occurring in conjunction with formula use. Nurses used a calculator to support the calculation in relation to 75 (56%) of the 135 items for which they used the formula. This stood in stark contrast to 3 (4%) of the 78 dose calculations for which nurses used a calculator in conjunction with a proportional reasoning strategy. For three of the five items, Items 1, 3, and 5, nurses made no use of calculators in conjunction with proportional reasoning strategies. The strong association between calculator use and formula use was consistent with the pattern of calculator use in clinical practice. During observation sessions, all calculator use was associated with formula use. No nurse used a calculator in conjunction with proportional reasoning, all such calculations having been performed mentally. On the questionnaire tasks, the proportion of calculations for which nurses used a calculator in conjunction with the formula was 56%. This proportion was not as high as that for calculations performed in the clinical setting where it was 82%. This suggests that when nurses are required to provide written answers in test-like conditions, having committed the formula to paper leads nurses naturally on to completing the arithmetical process using written arithmetical methods. They are less likely to switch to using a calculator to complete the computation. By contrast, when nurses use the formula in clinical practice, pen and paper are seldom used. Instead nurses are more inclined to pick up a calculator and key in the three values to complete the calculation. When nurses used calculators in conjunction with the formula, it was usually to perform the entire calculation, possibly in a single operation on the calculator, although it was not possible to confirm this from the working nurses provided. When a calculator was used in conjunction with a proportional reasoning strategy, nurses typically used it to calculate just one in a series of calculation steps, rather than for the entire calculation process. Nurses use of calculators to support different types of calculation strategy is now illustrated in relation to three items, Items 2, 3, and

240 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses Item 2 Figures 5.9 and 5.10 illustrate how two nurses used the formula and a calculator to calculate the dose in Item 2. Deidre used the calculator in the manner most commonly associated with formula use, namely, to perform the entire calculation by entering the values as follows: = (see highlighted steps in Figure 5.9). Figure 5.9. Formula method: Calculator used to perform entire calculation (N33, AH) By contrast, Pragati performed most of the steps in the calculation using penand-paper algorithmic methods and used the calculator only for the last step requiring multiplication of 3.75 by 2 (see Figure 5.10). Figure Formula method: Calculator used to perform last step only (N55, GH) 227

241 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses A third nurse, Neera, used a calculator for Item 2 to assist in applying a proportional reasoning strategy. Figure 5.11 shows her calculation method. Figure Proportional reasoning: Calculator used in last step only (N12, MH) Neera s calculation method involved mentally reducing the stock strength (80 mg in 2 ml) to the equivalent concentration of 40 mg per ml using proportional reasoning. Then, with the aid of a calculator, Neera set about finding how many lots of 40 mg there were in the 300 mg prescribed dose. She would need to give the same number of millilitres (7.5) because 40 mg was contained in each millilitre of the liquid medicine. Although Neera circled the entire answer, it seems she used a calculator to perform just the last step in the calculation process, the division operation, Item 3 Quan used a calculator in conjunction with the formula for Item 3, not to calculate the dose but to perform the metric conversion required prior to calculating the dose. He did this using the method of dimensional analysis. Figure 5.12 shows Quan s calculation method, including his use of a calculator (circled) to convert the prescribed dose from milligrams to micrograms. 228

242 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses Figure Formula method: Calculator used for metric conversion (N61, GH) Item 5 Thirty nurses (68%) used the formula for Item 5, 18 of them using a calculator to perform all or part of the calculation. Thirteen nurses (30%) used proportional reasoning strategies, all without the assistance of a calculator. Figure 5.13 illustrates the ratio version of the rule-of-three method 28 Ae used. Figure The rule of three (ratio version): calculator not used (N1, MH) 28 This method is similar to the method referred to as ratio-proportions, used primarily in the USA 229

243 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses Ae used this method for all five items in the questionnaire, performing all computations without a calculator. However, there was no evidence of her using the rule of three during observation sessions, a method that should have been obvious because it required the use of a pen and paper. Although I witnessed Ae administering twenty medicines during observation sessions, I elicited Ae s calculation method for only one of the five requiring a calculation. For that calculation, a very simple one involving a DSR of 2:1, Ae used repeated addition. Ae s use of the rule of three is particularly noteworthy for several reasons. First, Ae was the only nurse in the study who used the method. Second, it appears her use of the rule of three may have been linked to the fact that her elementary and high school education was completed overseas. Third, Ae reported this fact in the context of it being the only factor to have strongly influenced her ability to accurately calculate medicine doses (Question 13). Further, Ae reported that she had found nothing helpful in her nursing studies, completed in NSW, when she was learning how to calculate medicine doses (Question 20).The thing she reported finding least helpful in her nursing studies (Question 21) was following the formula which I learned from uni. The same associations between particular proportional reasoning strategies and the DSR of the medicine administration identified in relation to nurses calculations in clinical practice were also evident in their written solutions to the questionnaire tasks. Some of the strongest associations, indicated by the framed numbers in Table 5.20, were evident in the following items: Item 3: Multiplicative reasoning or repeated addition was strongly associated with the DSR of 2:1 (16 nurses (36%) used a doubling process); Item 4: A fraction operation or division process was strongly associated with the DSR of 1:2 (12 nurses (27%) used a halving process); and Item 1: Halving combined with addition 29 was strongly associated with the DSR of 5:2 (10 nurses (23%)) However, these associations were not as clear-cut or strong as they were in clinical practice, where for each of the ratios, 2:1, 1:2, and 3:2, in excess of 90% of the dose calculation problems were solved using the dominant proportional reasoning 29 In their working, three nurses expressed the inclusion of two whole tablets in the dose to administer as a multiplicative process rather than repeated addition 230

244 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses strategy associated with each ratio. Compared to the almost perfect matches between calculation strategy and DSR that applied in clinical practice, the weaker associations in relation to the questionnaire tasks were the result of two factors. First, nurses made far less use of proportional reasoning, preferring instead to use the formula. Second, there was greater variety in the types of proportional reasoning strategies nurses used for questionnaire tasks, compared to their use of simple strategies, such as the doubling, halving, and one-and-a-half times-ing processes they consistently applied in clinical practice. In Item 5, it could have been expected that nurses would use the strategy of halving combined with addition, the strategy strongly associated with the dose-tostock ratio of 3:2 that led to one-and-a-half tablets being required. However use of this strategy was vastly overshadowed by use of complex proportional reasoning. The reason for the expected strategy being used by only one nurse may have been that the 3:2 relationship between the prescribed mass and the stock mass may have been masked by the quantities being expressed in different measurement units The errors nurses made The 44 nurses who completed this part of the questionnaire made a total of eleven calculation errors and seven measurement errors. Eight nurses made a calculation error and seven nurses made at least one measurement error. The overlap between calculation errors, measurement errors, and poor syringe choice for the 44 nurses is illustrated in the Venn diagram in Figure

245 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses N = 44 Figure Number of nurses who made each type of error on pen-and-paper tasks Eight nurses made no calculation or measurement errors and chose an appropriate syringe for each of the three tasks where measurement of a liquid dose was required. Two nurses made no calculation errors and selected syringes appropriately. However on Items 2, 4, and 5 they failed to shade the syringes they had selected to show the volume of liquid they would administer. Consequently on these three items it was not possible to assess nurses dose measurement skills. These nurses therefore appear in the Venn diagram among the four nurses who made only measurement errors. The most errors were made by two nurses who made a calculation error, at least one measurement error, and demonstrated inappropriate syringe selection with respect to one task involving measurement of a liquid dose. The dose calculation strategies nurses used, their calculator use, and the calculation errors they made are now explored in more detail. Measurement errors and issues relating to syringe choice are reported in more detail in Classifying nurses calculation errors A calculation error was defined as failing to obtain the correct value of the dose to administer, or making a calculation error and failing to correct it in their working, even though they wrote the correct quantity at the end of their working. The eleven errors made in relation to dose calculations were surprising, given that I had 232

246 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses confirmed complete accuracy for the same nurses in relation to the 431 calculations they performed during observation sessions. Table 5.22 shows the six types of error identified, the items involved in relation to each, and the frequency of each type of error. Unless otherwise stated, for each item listed there was one error of the type named. Table 5.22 Frequency of types of error made Error type Items involved Total errors of this type n = 11 Correct formula set up but incorrect answer Items 2, 4, and 5 3 Incorrect metric conversion: milligrams micrograms Items 3 (1 error) and 5 (2 errors) 3 Transcription error Item 4 (2 errors) 2 Incorrect fraction operation but correct answer obtained Incorrect application of proportional reasoning Item 4 1 Item 5 1 Incorrect division process 30 Item 3 1 At least one calculation error was made on every item with the exception of Item 1. Items 4 and 5 drew the largest numbers of errors, four each. The two most frequently occurring types of error were nurses correctly setting up the formula for calculation but failing to obtain the correct answer, and nurses applying an incorrect conversion factor to convert a mass from milligrams to micrograms. When calculation errors were viewed in terms of the calculation strategy used, 8 (73%) of the 11 errors were made when nurses used the formula and 3 of the errors (27%) were made in association with proportional reasoning methods. The data did 30 Alternatively, the error may have resulted from inversion of the terms in the formula 233

247 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses not seem to support an association between errors made and the calculation strategy used. There were several reasons for this. First, there were too few errors made to draw a valid conclusion. Second, five of the eleven errors involved processes unrelated to nurses calculation strategies, namely metric conversion, and transcription of numbers. Third, in the case of one error made on Item 3, the nurse s method was unclear. Although the error was classified as an incorrect division process, an alternative interpretation was possible, that of the nurse applying the formula, but inverting the terms in the formula in error. The nurse with the poorest performance on the medicine administration tasks in the questionnaire was Emmy, a 26-year-old nurse in the neurology/trauma ward at Alexander Metropolitan Hospital, who had between one and three years nursing experience. Emmy made four calculation errors, shaded a syringe incorrectly, and made a poor choice of syringe to measure a dose. She used the formula for all the dose calculations and used a calculator for four of the five. Emmy s calculation errors included an incorrect conversion factor that she applied in both items requiring metric conversion, a transcription error, and a division error. Figures 5.15 and 5.16 show Emmy s faulty conversion in Item 3 and her shading of the incorrect answer of five tablets. Figure Emmy s incorrect metric conversion and fudged answer (N27, AH) 234

248 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses Figure Emmy s shading of the incorrect answer of five tablets (N27, AH) In regard to Items 3 and 5, Emmy twice incorrectly converted the prescribed dose from milligrams to micrograms by multiplying by a conversion factor of 100 instead of Her answer in each case meant she would have administered onetenth of the prescribed dose. Of particular concern in relation to Emmy s metric conversion errors was its consistency, suggesting she was applying an incorrect conversion fact that she was likely to repeat on all occasions that demanded a conversion from mg to micrograms, or vice versa. In Item 3, Emmy s conversion error had a flow-on effect that resulted in a final step requiring her to divide 12.5 by 62.5 instead of It seems that Emmy rejected the resulting nonsensical answer of 0.2 tablets, instead fudging her answer to a more reasonable five tablets by inverting the division operation (see Figure 5.15). She then shaded her incorrect answer on the diagram provided (see Figure 5.16). The data collected during observation sessions were checked to see if there was any evidence of these two nurses making errors in metric conversions in the medicines they administered. No comparison was possible since none of the medicines administered, nine in one case and six in the other, required a metric conversion. In Item 4, Emmy incorrectly transcribed 5000 international units, writing 500 IU instead. She then used a calculator to perform the calculation, obtaining the correct answer for what she had written, but a quantity which, if administered, would have resulted in the patient receiving a dose that was ten times larger than prescribed: 1 ml of heparin instead of 0.1 ml. 235

249 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses 5.16 Nurses descriptions of their calculation methods: Comparing the evidence Nurse participants were asked individually to describe their dose calculation methods as they administered medicines during observation sessions. During focus groups, held after observation sessions, dose calculation problems taken from observation sessions were the subject of further discussion about nurses dose calculation methods. Nurses also demonstrated their written calculation methods in response to the sample medicine administration tasks in the questionnaire they completed. For some nurses, these three sources of information were in alignment, and for others they were not. Information regarding nurses calculation methods obtained during focus groups is now examined. Comparisons between that information, nurses explanations of the methods they used in the ward, and the evidence from nurses responses to the questionnaire tasks illuminate some of the similarities and differences found. It also helps to gain an understanding of why sometimes the information from the three data sources appears to be in conflict Evidence from focus groups A total of 25 of the 73 participants attended one of the eight focus groups held, a minimum of one at each hospital site. The number of nurses attending each focus group varied from two to five. The small attendances were largely a result of difficulties in gathering more than a few nurses in one place at the times they were available. This was particularly the case at the largest of the hospitals, Alexander Metropolitan Hospital, where one of the more impromptu of the four focus groups, attended by just two nurses, was held in the nurses area of the Recovery ward while the nurses were observing patients in their care. Topics covered varied from site to site and mainly comprised topics I identified during observation sessions as warranting further in-depth investigation to get a range of perspectives from nurses. A semi-structured script was prepared for each site to investigate a selection of topics (see sample included as Appendix 4). Discussion relating to nurses calculation of medicine doses included: whether their current calculation methods differed from what they had learnt as students; 236

250 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses how often and in what circumstances they used the formula; and the extent to which they used calculators. Discussion was facilitated by a series of actual scenarios drawn from those I had witnessed during observation sessions. Portrayed on butcher s paper, the scenarios involved calculations that varied in mathematical complexity from very basic to quite difficult. Figures , illustrate how some of the scenarios were displayed at Gemmaville Rural Hospital. Figure Display of the heparin scenario and Scenarios 1 3 Figure Scenario 4 237

251 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses Figure Scenarios 5 7 A summary of the key issues discussed concerning nurses dose calculation strategies and the factors that influence them follows Comparison of calculation methods: Student versus practising nurse When nurses were asked how the calculation methods they used in the ward compared with those they were taught in their nursing training, they raised issues of calculator use, the methods nurses used to perform arithmetical processes, and the skills they had learnt at school and still used. For one nurse, Kylie, the only difference between the methods learnt at university and how she calculated doses now was that at university she was not permitted to use a calculator to calculate doses in exams, only when doing practice exercises. Now she was able to use a calculator on the ward, even though sometimes none was available, as occurred when I was observing her. Kylie noted, however, that when she was first employed at the hospital she undertook mandatory training on in-service days and had to pass a mathematics test before she was permitted to administer medicines. Under the test conditions, nurses were allowed the use of calculator only to check their calculations, having first calculated them without a calculator. The difference now, said Kylie, was that calculations were a lot easier and quicker when she used a calculator. Examination of Kylie s calculation methods during observation sessions revealed she used only proportional reasoning methods namely repeated addition and fraction operations. She made no use of the formula. Alice, a new graduate at Murraydale Regional Hospital, focused on the arithmetical processes she currently used in her calculations, such as the division 238

252 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses process, and how those methods differed from the methods she had been required to use at university, methods she described as both complicated and restrictive. Alice outlined why, following her employment at the Hospital, she had reverted to the simpler ways of calculating she had used prior to going to university, such as her way of performing division by cancelling. RG: In what way do they differ? Alice: The uni side, for some reason made it a lot more complicated than when I actually came and learnt here. Like, I was doing a more complicated way and I would end up stuffing up or something. So Nel, the educator, sat down with me and said: What you re doing is the harder way. Think about it. Alice said she explained to Nel that at university if she did it the simple way, she got into trouble from the lecturer because they wanted me to do it the more complicated way. To illustrate the complicated methods she was required to use at university, Alice gave the example of having to perform long divisions longhand, rather than by using cancelling techniques. To simplify the fraction 1000 they wouldn t let me chop off the noughts. Rather, she had to use the division process: 10 Ten into a thousand the complicated way, instead of allowing me to just do it the way I was always taught to get rid of whatever you could, first [by cancelling]. (Alice, N21, MH) Alice s preferred method was to cancel zeros as a way of dividing the numerator and denominator by ten to simplify the fraction. Alice was able to demonstrate to me that she understood what she was doing when she cancelled zeros, adding: But I just couldn t get it across to the lecturer. With Nel s encouragement, Alice had gone back to the simpler way of calculating. In the ward, she now used the methods she was most comfortable with, and felt confident using methods it appeared she had learnt at school. The theme of using methods learnt at school, raised by Alice, was also apparent in Gilbert s description of the methods he used in the ward. Gilbert, who worked in the surgical ward at Alexander Metropolitan Hospital, said that he felt very comfortable with mathematics, and that many of the arithmetic processes he used on a daily basis in his nursing practice were processes he had learnt at school in Mauritius, where he also completed his nursing education. He explained that during 239

253 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses his nursing education some new formulae were introduced, such as infusion rate formulae. However, all the basic principles remain the same [as at school], so, multiplication, division. Nurses claimed use of the formula versus reality I explored nurses calculation methods by asking them individually how they would calculate the dose in a particular scenario. Across the three hospitals a pattern emerged where nurses initial claims that essentially they adhered to the formula methods they were taught as students were not borne out in the discussions that followed. For many of the scenarios posed, even some that were mathematically complex, it became apparent that many nurses used methods that were unrelated to the formula they were taught, corroborating the evidence from observation sessions concerning a high rate of proportional reasoning strategies. Using the sample scenarios in this way helped to home in on nurses actual calculation methods and the circumstances in which they used them, rather than the methods nurses said they used. Through this process it became increasingly clear during observation sessions that nurses use of the formula was not nearly as widespread as some nurses initially indicated. Use of the formula seemed to be restricted to a narrowly defined set of circumstances, the most notable being where the numerical values in the medicine administration made the calculation difficult to perform mentally. This finding was borne out in observation sessions where use of the formula was restricted to medicine administrations with complex DSRs, largely paediatric doses. During focus group discussions, too, nurses indicated they used the formula for paediatric doses, and also for new medicines, medicines that were unfamiliar or not part of their normal routine, and medicines that were only available in a strength they had not previously used on a regular basis. Several nurses confirmed that they made little use of the formula in the adult wards they worked in at Murraydale Regional Hospital. Lee, for example, explained there was rarely a situation that required her to use the formula in the rehabilitation ward where she worked because calculations were usually fairly simple. Calculating paediatric doses using formula and calculator Nurses use of the formula when administering paediatric medicines was confirmed by Susie and Wendy at Murraydale Regional Hospital. Susie explained that, in her normal work in the intensive care unit, she had few calculations to do. 240

254 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses However, when she was recently asked to work in the paediatric ward, she quickly found she needed to recall and apply the formula to calculate the paediatric doses, but not necessarily otherwise. Wendy, a paediatric nurse with between four and six years of experience, explained that she continued to use the formula she learnt as a student, particularly working in paediatrics, because you ve got part doses. When you re doing sort of smaller amounts and the medication only comes in five hundred milligrams or a thousand milligrams and you re giving two hundred and fifty milligrams to a child, then, yeah, you need to work that out. You re very rarely giving whole doses [in paediatrics]. (Wendy, N14, MH) During a focus group, Roberta, a new graduate in the paediatric ward at Gemmaville Rural Hospital, had demonstrated her use of proportional reasoning for all the calculations except the more difficult Scenario 3. However, she staunchly adhered to a policy of using the formula and a calculator for paediatric doses. In response to Scenario 2, Roberta had instantly given the answer seventeen and a half as the number of millilitres of ibuprofen needed. Asked how she had got that amount, she worked through the mental processes she had used, demonstrating a very sound proportional reasoning method. When I recalled that the scenario was one I had taken from the paediatric ward a week or so previously when either she or her colleague had given the medicine, Roberta explained that in the actual ward situation, because she was giving the medicine to a child she would have got her calculator out. I asked Roberta why she would have got her calculator out in the ward, even though she had just demonstrated that she could calculate the dose using mental arithmetic processes. The following discussion ensued. Roberta: Cause kids are so precious. You don t want to make a mistake with them. RG: So, even though you ve done that very successfully in your head now, because it s a kid, and they re precious, and the dosages are very much more critical, you would have got your calculator out, doing it on the ward? Roberta: Yeah. And double checked. RG: So how would you have done it, using the calculator? Write it down. 241

255 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses Roberta then wrote down the calculation in accordance with the standard formula format. Later, in summing up how the two nurses present had used similar proportional reasoning methods for Scenario 2, I asked Roberta to expand on her approach to dose calculations in a paediatric ward. The discussion that ensued revealed her belief that the formula, used in combination with a calculator, was the best guarantee of obtaining an accurate dose, something that she saw as particularly important in relation to a kid s dose. RG: So for that one, you would not go first to your calculator unless it s a kid. And if it s a kid, you would go first to your calculator? Or might you do it mentally first? Roberta: No RG: Because you feel the calculator is safer? Roberta: Yes. RG: More guaranteed of accuracy? Roberta: Yes. Guaranteed. Probably quicker: you just punch it in. RG: It s not just the calculator either, it s a combination of using the formula, and a calculator to apply the formula, that you think is a safer than doing it as a mental process? Roberta: Yep. Gemma, who worked in the neonatal unit at Alexander Metropolitan Hospital, explained that she used the formula for unfamiliar medicines. When asked the version of the formula she used, initially had difficulty remembering it because she said she no longer related to the formula in word form. She simply used the format to locate the numbers ready for calculation using a calculator. Gemma: I think I forgot how to say it in words because I never use it [in words] any more. I know what I m doing but I don t actually write the formula down, I just say, OK if this is prescribed, how much do we have in stock? RG: So you ve got a mental schema, that this number goes there, this number goes there, and I multiply it by that? Gemma: Yeah. 242

256 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses The formula method and its attractions When asked about his dose calculation methods, Quan, who had completed his pre-registration education in the Philippines and had been nursing for more than three years, said the methods he had been taught included addition, division and the formulas. He claimed to use the formula a hundred percent of the time. I asked Quan to explain what it was about the formula method that worked so well for him. I think it s because it s simple to understand, it s easy to remember, he said. Very easy because it applies to most of the drugs, but not all. At my request, he wrote down the version of the formula thing he used, for example, for tablets. Quan s version of the formula is illustrated in Figure Figure Quan s version of the formula for calculating the dose (N61, AH) Quan explained the terms in the formula as follows: Desired [D], or the ordered dose, divided by have [H], or what stock, then times what kind of vehicle [V] one mil or two mils or five mils, whatever it is, or a tablet or ampoule. Quan clarified that the vehicle could be liquid or solid. I observed that Australian nurses tended to use a different term rather than vehicle, although the formula was, in essence, the same. Quan agreed when I asked him whether a correct interpretation of the term vehicle might be the way it s coming, how it comes, or the thing that it comes in Nurses perceptions of their use of calculators The general consensus among nurses during focus group discussions was that the level of difficulty of the calculation determined whether nurses used a calculator or not. However, discussion revealed individual differences between nurses regarding calculator use. 243

257 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses If it s hard. If it takes more than two brain cells, I use a calculator. (Trisha, N53, AH) Trisha was an agency nurse who worked in different wards at Alexander Metropolitan Hospital and always carried her own calculator. Always in paediatrics. (Unknown nurse) In solving dose calculations during observation sessions, the calculation methods nurses demonstrated revealed that calculators were not used in combination with proportional reasoning methods. Calculator use was very strongly associated with formula use, reinforcing the evidence from observation sessions and in relation to questionnaire tasks. Gilbert, who worked in the surgical ward at Alexander Metropolitan Hospital, indicated he usually did his calculations on a piece of paper or in his head, rarely using a calculator. Formula use was not always supported by a calculator, as Gail, a nurse in the rehabilitation and palliative care unit at Gemmaville Rural Hospital, demonstrated. Her use of the formula involved writing down the calculation in the formula format, simplifying fractions as far as possible, and then using algorithms, sometimes performed mentally, to complete the computation. Gail demonstrated her techniques in response to Scenario 3, as shown in Figure Figure Gail s application of the formula, combined with written and mental arithmetic processes (N57, GH) Younger, less experienced nurses seemed more inclined to reach for a calculator, especially in association with use of the formula. For example as new 244

258 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses graduate, Roberta, watched Gail calculating the metronizadole dose on paper, she commented: No, I don t get that, meaning she didn t understand the written and mental arithmetic processes Gail was using. She indicated that she was probably taught that way at school but had lost her facility with such operations, particularly those involving simplification of fractions and operations involving fractions. She now appeared to be very reliant on a calculator for such calculations. It seemed that decimal numbers were sometimes, but not always, a trigger for nurses to use a calculator. In Scenario 4 (see Figure 5.18), most nurses seemed sufficiently familiar with the relationship between the prescribed dose of 125 micrograms of digoxin and the tablet strength of 62.5 micrograms to be able to calculate the dose using mental arithmetic processes. Similarly in Scenario 5 (see Figure 5.19), many nurses were able to see the ratio between the prescribed dose of 12.5 mg of metoprolol and the tablet strength of 50 mg to enable mental calculation of the dose by halving 50 mg, and halving it again to get one quarter of a tablet as the dose to administer. However, in Scenario 6 (see Figure 5.19) the relationship between the prescribed dose of 37.5 mg of prednisone and the tablet strength of 25 mg seemed less obvious to many nurses. The increased difficulty resulting from decimal value in the 37.5 mg dose was, for some, a reason to use the formula and a calculator for the calculation. This was the case for both Quan and Mollie in the focus group at Gemmaville Rural Hospital. You can t really be certain in five to ten seconds that what you work out in your head is correct. So I would use the calculator just to be sure that it s the right quantity. Because that s a bit of a the decimal they re horrible. You can t divide twenty-five into thirty-seven-point-five. (Quan, N61, GH) 5.17 The apparent contradictions between nurses calculation methods Data relating to nurses dose calculation methods were compared from focus groups, questionnaire tasks, and observation sessions. The analysis revealed contradictions between the claims participants made about the methods they used and the evidence concerning the methods they actually used in the two different settings. There were many examples during focus groups where a nurse, when asked how they would calculate the dose in one of the sample scenarios, would initially say 245

259 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses they would use the formula. Then as they began to describe their calculation process, they would realise that there was a relatively simple relationship between the prescribed dose and the stock mass that would allow easy mental calculation of the dose. Nurses would then revert to using a proportional reasoning strategy instead of the formula. These apparent contradictions raised the possibility that what I viewed as a calculation may not have coincided with what some, possibly many, nurses regarded as a calculation. In their categorical claims to always use the formula it seemed there was an assumption the calculation was sufficiently difficult to warrant use of the formula The invisible nature of dose calculations I asked Kylie, a new graduate employed in the medical and palliative care ward of Murraydale Regional Hospital, how the methods she used in the ward compared with those she was taught as a student. The following conversation ensued. Kylie: All the formulas and everything is all the same that I learnt at school [i.e. uni] and here. RG: And do you use those now, on a regular basis, just as you did when you were learning? Kylie: Yep. We ve go to. So you give the right medication. RG: Can you expand on: We ve got to? Kylie: Well like if you ve got tablets, tablet form, like, you ve got to use those formulas. And if you have to figure out a drip rate yourself, you ve got to do it yourself. Well say if you ve got gentamicin, gentamicin only comes in 80 mg [per ml] and if you ve got three hundred [to give] like in the question [in the questionnaire], you ve got to figure it out yourself, like on a piece of paper or a calculator. You can t just guess. RG: So you would use the formula? Kylie: Yes. Yet despite Kylie s insistence that there was no alternative to using the formula for calculating doses, there was no evidence of her using the formula, either in the calculations I observed her performing during observation sessions, or in her written 246

260 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses calculations in response to the sample medicine administration tasks in the questionnaire. Kylie used proportional reasoning strategies, such as repeated addition or a fraction operation, for all seven medicine administrations I observed for which I elicited her calculation method, methods she also used in the questionnaire. This suggested that Kylie disregarded such processes as being calculations, and that true calculations were those for which she need a formal solution method, such as the formula, because she could not work them out using informal methods. Another example of this contradictory pattern came from Quan, who initially said the methods he learnt as a student had not changed, and that he still used the formula methods a hundred percent of the time. He then qualified his answer. But now it is more automatic, like you would know, like, if two tablets of digoxin you would say, oh, that s 125 [micrograms]. So it s more proficient. (Quan, N61, GH) By describing the process as automatic, Quan seemed to imply that the formula was not needed because the dose could be worked out without a formal calculation process. Nurses would just know the dose. As we worked our way through each of the seven medicine administration scenarios during the focus group, Quan responded each time to my question: How would you do that one in the ward? by saying: I would use the formula. Then one by one, he changed his mind, progressing in his thinking to a point where he demonstrated a proportional reasoning strategy that he said would be easier. Gilbert demonstrated a similar progression from formula to proportional reasoning in response to my asking him how he would calculate the 1 g dose in the paracetamol example (see Scenario 1, Figure 5.17) This was the most frequently occurring medicine administration across the three hospitals and required a very simple calculation. Initially Gilbert set up the calculation in accordance with the formula format. Yeah, that s simple. So one gram goes to one thousand milligrams. So divide by five hundred, equals two. (Gilbert, N30, AH) When I pressed Gilbert further and asked him to explain the calculation method he was using, and in particular why he had divided by five hundred, he did the calculation again but this time using proportional reasoning. 247

261 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses I can do it multiplication-wise. Five hundred times two comes to one gram. Not using [the] formula. It s just common sense. Shopping maths versus the formula Marion said she didn t have to even think about it to know how much paracetamol to give. However if someone asked her to calculate it, she would think: Marion: Five hundred milligrams times two equals a thousand milligrams. A thousand milligrams is one gram. RG: Again, common sense? You re not using a formula? Marion: I m not using anything more difficult than if I was grocery shopping. Gilbert said that he would use the formula for the digoxin example (see Scenario 4, Figure 5.18) where the prescribed dose was 125 micrograms and the stock available was 500 micrograms per 2 ml. He then qualified this by saying he could do it in his head without the need for a calculator. But because it s digoxin IV, so I write it down, just to be sure with myself. Marion, however, again said she would not use the formula, immediately describing a method based on proportional reasoning. Marion: This is the way I d do it. Like, I d see one-twenty-five mikes IV, and I know that it s smaller than five hundred micrograms. So I think, well how many times does a hundred and twenty-five go into five hundred? So I think, a hundred and twenty-five plus a hundred and twenty-five is two-fifty; two-fifty and two-fifty is five hundred. So I know that a hundred and twenty-five is a quarter of five hundred. So then I look at how many mils I ve got. I ve got two mils. So what s a quarter of two mils? It s point-five of a mil. So I don t go to any like, um, I don t do a calculation like strength in stock. You know. I just kind of I can see that one is smaller than the other, so I just kind of add up how many times the smaller one goes into the bigger one. And then I think, oh well, if that s gone into that four times, then it s got to be a quarter of the two mils. RG: So again it s shopping maths? Marion: Yeah. RG: What you d do in the supermarket? 248

262 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses Marion: Yeah, yeah, yeah! Wendy initially claimed that she used the formula for dose calculation, but then added the following proviso: Wendy: Unless it s a really simple calculation. Like, say you ve got to give two hundred and forty milligrams of gent [gentamicin], then you just I wouldn t bother working that out, I d just use the three lots of eighty. RG: What does it [gentamicin] come in? Wendy: It comes in eighty [mg in a 2 ml ampoule]. Wendy s explanations suggested that she perceived she was doing a dose calculation or working it out only if she needed to use the formula. Wendy passed off lightly those calculations where she used mental processes alone. She explained: I wouldn t bother working that out, apparently because she felt that working it out necessarily meant employing the formula. Abby agreed that her methods were more like Marion s grocery shopping approach. She explained that she couldn t even remember lots of the formulae she had learnt at university. She also explained why she felt more confident using her own logic than a formula. Abby: Yeah, I m shopping maths too. The formulas don t really Like they did initially work for me. But it has to sort of make sense in your head in order to be able to get it. And I don t sort of trust the formulas as much as I do my own sort of logic. RG: Can you explain why? That you trust your logic more than a formula you were told probably: This will always work for you? Abby: Yeah, I suppose if it s logical to me and making sense If I m like: This is how much is in a mil, and this is how many mils I need, then I can trust that. But whereas, if you re sort of doing the formula and using a calculator, I suppose, to work out that formula, then you re more at risk of making mistakes than if you sort of do it in a way that s logical to you. So I think I use shopping maths as well, a fair bit. The cues provided by the tools and artefacts of medicine administration It seemed that artifacts in the clinical environment and the physical actions associated with administering a medicine played a role in the calculation process. 249

263 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses They appeared to act as cues or tools for nurses in a way that made the process of determining the amount to administer appear to be more a matter of common sense than a mathematical process. Roberta, a new graduate working in the medical/surgical/paediatric ward at Gemmaville Rural Hospital, initially claimed that she used the formula she was taught all of the time. Roberta: That s how I ve been taught, and I still use that. However when asked whether she would use the formula to calculate the paracetamol dose (see Scenario 1, Figure 5.17), she retreated from her earlier answer and related her actual calculation process to the physical act of popping out tablets, one at a time. Roberta: It s just, well Pop out two! (laughs). Cause you know it s one gram. RG: OK, so when you pop out two, what s going on in your mind, Roberta? When you pop out two tablets? Roberta: Nothing! (laughs) I just pop out two because I know two [tablets] is a gram. Like, five hundred, five hundred, is a gram. RG: Right. Well that s what s going on in your mind: five hundred and five hundred is a thousand, which is a gram. Roberta: You don t kind of think of it. It appeared that each tablet she popped out corresponded to Roberta mentally adding another 500 mg. Roberta clearly did not regard her process of arriving at the dose to administer as being a mathematical process. Roberta s calculation methods in relation to six of the seven scenarios presented in the focus group (see Figures ) contradicted her claim of always using the formula. For these six scenarios, Roberta used proportional reasoning combined with mental arithmetic processes to correctly calculate each dose. Roberta s written answers to the questionnaire tasks did, however, provide partial support for her claim that she always used the formula. She used it for four of the five items analysed. For the fifth item Roberta used a fraction operation. Gail explained how she looked at the label on the bottle to assist her calculations. Gail would hold the bottle up and see, for example, that the tablets were 250

264 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses 25 mg (as in Scenario 6, Figure 5.19). Her thinking would then be more in terms of tablets and half tablets. Gail: I would say: I want thirty-seven-point five. What s the mathematical process? It s interesting see. It did make me think: having you on the ward has made me think: How s my brain working? (laughs) Yeah. I literally just look at the twenty-five and think: Thirty-seven [point-five]: that s an extra half a tablet. See, I don t think numbers, I just think: Thirtyseven and a half, and twenty-five: I want an extra half of that tablet. RG: OK. And it s the label that triggers some of that process? Looking at the label saying twenty-five milligram tablets? Gail: Mm. But if it doesn t work, then out I go [Gail mimics writing on paper]. Write it down: pen and paper! Gail s explanation reinforced my developing belief that nurses often do not always think in terms of mathematical processes and calculations as they administer medicines. Gail s comments highlighted the fact that it was only as a result of having me on the ward exploring with her the mathematical processes she used to determine doses that her awareness was triggered and she realised that what she was doing was indeed mathematical. Her explanation suggests having the actual bottle of tablets in her hand provided her with several cues that assisted her thinking. Reading the label and physically sighting the tablets reinforced that each tablet represented 25 mg of the medicine, and each half tablet, 12.5 mg. It seemed likely that without my questions focussing on the mathematical nature of medicine administration, in the ward Gail might have administered the 37.5 mg dose in Scenario 6 (see Figure 5.19), just as she had described, but without the awareness of it involving a mathematical process One method to calculate, another method to check It became apparent in one focus group that many nurses were not reliant on just one method to calculate doses. Several nurses explained how they would use a particular method for the calculation, and then use a different method to check it. Even though Gilbert said he frequently used the formula to calculate doses, he explained how he also checks with himself using other common sense methods as 251

265 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses well. A bit of formula, and look at the common sense of it, too, especially if it was an unfamiliar medicine. Marion confirmed that it was common practice for nurses to check their calculations. Marion: I think a lot of people do that. I always check myself. Like I ll work it out one way and then I ll work it out another way if I need to. You know, I ll use the formula for calculations and then I ll think, well, if I didn t have the formula, what would it be? Just to double check yourself. (Marion, N40, AH) Abby described a way of checking the answer if the calculation was too difficult to calculate using a method other than the formula (which, presumably, was how she had obtained the initial answer). If it s something that s really hard to work out without the formula, once you know the answer then you can do it the other way around. (Abby, N34, AH) I believe what Abby meant by doing it the other way round was to calculate the quantity you would be giving if you administered the calculated dose. For example, if the calculated dose was 4 ml, and the stock used was 10 mg per 2 ml, the administered dose would be 20 mg. Nurses would then check that this amount matched the dose prescribed. Investigating nurses ability to use a different method to check the accuracy of their calculations was one of the goals of the pen-and-paper calculation tasks in the questionnaire. In Marion s responses to the five tasks, her claim to always check her calculations using a different method was confirmed. In Item 1, in response to being asked how she would check that her answer was correct, Marion wrote: If I work a dose out mentally, I check it with a calculator. If I work it out with a calculator, I check it mentally. What Marion did not say, but was evident in her written answers to questionnaire tasks, was that when she calculated a dose using the formula she would sometimes check it using proportional reasoning and mental arithmetic, and vice versa. Two examples of Marion s pattern of alternating between formula and proportional reasoning methods are illustrated in Figures 5.22 and

266 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses Figure Formula and calculator to calculate; proportional reasoning to check (N40, AH) Figure Proportional reasoning and mental arithmetic to calculate; formula and calculator to check (N40, AH) 253

267 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses In describing her checking method for Item 4, it was clear Marion s suggestion of using a calculator was synonymous with using the formula. In Item 2 of the written tasks, Marion used the formula to both calculate and check the dose. She performed her initial calculation using a combination of written and mental arithmetic processes, set out in a series of written steps. Marion then checked the accuracy of her working by applying the formula again, but this time using a calculator to recalculate the dose. Her working and explanation of her checking process for Item 2 appear in Figure Figure Formula and written steps to calculate; formula and calculator to check (N40, AH) In the same item, Abby used the formula and a calculator to calculate the dose, and proportional reasoning and mental arithmetic to check the calculation. Abby s calculation and checking processes are illustrated in Figure

268 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses Figure Formula and calculator to calculate; proportional reasoning and reversing the calculation process to check (N34, AH) Gilbert similarly demonstrated in his questionnaire answers his stated practice of looking at the common sense of it to check his calculations. Figure 5.26 shows Gilbert s calculation using the formula followed by his common sense check in response to Item

269 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses Figure Formula to calculate; proportional reasoning and written arithmetic to check (N30, AH) For the initial calculation, Gilbert applied the formula, using a written process involving cancelling fractions, followed by a mental division process. To check his calculation, Gilbert used proportional reasoning and mental arithmetic. In the final part of the checking process, Gilbert wrote to find the number of millilitres corresponding to a mass of 60 mg. It is not possible to determine whether Gilbert was applying the formula to just this part of the calculation, or whether this expression was Gilbert s way of applying proportional reasoning to find the fraction of 2 ml represented by 60 mg The impact of mandatory checking on calculation methods Nurses use of one method to calculate and another to check was also evident in relation to the process of performing mandatory checks on doses prior to administration. During two different focus groups at Gemmaville Rural Hospital three nurses Gail, Quan, and Mollie, all indicated that they might use mental arithmetic and proportional reasoning to calculate the dose. Then, if it was an intravenous medicine needing a colleague to check, in their interaction with the fellow RN to verify the dose, they might use the formula to demonstrate how they calculated it. There seemed to be a perception that the appropriate method for checking a dose by showing someone else how they got their answer, was to use the formula. In response to Scenario 4 (see Figure 5.18), Quan and Mollie both agreed they could 256

270 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses quite easily calculate the 125 microgram digoxin dose in their heads by a process of starting with the stock ampoule (500 microg in 2 ml), halving the quantities (250 microg in 1 ml), and halving them again (125 microg in 0.5 ml). However, because it was an intravenous administration for which a mandatory check by a colleague was needed, the nurses would use the formula to recalculate the dose, thus justifying their answer (even though this did not constitute a truly independent check by the checking nurse, as was expected). Mollie: When you try and explain it to someone else, or explain how you got to your answer, it s easier to use a formula. I think. Do you think? Quan: Yeah. Nurses explanations conveyed the belief that their decision to use the formula when checking the calculation with a colleague was based on the fact that the formula was the universally accepted method, the proper way to do it. Gail: I would probably not use the calculator, but I would, um I d do it [on my own, mentally, as described] and then I d go out to [find a colleague] Because we always double check, and if someone said: Well, how did you get that?, then I d write it down on my little, tiny piece of paper that I have, to say: Well this is what I did. And they invariably will get a calculator out and double check it. RG: OK. And when you say: This is what I did, what would you write for them, on your piece of paper? Gail: Well, to make it look good, I d do this [laughs, and writes as she speaks]: three-fifty over a hundred, times five over one Gail proceeded to write out the calculation according to the standard formula format, as illustrated in Figure Figure Gail s written application of the formula to check a dose with another nurse (N57, GH) 257

271 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses Gail then explained how she might also work through her original calculation with the checking nurse, if time allowed. Gail: I d say: Well this is the way you can do it [using the formula]. But the way I did it in my head was this way. Depending on time. So it depends on the time factor really. RG: And you might check it a different way to how you actually calculated it yourself to get that dose? Gail: Mm. Because then I know I ve can feel safer. done it two different ways, and then I RG: OK. And why is it safer if you ve done it two ways? Gail: Because I guess if I ve used the calculator then I feel that that can t be wrong! RG: Unless you plug in the wrong values. Gail: Ah, yes. But that is the beauty of double checking. Because someone else comes along and says: You ve got it wrong. So then you go back, and you can easily pick up the mistake. RG: Mm. OK. So the double checking is a really vital tool in good nursing practice? Gail: Yep. RG: Which is why they ve come to that protocol? Gail: Mm Nurses varied capabilities to self-check Not all nurses appeared capable of self-checking their calculations using a different method, especially if they used a calculator. Roberta, a new graduate at Gemmaville Rural Hospital, appeared unable to find a different method to check her calculations. I asked nurses during focus groups whether, if they used a calculator for a calculation, they performed any check on the accuracy of their answer. Roberta replied as follows. 258

272 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses I will double do it in the calculator. So, get one answer, clear it, and do it again. Then get someone else to do it, maybe. (Roberta, N60, GH) Gemma, a nurse with more than nine years experience who worked in the neonatal unit of Alexander Metropolitan Hospital and had correctly used the formula and calculator for all five questionnaire tasks, appeared to have limited options to draw on for checking the accuracy of her calculations. In response to the question in Item 1 asking how the nurse would check their answer, Gemma replied as follows. To check, I would go through the calculation with the nurse by checking correct drug, correct dose, correct time to be given, correct patient and correct route to administer medication on medication chart. (Gemma, N24, AH) It seemed that Gemma s options for checking the accuracy of her calculations were restricted to the five rights of medicine administration. She appeared to have no method for ensuring the correct dose other than to ask another nurse to check it. In the three other questions requesting the same information, Gemma simply referred back to her answer to Item 1. By contrast, Lindie, another nurse from the same neonatal unit, who had a similar amount of experience, was able to demonstrate her ability to check her calculations using a different method. Like Gemma, for most of her calculations in the questionnaire, Lindie had applied the formula, but unlike Gemma, she had used written processes to obtain the answer. Lindie s checking techniques for the four items seeking a checking procedure included using a calculator to check her manual application of the formula, and a method she called reversing the calculation. This method involved cancelling and applying a multiplication algorithm. Figure 5.28 illustrates the calculation and checks Lindie performed in response to Item

273 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses Figure Formula to calculate; formula with calculator, and reversing processes to check (N23, AH) 260

274 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses 5.19 Calculation methods: Clinical practice versus mandatory tests In the course of focus group discussions, several nurses at the hospitals where annual testing was mandatory, Gemmaville Rural Hospital and Murraydale Regional Hospital, raised the issue of the additional demands on them in terms of the calculation methods they were required to use during annual tests. Annual testing at Alexander Metropolitan Hospital had been discontinued over a decade before the study. The practice was discontinued because calculation skills were regarded as a core requirement of all registered nurses, and it was not considered cost effective because of the staff resources needed to administer tests and the time away from their normal duties for nurses undertaking tests. Nurses drew a distinction between the methods they used to calculate doses in the ward and those they used in tests, explaining that in annual tests the formula was given to them and nurses were required to use it. Nurses were not permitted to use calculators. They were required to show their working and to state the unit of measurement in their answer. Two nurses at Murraydale Regional Hospital, Kylie and Lee, explained the difference in the methods they used in the two situations. Kylie described how she would work out some dose calculations in her head if she were doing them in the ward. However, in the mathematics exam, she would have to use the formula. Lee explained that she struggled in the annual test with having to do a written pen-and-paper calculation of an unfamiliar administration, such as a paediatric dose based on weight, something she would not normally do because she worked in the rehabilitation unit. Then I ve really got to think and double check. But when you ve got to write down what you do, because they want your written work, it is different to what you would do [on the ward]. (N18, MH) Not being allowed to use a calculator in the test made the task even more challenging for Lee. She noted that there were medicines she gave on a regular basis that required calculation, but which she no longer needed to calculate because, having given them so many times, she just knew it. However, in the test she would have to do the calculation long-hand using a division process and showing her working, just to obtain an answer she knew by heart. The example she gave was 261

275 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses calculating the infusion rate in millilitres per hour needed to administer 1000 ml of liquid over 12 hours. During discussion about the fact that in the test nurses always had to put it in the formula, there was a considerable amount of confused debate about what the actual formula was. It seemed clear that most of the five nurses present in the focus group did not have the formula at their fingertips and probably relied on it being given to them in the test. Kylie offered a version of the formula that was upside down. When I asked: So what s coming out here, with Kylie getting it upside down? three nurses immediately answered in unison: That s because [in the ward] you don t have to do it! ; You don t use it! ; You don t do it! Kylie selected the paracetamol example in Scenario 1 (see Figure 5.17) to illustrate the difference between the calculation method she might use in the ward, which was easier, and the method she would need to use in the test. Lee added: You have to use their formula that they give you. The nurses all agreed that the method they would use to calculate the dose in their head would not be acceptable in the test. They want you to use the formula and show all workings. You just can t write an answer, explained Lee Summary of nurses dose calculation strategies This chapter addressed that aspect of Research Question 1 relating to the strategies nurses use to calculate medicine doses in clinical practice, and Research Question 2, focusing on the factors that influence nurses choice of dose calculation strategy. The data collected in the Hospital Phase of the study from observation sessions, the questionnaire, and focus groups revealed some noteworthy similarities and differences between the methods nurses used to calculate medicine doses in different settings. The balance between nurses use of proportional reasoning and the formula changed in accordance with the context in which nurses encountered the problem. During observation sessions, proportional reasoning strategies dominated, and all associated computations were performed mentally. Nurses made little use of the formula, and calculator use was associated exclusively with application of the 262

276 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses formula. This combination was found predominantly in association with calculation of doses for paediatric patients. Nurses use of proportional reasoning in clinical practice involved almost exclusive use of scalar strategies. Nurses made no use of the rule of three, and very little, if any, use of the unitary method or functional strategies. In clinical practice, the link between nurses calculation strategies and the numerical characteristics of the medicine administrations was so consistent that the term dose-to-stock ratio (DSR) was introduced to represent the ratio between the prescribed mass, recorded on the patient chart, and the stock mass, written on the label of the pharmaceutical product used to administer the medicine. For four of the most commonly occurring DSRs during observation sessions, 1:2, 2:1, 3:2, and 3:1, nurses performed in excess of 90% of their calculations using the identified related strategy. In nurses written responses to medicine administration tasks in the questionnaire, the balance between their use of proportional reasoning strategies and the formula shifted dramatically from that observed in clinical practice. Nurses use of the formula changed from 12% of problems in clinical practice to 61% in relation to the questionnaire tasks. The same associations were detected in nurses solutions to the questionnaire tasks regarding their calculation strategies nurses for commonly occurring DSRs. However the association between the calculation strategies nurses used in response to the questionnaire tasks and the DSR was not as strong as the association that occurred in clinical practice. The strong link between calculators and formula, identified in clinical practice, persisted in nurses solutions to questionnaire problems, but to a far lesser degree. A difference was apparent between the calculation methods nurses used in clinical practice compared to those used on the questionnaire tasks. This difference related to nurses use of calculators in association with formula use. A strong association was identified in clinical practice between formula use, calculator use, and calculation of doses for paediatric patients. However the greatly increased use of the formula for the questionnaire tasks could not be attributed to the need to calculate doses for paediatric patients because the questionnaire contained no medicine administrations for paediatric patients. During observation sessions, nurses made no dose calculation errors, however several nurses made errors on the questionnaire tasks. Those errors were caused by 263

277 Chapter 5: The Strategies Nurses Used to Calculate Medicine Doses incorrect metric conversions that would have resulted in ten-fold overdoses, and transposition errors. During focus groups, when solving the sample dose calculation problems used to facilitate discussion, nurses reaffirmed their preference for proportional reasoning strategies demonstrated during observation sessions and when solving questionnaire problems. However, a pattern emerged where the methods nurses actually used to solve sample problems were frequently at variance with the formula method nurses initially said they would use. The apparent contradiction between the methods nurses claimed they used and the methods they actually used raised the possibility that many nurses had a different perception of the processes they used to determine the dose to administer to mine. These processes appeared to be viewed as calculations only if nurses were required to apply a formal procedure, such as the formula, especially if it was supported by a calculator. Many nurses appeared to view the informal, proportional reasoning processes they used in the observation sessions, always supported by mental arithmetic computations, as simply common sense rather than as a mathematical process of calculation. 264

278 6 Measuring Medicine Doses To be numerate means to be competent, confident, and comfortable with one s judgements on whether to use mathematics in a particular situation and if so, what mathematics to use, how to do it, what degree of accuracy is appropriate, and what the answer means in relation to the context. Coben (2000, p. 35) Accurate measurement of medicine doses is an important mathematical aspect of medicine administration, which, together with accurate dose calculation, ensures patients receive the correct quantity of medicine. This chapter presents the findings from the Hospital Phase of the study relating to nurses measurement of medicine doses. Together with Chapter 5, this chapter addresses Research Question 1. Data were collected primarily through observing and interviewing nurses during observation sessions as they performed routine administration of medicines. Data was also collected in the form of nurses measurement of doses calculated in response to sample medicine administration problems in Part 2 of the questionnaire. The chapter concludes with an account of several issues of concern relating to nurses dose measurement practices that emerged from the study. 6.1 Types of measurement task observed Measuring the dose accurately is the next task nurses perform after determining the quantity of medicine to administer. Measuring the quantity of medicine to be administered was often no more difficult than counting the required number of tablets or capsules in the case of solid medicines, or drawing the required volume into a syringe in the case of liquid medicines. Sometimes, however, the measurement task is far more complex, perhaps requiring several measurement processes, several measuring instruments and possibly several calculation steps Measuring instruments and techniques Measurement requirements were dictated by factors such as the form of the medicine (solid or liquid), patient characteristics (including adult or child, conscious or not, ability to swallow), and the route of administration nominated by the 265

279 Chapter 6: Measuring Medicine Doses prescribing officer. Some medicines were administered without the need for precise measurement. These included creams, ointments and other topical medicines. The 73 nurses who were observed administering medicines used a variety of measuring instruments to prepare and administer the 1571 medicines they administered. Table 6.1 summarises the frequency of use of primary measuring instruments and the administration routes associated with each instrument. Table 6.1 Frequency of use of primary measuring instruments, and associated administration routes Primary measuring instrument Associated administration routes Number (%) of administrations n = 1571 Counting Oral (tablets, capsules, drops), nasogastric tube 1121 (71%) Syringe Nebuliser/ inhaler IV, subcutaneous /intramuscular injection, oral, nasogastric tube, PEG a tube, nebuliser 259 (16%) Inhalation 66 b (4%) Measuring cup Oral, nasogastric tube 40 (3%) Bag Intravenous 16 (1%) Bottle Intravenous, oral 16 (1%) Insulin pen Subcutaneous injection 5 (0%) Electronic infusion pump Intravenous infusion 5 (0%) Other c Various 4 (0%) Not recorded /unknown Various 39 (2%) a b c PEG = Percutaneous endoscopic gastrostomy Included 21 administrations where the number of puffs, capsules or doses were counted Included nasal spray and topical applications The form of the medicine, solid or liquid, and the administration route largely determined nurses selection of measuring instrument and how it was used. Most medicines in solid form such as tablets and capsules were measured by counting. 266

280 Chapter 6: Measuring Medicine Doses Liquid medicines were measured using medicine cups, kitchen cups, syringes, prefilled bags and bottles. In addition, nurses used a number of medicine-specific and route-specific measuring devices, primarily to administer liquid medicines. These devices included: insulin-pens containing cartridges pre-filled with insulin (National Patient Safety Agency, 2010), with dial-up dosing scales; nebulisers and inhalers, some featuring metering devices or self-loading functions; syringe drivers; and electronic infusion pumps. Nurses sometimes used more than one instrument to administer a medicine. Primary measuring instruments were those I recorded as being the most important instrument used to measure the dose. The most commonly used measuring instruments will now be examined in more detail. Measurement by counting Nurses used counting to measure more than two-thirds of the 1571 medicines administered during the observation sessions. Nurses counted doses mainly in relation to medicines administered in solid form, specifically tablets, capsules and sachets, administered orally or by nasogastric tube. Counting was used to measure 1071 (93%) of the 1147 oral doses and 20 (69%) of the 29 doses administered by nasogastric tube. Counting of vials, bags, drops, and puffs was the measurement technique used for some liquid and atomised medicines. The 1121 counted medicines included: 20 administrations by nasogastric tube (crushed tablets, capsules and the contents of sachets); 12 administrations of eye and ear drops; and 16 medicines administered topically, via gastric PEG, dermal patch, or by intravenous infusion (e.g. counting the number of vials needed to prepare a reconstituted solution for intravenous administration). 267

281 Chapter 6: Measuring Medicine Doses Measurement using syringes Syringes were the most commonly used device for measuring liquid medicines. Syringes were used in a broad range of clinical situations to prepare, measure, and administer medicines by a variety of administration routes. Syringes were the measurement instrument most commonly used to administer medicines to paediatric patients. Of the 65 medicines administered to paediatric patients, 42 (65%) were measured by syringe. Syringes graduated in millilitres ranged in size from 1 ml to 60 ml and included 10 ml and 20 ml oral paediatric syringes. Syringes graduated in international units of insulin and specifically designed to administer insulin were used in two sizes, 50-unit and 100-unit. Syringes were also essential equipment for reconstituting to liquid form medicines, typically antibiotics, supplied in powdered form because that form is more stable. Table 6.2 shows the breakdown of nurses use of syringes by administration route. Table 6.2 Administration routes for which a syringe was used to measure the dose Administration route Number (%) of administrations n = 259 Intravenous 131 (51%) Subcutaneous injection 87 (34%) Oral 23 (9%) Other a 12 (5%) Not recorded 6 (2%) a Other included nasogastric tube, nebuliser, intramuscular injection, PEG tube, and topical applications Only about one-third of nurses use of syringes was related to administering medicines by injection. The majority of syringe use for measuring medicines, 51%, was in relation to medicines administered intravenously. Most of the 23 oral medicines measured with a syringe were administered to paediatric patients in oral syringes. Manufacturers incorporate safety features into the design of oral syringes, colouring them brightly and designing them so a needle 268

282 Chapter 6: Measuring Medicine Doses cannot be attached. These safety features are designed to allow a clear distinction to be made between oral syringes and syringes used to administer liquids subcutaneously and intravenously. These precautions are designed to minimise wrong route error, particularly in relation to paediatric patients. An oral syringe is shown in Figure 6.1. Figure 6.1. A brightly coloured 1 ml oral syringe to which a needle cannot be attached Although subcutaneous administration accounted to 87 (34%) of the medicines measured using syringes, only six medicines were involved: enoxaparin, heparin, insulin, morphine, metoclopramide and octreotide. Enoxaparin and heparin accounted for the majority of subcutaneous administrations, however, the frequency of using these two medicines varied considerably between hospitals, as noted in Without exception, enoxaparin was administered in a single concentration of 100 mg per ml from prefilled singe-dose syringes in volumes ranging from 0.2 ml to 1.0 ml. Administration of heparin was split almost equally between Murraydale Regional Hospital and Alexander Metropolitan Hospital. None of the 29 recorded administrations of heparin occurred at Gemmaville Rural Hospital, in contrast to the pattern of use of enoxaparin across hospitals. Figure 6.2 shows a single-dose prefilled syringe of enoxaparin of strength 20 mg in 0.2 ml and the package information. 269

283 Chapter 6: Measuring Medicine Doses Figure 6.2. An enoxaparin (Clexane) prefilled syringe (Image provided courtesy of NSW Therapeutic Advisory Group. Visit Measuring doses administered via inhalers and nebulisers Counting of tablets, puffs, and doses accounted for many of the 66 medicines administered via inhalers and nebulisers. Syringes were used to measure a small number of doses stated in millilitres. Prescriptions for medicines administered via inhalers and nebulisers recorded during the study illustrate the breadth of the skills nurses need to administer different products, using a range of stock formulations, measuring instruments, and mechanical delivery devices to accurately measure and administer bronchodilators and anti-asthmatic medicines. Five examples of medicine administrations taken from the study follow. They illustrate the doses prescribed, measurement units, and stock formulations involved in administering medicines via inhalers and nebulisers. Examples of medicine administrations involving inhalers and nebulisers: one puff of fluticasone furoate 18 micrograms of tiotropium bromide from capsules containing 18 micrograms per capsule 2.5 mg dose of salbutamol from vials delivering 5 mg per 2.5 ml 500 micrograms of ipratropium bromide from ampoules containing 500 micrograms per 1 ml 270

284 Chapter 6: Measuring Medicine Doses two 500 microgram doses of terbutaline from a self-metering inhaler. Measuring cups Measuring cups of different sizes, 30 ml, 50 ml, 60 ml, and 250 ml kitchen cups were used to measure liquid medicines for 40 administrations. Thirty-nine were administered orally and one was administered through a nasogastric tube. Other measuring devices Large volumes of medicines and therapeutic fluids are often administered from sealed plastic bags and glass bottles. Like prefilled syringes, bags and bottles with the volume printed on the label fulfil the role of both container and measuring instrument. The recorded measuring instrument for 16 medicine administrations was a bag, and for a further 16 administrations, a bottle. The sizes of bags were 50 ml, 100 ml, 200 ml, 250 ml, and 1000 ml (1 L). Metronidazole, sodium chloride, Hartmann s solution, and packed red blood cells were some of the pharmaceutical products administered intravenously from bags. Ten of the medicines administered from bottles were administered by intravenous infusion form and six were administered orally. One gram doses of paracetamol, supplied in 100 ml bottles labelled 1 g solution for infusion, accounted for all but one of the 16 medicines administered intravenously. Five of the six oral doses in bottles were 140 mg doses of liquid methadone, each prepared as a single dose by the hospital pharmacy, very likely for the same patient. When medicines in bags and bottles were administered by intravenous infusion, the nurse usually hung the bag, or the upturned bottle, on a stand and regulated the flow via an infusion pump. Figure 6.3 shows an electronic pump administering a medicine by intravenous infusion via a burette from bags suspended from a stand. 271

285 Chapter 6: Measuring Medicine Doses Figure 6.3. An electronic pump and apparatus administering an intravenous infusion to a paediatric patient (Photo courtesy of Kylie Gillies) The use of an infusion pump requires the nurse to perform an additional measurement process. The nurse enters into the digital display on the pump the volume to be infused (in ml) and the period of time over which the infusion is to run (in hours or a fraction of an hour). The infusion rate in millilitres per hour can then be selected on the display. The benefits of single-use medicines Benefits flowed from the availability, and nurses routine use, of prefilled syringes administered mostly by subcutaneous injection, and pre-packaged bags and bottles of medicine and fluids, administered primarily by intravenous infusion. Benefits included savings in nurses time spent in calculating and measuring doses, and a reduction in the risk of harm to patients resulting from calculation and 272

286 Chapter 6: Measuring Medicine Doses measurement error. Benefits relating to calculation of medicine doses were discussed in The benefits of prefilled syringes of enoxaparin relating to measurement of medicines stemmed from nurses being able to give the required dose simply by administering the contents of the prefilled syringe matching the dose prescribed. Ready-to-use bags and bottles of liquid medicines saved nurses time by having a suitable volume available for administration without measurement being necessary. This was the case for all but one dose, an in-between dose of 50 mg that needed to be both calculated and measured. Nurses at Gemmaville Rural Hospital benefitted most from the use of both prefilled syringes of enoxaparin and bags of other medicine and fluids than nurses at either of the other two hospitals. Half of the 46 doses of enoxaparin were administered at Gemmaville Rural Hospital compared to 15 (33%) at Murraydale Regional Hospital and 8 (17%) at Alexander Metropolitan Hospital. All doses of enoxaparin were administered by subcutaneous injection with the exception of 8 doses that were administered by intravenous infusion with dialysis in the renal ward at Murraydale Regional Hospital. Although only 16 medicines were administered from bags, the fact that 11 (69%) of them occurred at one hospital, Gemmaville Rural Hospital, compared to 1 (6%) at Murraydale Regional Hospital and 4 (25%) at Alexander Metropolitan Hospital, suggests hospital-related factors may underlie these differences in use. Further research may be warranted to investigate the marked discrepancies between hospitals in nurses use of prefilled syringes and bags of other medicines, especially if the use of single-dose and single-use products is associated with low rates of measurement error Multi-stage measuring processes For some medicines measuring the medicine ready for administration was a multi-stage process involving at least two measuring instruments, recorded in the spreadsheet as measuring instrument 1 and 2. Medicines administered by intravenous infusion accounted for almost all of these administrations. A total of 136 medicine administrations were recorded where more than one stage and one instrument were involved in the measurement process. Measurement processes for these administrations involved the use of equipment such as 273

287 Chapter 6: Measuring Medicine Doses intravenous pumps, intravenous giving sets, Injectomat devices, and syringe drivers as the second measuring instrument, a syringe generally being recorded as the first measuring instrument. An example illustrating the complexity of the measuring tasks sometimes required of nurses was an order for 365 mg of the antibiotic benzylpenicillin to be administered by intravenous infusion to a child in the paediatric ward of Gemmaville Rural Hospital. Accurate measurement of the medicine required the nurse to perform four different measurement processes. The flowchart in Figure 6.4 shows the four stages of the measurement process used to prepare the 365 mg dose of benzylpenicillin for administration. Figure 6.4. Flowchart showing the four-stage measurement process The first stage of the measurement process involved the nurse creating a reconstituted solution from a 600 mg vial of powder, guided by a protocol contained in the Australian Injectable Drugs Handbook (Society of Hospital Pharmacists of Australia, 2011) the nurse consulted. The protocol for forming a reconstituted solution of benzylpenicillin specifies the addition of 9.6 ml of water for injection to 600 mg of powder to form a 10 ml solution. The nurse used a 10 ml syringe to measure the diluent, drawing up 9.6 ml of liquid. The very precise 9.6 ml volume of diluent is carefully designed to allow for 274

288 Chapter 6: Measuring Medicine Doses displacement of the powder so the volume of the final solution is exactly 10 ml. This volume results in a solution of concentration 600 g in 10 ml, affording numerical simplicity for subsequent calculations, including calculation of the dose to administer. The final stage of measurement involved the nurse programming an electronic infusion pump to ensure the correct quantity of medicine was administered at a constant rate over the prescribed time. The display on the pump indicated the infusion rate was 20 ml per hour. 6.2 Measurement issues emerging from the study Two issues concerning measuring medicine doses emerged from the study. The first issue was excess volume of liquid in sealed ampoules and how nurses dealt with the excess volume. The second issue the type and capacity of the syringes nurses selected to measure small volumes of liquid medicines and the implications for accurate dose measurement. No attempt was made to judge the clinical significance of poor syringe choices because such judgements were beyond the scope of the study. Suffice to say that many of the medicines at the centre of the issues identified are among high-alert medicines listed globally as being medicines most frequently implicated in medication errors. These high-alert medicines include insulin, antithrombotics (e.g. heparin and enoxaparin), narcotics (e.g. morphine) and insulin (Australian Commission on Safety and Quality in Health Care, 2017; Institute for Safe Medication Practices, 2014; The Joint Commission, 2008) Volume of liquid in ampoules Single-dose ampoules are small, sealed, glass containers holding the volume of medicine intended for a single administration. Nurses snap off the glass top and withdraw the solution from the ampoule using a syringe with a needle attached. The concentration of the medicine appears on the label; usually the mass of the active medicine in a given volume of solution. Examples of ampoules observed during observation sessions included: heparin 5000 IU in 0.2 ml; morphine 10 mg in 1 ml; 275

289 Chapter 6: Measuring Medicine Doses clonidine 150 micrograms per ml; and noradrenalin 2 mg in 2 ml. in 0.2 ml. Figure 6.5 shows an ampoule and packaging information for heparin 5000 IU Figure 6.5. Ampoule and packaging information for heparin 5000 IU in 0.2 ml (Images provided courtesy of Pfizer Australia) Figure 6.6 shows packaging information for ampoules of morphine sulphate 10 mg in 1 ml. Figure 6.6. Packaging information for morphine 10 mg in 1 ml (Image provided courtesy of Pfizer Australia) 276

290 Chapter 6: Measuring Medicine Doses Measuring heparin doses An issue became apparent during observation sessions concerning inconsistencies in the volume contained in ampoules of heparin nurses used to administer the commonly prescribed 5000 IU dose. When nurses measured the liquid they withdrew from the ampoule, ensuring it measured exactly the required 0.2 ml, I observed a small volume remained in the ampoule, indicating the contents of the ampoule exceeded the 0.2 ml indicated on the label. Subsequent enquiries to manufacturers of heparin ampoules and pharmacists at the hospitals confirmed the phenomenon of excess volume in ampoules and endorsed my concern that administering the entire ampoule without measuring it was not sound practice. The manufacturer advised that overfill in ampoules is the amount of extra medication included in the vial to ensure that the labelled contents can be administered (Pfizer Australia representative, personal communication, 27 April, 2017). Both manufacturers and hospital pharmacists advised that nurses should always expel any overfill so that they administered exactly the dose prescribed. Heparin appeared to be a frequently administered medicine, thus providing an opportunity to monitor and record variability between apparently identical ampoules and observe how nurses managed the variability. When circumstances allowed I asked nurses at the two hospitals where heparin was prescribed, Murraydale Regional Hospital and Alexander Metropolitan Hospital, to measure the actual volume they were able to withdraw from ampoules. I also asked one nurse at Alexander Metropolitan Hospital who administered heparin frequently in the medical ward to keep a record for several days of the volume in heparin ampoules she used in her medicine rounds. However, the data collection process produced nothing additional to that provided during observation sessions. Thirty of the 33 heparin administrations I observed involved stock ampoules labelled 5000 IU in 0.2 ml. These doses were administered by 18 nurses in a wide range of wards at the two hospitals and by two different routes. For example: 18 heparin administrations occurred at Murraydale Regional Hospital and involved seven wards and nine different nurses; 15 occurred at Alexander Metropolitan Hospital and involved six wards and nine different nurses; 29 doses were administered by subcutaneous injection in roughly equal numbers at the two named hospitals; and 277

291 Chapter 6: Measuring Medicine Doses 4 doses were administered intravenously. Ultimately volume data were collected for 19 heparin administrations. The amount of liquid the nurse was able to withdraw from the ampoule was measured and recorded. For a further three ampoules a surplus was noted but the excess volume was not measured. For many of these administrations I was also able to ascertain how the nurse managed the overfill, or overage as it was referred to by some nurses during the study and by representatives of pharmaceutical companies I interviewed subsequently. In all 19 ampoules the volume exceeded the 0.2 ml indicated on the label by between 10% and 70%. The average excess volume was 41%; the most frequently recorded overfill was 50%, consequently six ampoules contained 0.3 ml rather than the 0.2 ml indicated on the label. Nurses management of overfill in ampoules The way nurses managed overfill in heparin ampoules varied. When nurses administered heparin, regardless of whether an overage was recorded for the event, I was able to elicit from nurses how they managed excess volume in heparin ampoules. Nine (64%) of the 14 nurses interviewed indicated or demonstrated their practice was to discard any excess volume so they administered only the 0.2 ml before administering the volume required. Five nurses (36%) indicated they would give the entire contents of the ampoule regardless of how much was actually contained within it. Nurses responses to how they responded to of overfill in heparin ampoules was therefore divided roughly in the ratio 1:2. For each nurse who administered the full contents of the ampoule there were approximately two others whose practice was to discard the excess. Nurses explanations in support of their practice of discarding excess volume included: The ampoule has more [than 0.2 ml]. So that s just so if you get an air bubble you can flick it and you ve got enough [solution] to make it. (Olivia, N25, AH) It always comes in more than that [0.2 ml] volume. It s misleading. You can't assume the vial holds exactly 0.2 ml: sometimes it s 0.22 ml, but this one is 0.3 ml. (Lee, N18, MH) 278

292 Chapter 6: Measuring Medicine Doses Lee then told me the story of a drug error avoided: a nurse was told by a supervisor not to "shoot off" the extra volume. She did though surreptitiously, when the supervisor s back was turned in order to avoid an error. Susie s explanation for administering the entire contents of the ampoule was: I always give what s in the ampoule because they re pre-loaded. (Susie, N22, MH) An argument for administering the entire contents of heparin ampoules A very conscientious and experienced nurse, Marion (N40), at Alexander Metropolitan Hospital presented a very persuasive argument as to why, in the case of heparin administered subcutaneously, accurate measurement of the dose was not warranted. Her argument was expressed in an observation session during which she knowingly administered two doses of heparin measuring 0.26 ml and 0.28 ml, exceeding the prescribed dose of 5000 IU by 30% and 40% respectively. As Marion prepared the second heparin injection, stating that she had drawn up 0.28 ml into the syringe from the 0.2 ml ampoule an amount that would deliver 7000 IU to the patient instead of the 5000 IU prescribed she explained to me (RG) her philosophy regarding excess liquid in ampoules. Marion: Well, I went to a course. Like years ago I did a course, and I went to [Pharmaceutical company} Health Care we do IV [intravenous] classes and they said that they always even though it says, like a litre or 500 ml, they always put in an extra ten percent. And I ve noticed that with ampoules as well. And I tend to feel that whatever is that it s not necessary for me to go from point two-six to point two. Because I think that whatever was in the ampoule was 5000 units anyway. (Marion, N40, AH) Marion outlined the clinical factors she was taking into account when she decided not to measure the volume or discard any excess over 0.2 ml. Marion: If it was a vasoactive medication, if it was an inotropic medication that affected his heart rate, heart rhythm, blood pressure, if it affected his vascular smooth muscle tension, then I d be a lot more particular about my precise dosing. But in something like subcutaneous heparin, it really doesn t matter if I give, you know, a little bit over point two-four, point two-six, point two-eight it s not going to make an appreciable difference to the patient. If it was something like noradrenalin, then I d have a different philosophy. So phhhh, you know, if I m going to give it subcutaneously and if it s a dose 279

293 Chapter 6: Measuring Medicine Doses that, you know, fits everybody, there s no it doesn t really matter! It s not being measured in mikes-per-kilo-per-minute [micrograms per kilogram per minute]. It s just five thousand units BD [twice daily]: everybody gets it! RG: So you make a judgement based on the medication that you re giving as to how critical it is: the exact measurement or not? Marion: Yeah. It s a subcutaneous injection. So there s a lot of factors that go into how much the patient actually gets. You know? How much gets through from their subcutaneous tissue. It would depend on because this is a onesize-fits-all. It doesn t matter whether my man weighs forty kilos or a hundredand-forty kilos, I m still going to give him five thousand units of heparin BD [twice daily]. Marion confirmed that her sense of what is critical and what is not is something a nurse learns through experience: It s not something a new graduate nurse would necessarily have. But she also acknowledged that not every one might agree with her particular stance on overages in heparin ampoules. RG: So you just get a sense for this? I mean a new grad [graduate], for example, they d have to sort of pick this up on the way: what to be careful of, what s critical and what s not? Marion: Yeah, I mean they do put it down to point I mean if I ve got a student with me they re very certain to make sure it s point two of a mil and that s fine. I mean, whatever they do it doesn t matter. RG: So you have moved on in your experience to the point where you can make these judgement calls based on your experience? Marion: Yes. I guess I mean I may be wrong. I could have somebody tell me: No, no, no! You must give point two of a mil only, because that will make a crucial difference to the patient. But I don t see that. Marion s belief was that overfill in ampoules was the manufacturer s way of allowing for loss during the administration process. In the case of the heparin injections, Marion had taken into account any negative effects on the patient that might result from her giving slightly more than the prescribed dose. She considered the nature of the drug and its pharmacology, as well as the administration route by which she was administering it. She also made a judgement that because the same dose of 5000 IU is prescribed for all patients, regardless of physical characteristics 280

294 Chapter 6: Measuring Medicine Doses such as their weight, it was not critical that she give the exact volume required to deliver the prescribed dose. Excess volume in ampoules of other medicines Having been alerted to the issue of overfill in heparin ampoules, I also began to monitor variability in ampoules containing other medicines whenever the opportunity arose. Other medicines monitored were ampoules of morphine, clonidine, milrinone, iloprost, and noradrenalin. None of these medicines was administered more than twice with the exception of morphine which was administered 17 times. Table 6.3 shows overfill recorded for single doses of three of these medicines. Table 6.3 Overfill recorded for iloprost, morphine, and noradrenalin ampoules Medicine Labelled concentration % overfill Morphine 50 micrograms in 0.5 ml 20% Noradrenalin 10 mg in 1 ml 25% Iloprost 2 mg in 2 ml 8% As was the case in relation to heparin ampoules, the issue of excess volume in other ampoules was unlikely to have arisen without me actively pursuing it with nurses when the opportunity presented itself. The surprised reaction of some nurses to this phenomenon is illustrated in an administration event involving administration of a 20 mg dose of morphine, administered subcutaneously by Kylie at Murraydale Regional Hospital. Kylie had less than 12 months experience as an RN and almost three years of additional experience as an Assistant in Nursing. Kylie and her colleague, Bob, whom she had asked to perform the mandatory check of her administration, grappled with the issue of excess volume in the ampoules of morphine Kylie used to prepare the dose. After Kylie had drawn up the contents of two morphine ampoules labelled 10 mg in 1 ml in a 3 ml syringe, I asked her to measure the volume in the syringe. Kylie seemed surprised and perplexed when she found the volume measured 2.5 ml, 25% more than the 2 ml volume expected. 281

295 Chapter 6: Measuring Medicine Doses The conversation that ensued between Kylie, checking nurse, Bob, and myself revealed the lack of familiarity of these two nurses with the concept of overfill in ampoules. Kylie explained to Bob what she had found, showing him the syringe and two empty ampoules. Kylie: See, it s two-point-five. So I ve just drawn up these. One mil plus one mil is two mils. Bob: So they ve put extra in there for spillage? Kylie: Yeah, totally! Bob: I don t know. I don t know. RG: There s an anomaly here, and it s not just with you, Kylie. I ve been observing this across all my observations. Bob: Right. What have people been Have people been measuring out a mil and discarding the rest? RG: Well, I m not sure if it s the same drugs, but there s been two views. One view is that you discard Bob: Discard the balance? RG: the balance. So that you only have two mils, because what you want should be in 2 mils, not more. Bob: Yes. RG: And the other view is that it s pre-measured. Kylie: It s already in a vial. Bob: Yeah. RG: Use what s there, assuming that that s one mil in each vial. Discussion then took place about who to consult to clarify the issue of overfill in ampoules. Bob suggested speaking to the source either the pharmacist or the manufacturer. Then Kylie, who had disappeared without saying anything, returned, having apparently found the pharmacist nearby and sought her advice. Kylie announced stridently: Kylie: So, I don t have to write it up in the book [drug register]. 282

296 Chapter 6: Measuring Medicine Doses RG: There s always an overage in them? Kylie: Yep, in the little ampoules. RG: So you should discard the surplus? Kylie: I will discard the rest, so I will take it down to two. But I don t have to write it up in the book because you know. But that s what she said: I just talked to the pharmacist. Kylie then proceeded to administer exactly 2 ml of morphine, having first expelled the 0.5 ml surplus from the syringe. Having been alerted to the overfill issue during this administration, it seemed Kylie s primary concern had been that she would have to account for the liquid she expelled by entering it in the drug register. Perhaps she was concerned about the time this would take and the inconvenience of the task and was therefore relieved to find it was not required of her Selecting syringes for measuring small volumes Two issues of concern emerged from the observation study regarding nurses choice of syringe to measure small volumes of medicine. These issues related to: the unit of measurement in which the syringe was calibrated, millilitres or international units of insulin, and whether that scale matched the measurement task; and the capacity of the syringe selected (e.g. 1 ml, 3 ml, 5 ml, etc.) and whether the scale on the syringe afforded optimal measurement accuracy. Suitability of syringe scale for task During the observation sessions, nurses frequently selected insulin syringes, graduated in one system of measurement, international units of insulin, to measure and administer doses stated in a different type of measuring system, namely millilitres. Nurses followed this practice at two hospitals, Murraydale Regional Hospital and Alexander Metropolitan Hospital. No heparin was administered at Gemmaville Rural Hospital during the period of the study. Nurses at Gemmaville Rural Hospital used insulin syringes to measure and administer insulin only. Many instances were recorded of nurses using insulin syringes to measure heparin doses, for which the most commonly prescribed dose, 5000 IU, is available in ampoules containing 5000 IU in 0.2 ml. Two sizes of insulin syringe were in 283

297 Chapter 6: Measuring Medicine Doses common use during the study: syringes of 100 IU capacity and 50 IU capacity, the latter syringes intended for administering small doses of insulin. Nurses used of insulin syringes of both sizes to measure insulin and heparin, an anticoagulant routinely used for surgical patients in some hospitals. An exact equivalence between the two measurement systems, international units of insulin and millilitres of any liquid, does exist. 100 international units of Unit 100 (or U 100) insulin (see Figure 6.8) are contained in a volume of 1 millilitre. Similarly 50 international units of insulin are contained in a volume of 0.5 millilitres. The scale and reverse side of a 100-unit syringe are illustrated in Figures 6.7 and 6.8. Figure 6.7. The scale on a 100-unit insulin syringe graduated in international units of insulin Figure 6.8. Reverse side of 100-unit insulin syringe indicating that 100 international units of insulin are contained in 1 ml of liquid and The scale and reverse side of a 50-unit syringe are illustrated in Figures

298 Chapter 6: Measuring Medicine Doses Figure 6.9. The scale on a 50-unit insulin syringe graduated in international units of insulin Figure Reverse side of 50-unit insulin syringe indicates that 50 international units of insulin are contained in 0.5 ml of liquid When nurses used an insulin syringe to measure 0.2 ml of heparin, they did so without being able to locate 0.2 ml on a millilitre scale because there is none. The only reference to millilitres on 100-unit and 50-unit syringes is the 1 ml and 0.5 ml notations on the reverse side of the syringe (see Figures 6.7 to 6.10). These notations indicate only that 100 IU of insulin solution is contained in 1 ml and 50 IU is contained in 0.5 ml. To safely use such a syringe to measure a dose stated in millilitres, the nurse must first apply a conversion factor between millilitres and international units of insulin. However, it is very unlikely that nurses actually know or apply such a conversion factor. It is more likely they have memorised that 0.2 ml of heparin can be administered by drawing the medicine up to the 20-unit mark on an insulin syringe, either of 50-unit or 100-unit size. This practice is ill-advised because it introduces the opportunity for measurement error caused by confusion between measurement units. By contrast, if 285

299 Chapter 6: Measuring Medicine Doses the nurse uses a 1 ml syringe to measure the 0.2 ml dose, the measurement task is straightforward on the millilitre scale, posing minimal risk of measurement error. Figure 6.11 illustrates a 1 ml syringe on which the 0.2 ml mark can be clearly seen (it appears as.2 ). Figure The scale on a 1 ml syringe The prevalence of using insulin syringes for non-insulin medicines, specifically 0.2 ml doses of heparin, was evidenced by the fact that on 23 (59%) of the 39 occasions I observed nurses using insulin syringes, the nurse was preparing to administer heparin rather than insulin. Nurses made approximately equal use of 50- unit and 100-unit insulin syringes for administering 0.2 ml heparin doses. At Murraydale Regional Hospital, the first hospital I visited, the percentage of heparin doses measured with an insulin syringe was at least 63% and may have been as high as 88%. The variability is the result of not having made a clear enough distinction in recording the measuring instrument between nurses using 1 ml millilitre syringes and 100-unit insulin syringes of 1 ml capacity. For the same reason, at Alexander Metropolitan Hospital the percentage of heparin doses measured with an insulin syringe was at least 93% and may have been as high as 100%. Syringe capacity and accuracy of measurement I examined 139 volume measurements using syringes and rated nurses choices of syringe as appropriate or inappropriate by comparing the capacity of the syringe to the volume being measured. Syringes used for these measurements included a range of sizes of hypodermic syringe calibrated in millilitres, oral syringes calibrated in millilitres, and insulin syringes calibrated in international units of insulin. 286

300 Chapter 6: Measuring Medicine Doses The criterion used to determine whether the syringe selected was appropriate for the measurement task was the answer to the question I posed in analysing the data. The question I posed was: Would a smaller syringe with a more finely graduated scale have achieved greater measurement accuracy? Syringe choices were rated appropriate if the answer was no, and inappropriate if the answer was yes. Overall, 47 (34%) of the 139 syringe choices analysed were deemed inappropriate, judged against the criterion described. The poorest syringe choice related to the selection of standard syringes graduated in millilitres. For these syringes, 32 (32%) of 99 nurses choices were judged as inappropriate. These syringes (sometimes referred to as tuberculin (1 ml) and hypodermic syringes (all others)) were available in a range of different sizes (e.g. 1 ml, 3 ml, 5 ml, 10 ml, 20 ml, etc., up to 60 ml). The broad availability of sizes appeared to contribute to nurses poor choices of syringe capacity. Table 6.4 summarises the 139 syringe choices by hospital, categorising them as appropriate or inappropriate for the measurement task on the basis of the criterion described. Table 6.4 Appropriateness of syringe capacity for task: by syringe type and hospital Type of syringe and unit of measurement Standard (millilitres) (n = 99) Oral (millilitres) (n = 5) Insulin (international units) (n = 35) Total (n = 139) Appropriate choice of syringe Inappropriate choice of syringe GH a MH AH Total GH MH AH Total a AH = Alexander Metropolitan Hospital; MH = Murraydale Regional Hospital; GH = Gemmaville Rural Hospital 287

301 Chapter 6: Measuring Medicine Doses The total number of syringe choices for each of the three hospitals was similar: 49 for both Gemmaville Rural Hospital and Alexander Metropolitan Hospital and 41 for Murraydale Regional Hospital. There was a significant difference between hospitals, however, in the proportion of occasions on which nurses made inappropriate syringe choices. A Chi-squared test of independence (p < 0.05) concluded that nurses at Murraydale Regional Hospital made more poor syringe choices than expected compared to nurses at the other two hospitals. The proportion of poor syringe choices at Murraydale Regional Hospital was 49% compared to 18% at Gemmaville Rural Hospital and 37% at Alexander Metropolitan Hospital. Accuracy using syringes graduated in millilitres An example illustrating nurses selection of syringes of greater than optimal capacity was Liesel s use of a 3 ml syringe to administer heparin from ampoules labelled 5000 IU in 0.2 ml. During a single observation session at Murraydale Regional Hospital, Liesel administered two 5000 IU doses to two different patients. Accuracy ten times greater could have been achieved by using a 1 ml syringe. Figure 6.12 shows 1 ml and 3 ml syringes for comparison. Figure The graduations on the scales of 1 ml and 3 ml syringes As Figure 6.12 illustrates, the long thin barrel of a 1 ml syringe provides a finely graduated scale on which the smallest interval between graduations is onehundredth (0.01) of a millilitre. On a 3 ml syringe, the smallest interval between graduations is 0.1 ml. 288

302 Chapter 6: Measuring Medicine Doses The maximum probable error in reading the scale on a measuring instrument with the naked eye is one half of the smallest unit of measure (Alldis & Kelly, 2012, p. 34). Therefore using a 1 ml syringe, the maximum probable error is ml, compared to 0.05 ml using a 3 ml syringe. Thus, the maximum probable percentage error for a measurement of 0.2 ml is 2.5% using a 1 ml syringe and 25% using a 3 ml syringe. Therefore using a 1 ml syringe affords ten times the accuracy of a 3 ml syringe. The comparative errors described underscore the importance of nurses selecting the syringe of smallest capacity that will accommodate the volume to be measured. Examination of my record of the clinical circumstances and environmental factors surrounding the medicine administration suggests the complexity of the medicine preparation process may have sometimes contributed to nurses inappropriate syringe choice. The following example illustrates one such case. Example (Event #1500) In the emergency department of Gemmaville Rural Hospital, the nurse used a 10 ml syringe to administer a 10 mg dose of morphine as a push, a dose administered into a vein in the patient s arm rather than being infused over time. The nurse selected a stock ampoule of morphine containing 10 mg in 1 ml to administer the dose. Following the hospital protocol for the administration, she first diluted the morphine by combining it with 9 ml of normal saline so that the morphine would be better tolerated by the patient. The nurse did this by drawing up 9 ml of normal saline into a 10 ml syringe. Then she withdrew liquid from the morphine ampoule. When I asked if she had withdrawn the entire contents of the ampoule, she replied: No, only enough to make the total volume up to 10 ml (as the protocol required). The nurses technique resulted in her using a large 10 ml syringe, offering little precision, to measure a very small 1 ml volume of morphine. The alternative option was to use a 1 ml syringe to separately measure the critical morphine component in the medicine administration. Her measurement would then have been twenty times more accurate than the accuracy she achieved using the 10 ml syringe, based on a comparison of maximum probable percentage errors. Poor measurement accuracy resulted from the nurse s technique of continuing to use the 10 ml syringe, selected for the dilution process, for a measurement to which it was not suited. The contrast in the scales of the two syringes and the 289

303 Chapter 6: Measuring Medicine Doses accuracy they can achieve is illustrated in Figure 6.13 which shows a 10 ml and a 1 ml syringe. Figure Comparing the accuracy of 1 ml and 10 ml syringes It is possible too, that the environment in the emergency ward on the morning the nurse administered the morphine dose contributed to the nurse s flawed technique on the day. I noted at the time that the scene in the ward was chaotic: the nurse can't find a free nurse to check her medication. The nurse had told me: There are no beds in the wards so patients are backed up in Emergency. It was a bad night last night and it s been bad for a week! The importance of selecting a syringe of the most appropriate size to optimise accuracy was further highlighted during a focus group by Wendy, a 52-year-old nurse who had been an RN for approximately five years. Wendy described the difficulty she sometimes experienced measuring very small volumes prescribed for the patients in the paediatric ward where she worked. She explained how she sometimes found it difficult to achieve the high level of accuracy she sought with old eyes and little lines [on the scales of syringes]. I actually do struggle a little bit with morphine, because we give such small doses. Like, we can have orders for two-point five or even one milligram in paediatrics. I do struggle because they re such small amounts, you know. And you wonder how accurate they are, actually. It s not a huge issue, but it is an added stress when you ve got really any medication that s under a mil because you re using such small amounts and the differences, I suppose, can make a big difference to the amount you re actually giving. (Wendy, N14, MH) 290

304 Chapter 6: Measuring Medicine Doses Accuracy using insulin syringes When nurses used insulin syringes to measure doses, whether insulin or heparin, poor judgement in selecting syringes of optimal capacity for the measurement task was again evident. Their choice between syringes of 50-unit or 100-unit capacity syringes frequently appeared to have been made without reference to the accuracy of the syringe in relation to the measurement task. Nurses often seemed to disregard the issue of measurement accuracy when they selected an insulin syringe to measure medicines, whether insulin or heparin. Nurses frequently used 100-unit syringes to measure volumes less than 50 IU for which a smaller 50-unit syringe would have achieved greater accuracy. Examples included nurses drawing up volumes of 4, 12 and 16 international units of insulin. Nurses made equal use of 100-unit and 50-unit syringes for measuring 0.2 ml of heparin, where 50-unit syringes would have provided greater accuracy. For 14 (40%) of the 35 volumes measured using insulin syringes, nurses made a poor syringe choice in selecting a 100-unit syringe (see Table 6.4). The smallest interval on a 100-unit syringe is 2 units (see Figure 6.7) compared to 1 unit on a 50- unit syringe (see Figure 6.9). Thus, the more precise 50-unit syringe would have achieved twice the accuracy. 6.3 Nurses performance on measurement aspects of penand-paper tasks Part 2 of the questionnaire nurses were asked to complete at the conclusion of the observation sessions comprised sample medication administration tasks designed to investigate nurses performance on pen-and-paper calculation and measurement tasks posed in the form of word problems. An overview of nurses performance on the measurement aspects of the five tasks analysed was presented in Nurses measurement skills were assessed on the basis of their shading of the doses they had calculated on the illustrations provided. They shaded the number of tablets they would administer and, in the case of liquid medicines, selected an appropriate syringe from the four illustrated and shaded on it the dose they would administer. A measurement error was defined as failure to shade the diagram to correctly illustrate the calculated dose (even if the calculated quantity was incorrect). A poor syringe choice was defined as selecting a syringe: (a) larger than necessary to 291

305 Chapter 6: Measuring Medicine Doses achieve optimal accuracy in relation to the volume to be measured; or (b) calibrated in a unit of measure different from the unit in which the volume to be measured was expressed. Of the 44 nurses who completed this part of the questionnaire, 31 made at least one type of measurement error or poor syringe choice on the 5 items analysed (see ). Incorrect measurement of doses and poor choices of syringe type and capacity, were identified as areas of weakness. Nurses made a total of 9 measurement errors 31 on the questionnaire tasks compared to no detected measurement errors during observation sessions. Nurses made 31 poor syringe choices. These areas of weakness identified in relation to the questionnaire items were identical to those identified in relation to the volume measurements nurses made during observation sessions. Nurses performance on the five measurement tasks is now explored in more detail Nurses measurement errors The most frequent type of measurement error was the nurse shading a volume one-tenth of the calculated dose. One nurse made this type of error on two of the three items that required shading a volume. Examples included shading: 0.75 ml instead of 7.5 ml (Item 2, two occurrences); 0.01 ml instead of 0.1 ml (Item 4, one occurrence); 0.3 ml instead of 3 ml (Item 5, one occurrence); and 0.35 ml instead of the (incorrectly calculated) 3.5 ml dose (Item 5, one occurrence). For each questionnaire item, Table 6.5 shows the types of error made and the number of nurses making them. 31 Three errors related to nurses failing to shade the dose on the syringe they had correctly selected 292

306 Chapter 6: Measuring Medicine Doses Table 6.5 Types of measurement error made and the number of nurses making them, by item Type of measurement error Volume shaded was stock volume, not calculated volume Volume shaded was one tenth the calculated volume Nurse shaded beyond the end of the scale on syringe Item 1 n = 0 Number of measurement errors made Item 3 Item 4 n = 0 n = 3 Item 2 n = 2 Item 5 n = 2 All Items n = Choice of syringe for measuring volumes Three of the items in the questionnaire, Items 2, 4, and 5, required shading a volume of medicine to be administered. Twenty-eight nurses made a poor selection of syringe in relation to one of these items. Three of these nurses made a poor syringe selection in relation to a second item. Item 2 exposed an unexpected issue concerning nurses misconceptions about how to achieve optimal accuracy in measurement. Nurses also made poor syringe choices on this item, selecting syringes of larger capacity than necessary. For each item 32, Table 6.6 shows the types of inappropriate syringe selection made and the number of nurses making that selection. 32 No poor syringe selections were recorded for Items 1 and 3 293

307 Chapter 6: Measuring Medicine Doses Table 6.6 Type of poor syringe selection, and the number of nurses making them, by item Description of poor syringe selection 20 ml syringe used to measure 7.5 ml 7.5 ml shaded on both 10 ml and 20 ml syringes Split 7.5 ml volume between two syringes 3 ml syringe used to measure 0.1 ml 0.1 ml shaded on both 1 ml and 3 ml syringes Insulin syringe (100-unit) used to measure 0.1 ml 10 ml syringe used to measure 3 ml 6 ml syringe used to measure 3 ml No. of nurses making the selection Item 2 n = 6 Item 4 n = 9 Item 5 n = Accuracy of measurement: Splitting the volume between two syringes In Item 2 requiring nurses to select an appropriate syringe to administer the 7.5 ml calculated dose and shade it, curiously three nurses split the volume, each in a different way. It appeared they did this believing this measurement procedure would achieve optimal accuracy of measurement. The ways in which the nurses, split the 7.5 ml volume are described numerically and illustrated in Table

308 Syringe 2 Syringe 1 Chapter 6: Measuring Medicine Doses Table 6.7 Three ways in which nurses split a volume between two syringes Details of the splitsyringe measurement Capacity (ml) Shaded volume (ml) Nurse and hospital identification N40, AH a N56, GH N54, GH Capacity (ml) Shaded volume (ml) The nurse s representation of the measurement process a AH = Alexander Metropolitan Hospital; MH = Murraydale Regional Hospital; GH = Gemmaville Rural Hospital 295

309 Chapter 6: Measuring Medicine Doses The fact that the three nurses, all of whom had more than nine years experience as RNs, believed that optimal accuracy could be achieved by splitting the volume between two syringes suggests that they were uncomfortable about including the small, fractional amount of 0.5 ml in the volume they drew up on a syringe on which the smallest graduation was 0.2 ml. It seems they believed the fractional 0.5 ml should be separately measured on a more finely calibrated scale because it warranted greater accuracy than the integral 7 ml part of the measurement. Confirmation of this explanation for splitting the measurement came in the comment of Marion (N40, AH), a nurse in the cardiothoracic intensive care unit at Alexander Metropolitan Hospital, written at the bottom of her illustration, particularly the last sentence of it (see Table 6.7). I would use 2 syringes since I need 5 mls plus 2½ mls. I can t accurately get 7½ mls on 1 syringe. (Marion, N40, AH) There was an apparent contradiction in the nurses techniques, however, in terms of their quest for optimal accuracy. On the one hand the nurses concern about achieving maximum accuracy resulted in nurses separate measurement of the fractional 0.5 ml part of the dose. On the other hand, any gain in accuracy they believed they had achieved by splitting measurement of the volume in this way was offset by the accuracy lost through selecting syringes larger than optimal. Nurse N40, AH, used a 10 ml syringe to measure a 5 ml dose where a 5 ml syringe would have achieved greater accuracy. Nurse N56, GH, used a 20 ml syringe to measure a 7 ml dose where a 10 ml syringe would have achieved greater accuracy. Nurses N56, GH and N54, GH used a 3 ml syringe to measure a 0.5 ml dose where a 1 ml syringe would have achieved greater accuracy. 6.4 Summary of nurses measurement of medicine doses This chapter addressed that aspect of Research Question 1 relating to the strategies nurses use to measure medicine doses in clinical practice. Nurses measurement of medicine doses in response to tasks posed in the questionnaire is also described. In Chapter 8 Discussion, nurses performances on dose measurement 296

310 Chapter 6: Measuring Medicine Doses tasks in these two contexts are compared and the effect of problem setting on the performance of nurses is discussed. Several issues relating to the use of syringes to measure medicine doses emerged from observation sessions and the questionnaire. The first issue concerned the excess volume in ampoules provided by manufacturers to ensure the labelled volume was available to nurses, and how nurses managed overfill. Ampoules of heparin and several other medicines were monitored during observation sessions to determine the extent of overfill and nurses were interviewed about their responses to overfill. The second issue of concern was the widespread practice of nurses using insulin syringes, graduated in international units of insulin, to measure doses of heparin stated in millilitres, a practice that potentially increases the risk of measurement error. The third issue related to nurses poor judgement in their choice of syringe capacity for measuring medicine doses, and the associated reduction in measurement accuracy when nurses select syringes of greater capacity than necessary. 297

311 7 The Teaching of Medicine Dose Calculation and Measurement Skills The learner should never be told directly how to perform any operation in arithmetic. Nothing gives scholars so much confidence in their own powers and stimulates them so much to use their own efforts as to allow them to pursue their own methods and to encourage them in them. Warren Colburn 33 (1830, as cited by McIntosh,1998, p. 48) Chapter 7 presents findings relating to how nursing students are taught to calculate and measure medicine doses. The information was obtained using an online questionnaire to academic staff employed by Australian universities offering preregistration nursing education programs. The questionnaire was used to obtain information from coordinators and teachers of units of study that included medicine dose calculations. Academic staff provided information about the strategies students were taught to calculate doses, how those strategies were determined, and the ways in which instruction was delivered. Participants also provided information about practices relating to the teaching of dose measurement skills. Resources used to support student learning were canvassed, and the methods used to assess dose calculation and measurement skills were explored. Staff perceptions were sought in relation to the extent and nature of difficulties experienced by students in gaining competence in dose calculations, and by staff in teaching dose calculations. Opinions were sought on how such difficulties might be solved. 7.1 Participants and their universities Sixty-five staff from 43 campuses of 28 different universities participated in the online questionnaire (see sample pages in Appendix 6). Every state and territory in Australia was represented in the data. The number of responses included in the data was reduced to 64 after excluding incomplete data from one participant on the 33 Text of an address to the Americal Institute of Instruction, Boston 298

312 Chapter 7: The Teaching of Medicine Dose Calculation and Measurement Skills grounds that the few questions answered contributed little of value to the study. Individual participants were coded S1 to S64. I contacted the Head of School or equivalent at 35 universities; 33 of them (94%) agreed to distribute to targeted staff the Invitation to participate I then sent them. In terms of the universities represented, the response rate was that 28 out of 35 (80%) of invited universities participated in the questionnaire. Despite my following up with a reminder to distribute to staff, five universities whose Head of School had agreed to distribute the Invitation to participate failed to produce a volunteer. It is not known whether this occurred because the Head of School did not send the invitation to staff or simply because no staff members responded. As participants worked their way through the questionnaire the number who failed to respond to questions gradually increased. Initially this number was six (after about twenty questions) then it increased to a fairly steady 11 and finally rose to 14 or 15 for the last few questions in the questionnaire. Throughout Chapter 7, references to the questionnaire will appear as a question number together with a page number, as the questions could not be numbered consecutively. The page numbers refer to pages in the actual questionnaire rather than the page numbers in the Appendix Campuses represented in the data The number of campuses represented per university ranged from one (20 universities) to three (3 universities). The number of participants per university ranged from one (12 universities) to six (1 university) with an average of 2.3 participants per university. Table 7.1 provides a summary of the distribution of participants by state or territory, and according to the universities and campuses they represented. 299

313 Chapter 7: The Teaching of Medicine Dose Calculation and Measurement Skills Table 7.1 Number of universities, campuses and participants by state and territory State No. (%) universities represented n = 30 a No. (%) campuses represented n = 43 No. (%) participants n = 64 NSW 11 b (37%) 15 (35%) 25 (39%) Victoria 7 (23%) 11 (26%) 13 (20%) Queensland 4 c (13%) 8 (19%) 13 (20%) Western Australia 3 c (10%) 3 (7%) 5 (8%) South Australia 2 (7%) 3 (7%) 3 (5%) Tasmania 1 (3%) 1 (2%) 2 (3%) Northern Territory 1 (3%) 1 (2%) 2 (3%) Australian Capital Territory 1 (3%) 1 (2%) 1 (2%) a b c 28 distinct universities: Two universities had participants from campuses in two different states Two of the universities had participants from a campus in NSW and another state One of the universities had participants from a campus in WA and another state Employment status and role of participants Fifty-nine of the 64 participants (92%) were employees of the university s School of Nursing 34 (or a similarly named unit). The status of the remaining five respondents was as follows: member of a student learning or academic support unit (2 respondents) member of a mathematics department carrying out service teaching (1 respondent) casual/sessional member of staff in the School of Nursing (1 respondent) other: coordinator/manager of electronic drug calculations programs for nursing and pharmacy students (1 respondent). 34 All such units will be referred to in the thesis as the School of Nursing. 300

314 Chapter 7: The Teaching of Medicine Dose Calculation and Measurement Skills Question 3, p. 3 sought information from participants about their role in the unit. At the end of the questionnaire, Question 1, p. 58 and Q1, p. 59 asked participants if they had coordinated or taught any other units of study involving medicine dose calculations during the previous 12 months, and if so how many of each. Table 7.2 gives a summary of the responses. Table 7.2 Participants by role and other similar units coordinated or taught (n = 64) Role in unit of study No. (%) participants n = 64 No. of participants coordinating other units n = 9 No. of participants teaching other units n = 19 Coordinator 8 (13%) 2 2 Coordinator and teacher 27 (42%) 5 9 Teacher 29 (45%) 2 8 Approximately one third of participants reported having coordinated or taught additional units of study involving medicine dose calculations during the previous twelve months. With one exception, the number of such units of study varied from one to seven. The exception was a teacher who had coordinated one unit and taught 25 additional units of study. However it should be noted that online learning was the sole means of delivering instruction in medicine dose calculations in the unit this participant described. 7.2 Units of study Fifty-two distinct units of study were described. Questions 4 and 5, p. 2, sought information about the type of program in which the unit was studied, and the length of the program if studied full-time and completed in minimum time. Table 7.3 summarises the responses. 301

315 Chapter 7: The Teaching of Medicine Dose Calculation and Measurement Skills Table 7.3 Program type and length (n = 64) Program type Undergraduate (UG) No. of programs % of programs Length of program (full-time study) years a Masters years Combined UG and masters and 2 years respectively b Diploma year a Exceptions were three programs: one was two years long, one had a two-year option in addition to the three-year program, and one was studied over 3.5 years b In one of these programs, the undergraduate program was studied over three years, and the masters over five trimesters Among the 58 participants who said the unit was studied in an undergraduate program, 30 (52%) said it was studied in first year, 13 (22%) in second year, eight (14%) in third year, and one unit in the fourth year of a three-and-a-half year program. Six participants said the unit was studied in all years of the program, a response that suggested they had misinterpreted the question. Among the seven participants who said the unit was studied in a masters program, three participants (43%) said it was studied in first year, two (29%) in second year, and one in all years of the program (14%). One participant gave no response Extent of focus on calculation of medicine doses For many of the units of study, the unit name suggested that medicine dose calculations formed just a small part of a much more comprehensive unit e.g. Nursing Clinical Skills, Nursing and Health Breakdown The names of other units of study suggested that the unit had a much sharper focus on medicines, dose calculations and medicine administration, for example, Quality Use of Medicines in Nursing, Pharmacology for Nurses Question 1, p. 4 asked participants to estimate the percentage of the unit devoted to medicine dose calculations. Estimates from 58 respondents ranged from 302

316 Chapter 7: The Teaching of Medicine Dose Calculation and Measurement Skills 1% to 75% of the unit. Thirty-five participants (60%) believed that no more than 15% of the unit was devoted to medicine dose calculations, while 12 respondents (21%) estimated the percentage to be between 15% and 30%. The three respondents (5%) who put the estimate at greater than 40% included one participant who noted the unit was a half credit preparatory skill development unit. Four respondents (7%) were unsure and four (7%) gave an explanation but not an estimate Entry level mathematics prerequisites for students Question 6, p. 2 asked participants to select the option that best described the School policy regarding the mathematics background of students entering the program. Table 7.4 summarises the responses. Table 7.4 Mathematics achievement level required on entry to program (n = 64) Entry-level mathematics achievement No. of respondents % of respondents A minimum level of mathematics is required An assumed level of mathematics applies Other (please specify) 2 3 There is no required or assumed level of mathematics Unsure Question 1, p. 3 asked participants to state the required or assumed level of mathematics, if that applied. Seven (26%) of the 27 participants who said that a required or assumed level of mathematics achievement applied gave Year 12 as the level, while ten (37%) gave Year 10 or a lower level. For seven participants (26%) the level of mathematics required or assumed was not able to be reliably determined from the response, while three participants (11%) were unsure of the level that applied. 303

317 Chapter 7: The Teaching of Medicine Dose Calculation and Measurement Skills 7.3 Teaching medicine dose calculations Question 2, p. 4 asked participants to select one or more of the options offered to indicate the modes used to deliver instruction in medicine dose calculations. The responses are summarised in Table 7.5. Table 7.5 Modes used to deliver instruction in medicine dose calculations (n = 64) Instruction mode No. of participants % of participants Lectures Tutorials Laboratory sessions Clinical placements Online learning Supplementary sessions provided by student learning unit or academic support unit Unsure - - Other a 3 5 No answer 1 2 a Other modes included a one-off lecture at the beginning of semester, and supplementary sessions provided by the unit coordinator and teachers Online learning and laboratory sessions were the two most frequently reported modes for delivering instruction in medicine dose calculations. The number of modes used to deliver instruction in medicine dose calculations varied from one to six. Most of the 63 respondents reported that multiple delivery modes were employed, with only ten participants reporting that a single mode was used Resources used to support student learning In response to Question 1, p. 6, 58 participants selected from the available options to indicate the types of resources students used to support their learning of 304

318 Chapter 7: The Teaching of Medicine Dose Calculation and Measurement Skills medicine dose calculations in the unit and whether the resources were prescribed or recommended. Table 7.6 provides a summary of the responses. Table 7.6 Types of prescribed and recommended learning resources used (n = 58) Type of resource Prescribed Recommended Total Commercially available text/reference book In-house printed learning materials Commercially available online or computer-based learning program In-house online or computerbased learning program Text and reference books were the most commonly used type of learning resource, with a greater number of these being recommended than prescribed. Almost all in-house printed materials were developed within Schools of Nursing, an exception being supplementary materials developed by the Mathematics Learning Centre (S22). Questions 2 5, pp. 6 7 asked participants to name or give a description of the resources students used in the unit. Table 7.7 provides a summary of the resources the participants described. 305

319 Chapter 7: The Teaching of Medicine Dose Calculation and Measurement Skills Table 7.7 Learning resources described by participants (n = 50) Commercial resources In-house printed resources In-house online or computer-based resources Text or reference books Workbooks, self-directed learning packages Workbooks, activities and study aids CD-ROMs Web sites some costfree, some linked to a text Course materials and modules within learning guides Worksheets and tutorial materials Lecture notes and handouts Lab workbook/manual Quizzes, practice questions PowerPoint tutorials Posters on walls in labs Lectures with practice tests, sometimes with interactivity or feedback Quizzes and practice tests Videos The fifty participants who responded nominated a total of twelve different text or reference books, with individual participants listing up to five books that were recommended or prescribed for students. Respondents described many online and computer-based resources, designed and developed within the university, usually but not always by academic staff within the School of Nursing. An exception was a report of a Student Learning Unit numeracy web site with on-line exercises to assist students with the necessary numeracy skills (S36) Staff delivering instruction Question 1, p. 5 asked participants to select at least one of the options offered to indicate the category or categories of staff responsible for giving formal instruction in medicine dose calculations. If the participant selected more than one category, Question 2, p. 5 asked them to indicate which category of staff took primary responsibility. Table 7.8 shows each option and how many times it was selected by the 61 respondents. The final column shows the responsible staff in the 24 instances (39%) 306

320 Chapter 7: The Teaching of Medicine Dose Calculation and Measurement Skills where the participant indicated a single category of staff was responsible for instruction. Table 7.8 Responsibility for instruction in medicine dose calculations (n = 61) Staff giving instruction Academic staff from School of Nursing Clinical facilitators supervising students during clinical placements Academic staff from mathematics department carrying out service teaching Academic staff from student learning unit or academic support unit No. of participants Primary responsibility Sole responsibility Unsure Other a 8 3 b 2 c a b c Other included an online learning program (3 respondents), Clinical Nurse Educators, and private tutors. Responses included online learning program (2 respondents) and Clinical Nurse Educators (1 respondent). Online learning program was the sole means of instruction. Academic staff from the School of Nursing were most commonly responsible for giving instruction in medicine dose calculations, taking either sole or primary responsibility for instruction. Thirty-seven participants (61%) reported that the responsibility for teaching medicine dose calculations was shared by up to four different categories of staff. The most common sharing arrangement, reported by 26 (43%) of the 61 respondents, was for academic staff from the School of Nursing to take primary responsibility and for clinical facilitators to take a supporting role, instructing students during clinical placements. In some cases this combination was further supplemented by support from staff of a student learning unit or academic support unit or a mathematics department. A further 7 respondents (11%) reported some 307

321 Chapter 7: The Teaching of Medicine Dose Calculation and Measurement Skills sharing involving academic staff from a student learning or academic support unit, with a further 4 respondents (7%) reporting other sharing arrangements. When online learning was the primary mode for delivering instruction in medicine dose calculations, this mode of learning was less likely to be supported by face-to-face instruction. Two participants reported that students were expected to complete their online instruction as mastery learning without input from staff. The estimates participants gave for the number of staff involved in delivering instruction in medicine dose calculations in the unit varied from 1 to 15++ (Q3, p. 5). The involvement of four or five staff members in delivering instruction was the most common scenario, based on the median value of participants estimates. However, as one respondent noted, if one included staff supporting the application of skills in clinical scenarios, the number of staff involved would be considerably higher Basis for selecting staff Question 4, p. 5 asked participants to select one of the options to complete the sentence: Staff are usually selected to teach units involving medicine dose calculations. Table 7.9 summarises the responses. Table 7.9 Reasons staff are usually selected to teach units involving dose calculations (n = 62) Reason for selection For reasons unrelated to their ability to teach the associated mathematical skills Because they have prior experience in teaching medicine dose calculations Because they have a strong personal interest in, and/or aptitude for, teaching medicine dose calculations Because they have formal mathematics teaching qualifications No. of participants % of participants Unsure 7 11 Other a 5 8 a Other included Clinical Nurse Educators, private tutors, and reports that staff did no teaching because online learning was used (3 respondents). 308

322 Chapter 7: The Teaching of Medicine Dose Calculation and Measurement Skills Of the 62 responses, the most frequent was for reasons unrelated to their ability to teach the associated mathematical skills. The 28 participants who selected this response included eight who had selected Other and then gave a reason for staff being selected that was, in fact, unrelated to the ability to teach the associated mathematical skills. These reasons included: suitability to teach the subject (S10 & S23); availability of staff (S54); and expertise in Mental Health Nursing (S29). Just one participant, a permanent or contract staff member in the School of Nursing, reported that having formal mathematics teaching qualifications was the reason for selecting staff to teach units involving medicine dose calculations. Among those who gave other reasons for staff being selected, one nominated recent clinical experience (S62), and another stated that selection was based on a combination of the above [i.e. the four options specified] they need the maths skills BUT they need to have demonstrated an understanding of the level and context of the mathematics being taught (S1, staff member of mathematics department coordinating the preparatory skills development unit). In summary, instruction in medicine dose calculations was most often delivered by School of Nursing staff, supported by clinical facilitators and specialist learning support staff. Student learning was supported by a range of text and reference books, commercial and in-house online and printed learning resources. 7.4 The calculation strategies taught Two questions concerning medicine dose calculations were at the heart of the online survey: Who determines the calculation strategies students are taught? What calculation strategies are students taught? The remainder of Section 1.4 addresses these two questions Policy on calculation strategies Question 1, p. 8 asked participants to select a response from the options offered to complete the sentence: The calculation strategies staff teach students to use for calculating medicine doses and intravenous infusion rates in this unit are:.. Table 7.10 shows the responses. 309

323 Chapter 7: The Teaching of Medicine Dose Calculation and Measurement Skills Table 7.10 Policy on the calculation strategies taught to students (n = 58) Policy applied No. of participants % of participants Strictly prescribed by School of Nursing a 16 28% Recommended by School of Nursing b, but not compulsory 15 26% Left entirely to discretion of teaching staff 24 41% Unsure 2 3% Other 1 2% a b Includes one report of other where students learnt solely via an online learning program Includes one report of other where the strategy was recommended by the Unit Chair Forty-one percent of respondents said that the calculation strategy or strategies taught were left entirely to the discretion of teaching staff. However, a greater proportion of respondents, 54%, indicated that the School of Nursing determined the calculation strategies taught, either by prescription or recommendation Determining the calculation strategies taught A two-pronged approach was used in investigating the strategies students were taught for calculating medicine doses. First, with respect to the 50% of respondents who reported that the calculation strategy was prescribed or recommended by the School of Nursing, the strategy prescribed or recommended was taken to be the strategy taught. Second, with respect to the 41% of respondents who reported that the calculation strategy was left entirely to the discretion of the teacher, the data collected did not allow clear identification of the calculation strategies actually taught. Rather, the information sought from all participants was their preferred calculation method. The personal preferences of respondents are discussed later and used to give an indication of what strategies might have been taught when teaching staff had sole discretion to determine the calculation strategy they taught. It is acknowledged that this process may have resulted in a discrepancy between the information obtained and the actual calculation strategies taught when it was discretionary. 310

324 Chapter 7: The Teaching of Medicine Dose Calculation and Measurement Skills A sample medicine dose calculation problem complete with four worked solutions and a fifth option of other (pp. 9 10) was used to determine the strategy or strategies taught in each of the two scenarios described above. Calculation strategy prescribed or recommended to be taught Table 7.11 shows the responses when calculation strategy taught was determined by the School of Nursing (Q1, p.11). Table 7.11 Calculation strategy prescribed or recommended by School (n = 31) Prescribed or recommended calculation strategy Prescribed n = 16 Number of responses Recommended n = 15 Total (%) n = 31 Dimensional analysis (3%) Formula without units (10%) Formula with units (65%) Proportional reasoning Other (19%) Unknown a (3%) a The formula with units was known to be taught in the nominated online learning program. Five of the six respondents who selected other reported that the prescribed or recommended approach was to teach several different calculation strategies and each nominated both formula-based and non-formula-related strategies. The remaining respondent who selected other indicated that the calculation strategy was determined by the online learning program used to instruct students. By consulting the list of resources provided by the participant, it was confirmed that the formula, with units, was the calculation strategy used and so by default the formula was the prescribed strategy. The formula as prescribed or recommended calculation strategy Of 31 respondents, 24 (77%) indicated that the formula was the sole calculation method prescribed or recommended by the School. 311

325 Chapter 7: The Teaching of Medicine Dose Calculation and Measurement Skills Combining these 24 reports with the five reports indicating that the formula was among the mixed strategies prescribed or recommended, it is apparent that the formula was taught in 29 of the 31 cases (94%) where the calculation strategy was determined by the School. Teaching non-formula-related methods as prescribed or recommended strategy A total of six participants indicated that one or more non-formula-related strategies were prescribed or recommended by the School. The only non-formularelated strategy nominated as the sole calculation strategy prescribed was dimensional analysis. The unit in which dimensional analysis was taught was studied in the second year of a three-year undergraduate degree. The respondent was both the coordinator and the teacher in this unit. Five participants indicated that non-formula-related methods were among the mixed calculation strategies prescribed or recommended by the School. They gave the following descriptions of the teaching approach taken. We show students the different methods and discuss them. We tend to the formula (Solution C with units) as we believe that this is what is taught in the next semester but show them the relation between that and proportional reasoning. (Recommended strategy, S1, coordinator of preliminary skills development unit) We offer students the ratio proportions and the formula (with units) methods so all calculations are done BOTH ways so students may choose. (Prescribed strategy, S2) In third year we don t prescribe a method but provide examples of each of these ways. Students learn and apply maths differently and we accept any of the above methods in third year if it is sound and reaches the correct answer. (Recommended strategy, S22) All four approaches are used we support the student s individual learning style. It is dangerous to force a student down a particular approach. (Prescribed strategy, S23) Unit teaches both solution B [formula without units] and solution D [proportional reasoning] [as] recommended by the Unit Chair, reinforced by the teaching materials utilised (e.g. tutorial scenarios and guides) and supported by the recommended textbooks. (Recommended strategy, S3) 312

326 Chapter 7: The Teaching of Medicine Dose Calculation and Measurement Skills Question 1, p. 13 asked participants to select from the five options provided the solution that most closely resembles your preferred calculation method the method that, given entirely free choice, you would demonstrate to students for solving problems similar to the sample problem. Table 7.12 provides a summary of the responses. Table 7.12 Personally preferred calculation strategy by role in unit (n = 54) Personally preferred calculation strategy Coordinator n = 8 Participant s role in unit Coordinator and teacher n = 25 Teacher n = 21 Total (%) n = 54 Formula with units (74%) Formula without units (9%) Dimensional analysis (4%) Proportional reasoning (4%) Other (9%) Among the five respondents who selected other was one who indicated their preference was to demonstrate the ratio method to students, a method not listed in the options offered. Two participants expressed a preference for mixed strategies that included non-formula-related methods as well as the formula. Of these, one indicated that their preference was to demonstrate to students all four approaches identified in the question. This participant reiterated the risks associated with forcing students to use a particular approach that they had noted when describing the same approach as the strategy prescribed by the School. The other participant indicated their preference was to demonstrate both the formula and proportional reasoning methods, noting that this was the same approach that the Unit Chair recommended. Two participants indicated that the question was not applicable as they had no role in teaching medicine dose calculations because students learnt via an online program. 313

327 Chapter 7: The Teaching of Medicine Dose Calculation and Measurement Skills The formula as personally preferred calculation strategy Forty-five (83%) of 54 respondents indicated that the formula was their preferred calculation method. If one adds two reports indicating a personal preference for mixed calculation strategies, then 47 (87%) of 54 respondents of participants reported the formula among their preferred calculation strategies. One might infer then, that for the vast majority of teachers, the formula was likely to be the sole calculation strategy taught or one of several calculation strategies taught. Non-formula-related methods as personally preferred calculation strategies Seven participants (13%) indicated that non-formula-related methods were among the calculation strategies they would demonstrate to students, either as the sole calculation strategy demonstrated in the case of five participants, or as one of several methods demonstrated in the case of two Including measurement units in formula Including units of measurement in the solution process when the formula was taught was far more common than not including units. Of the 21 respondents who selected the formula as the calculation strategy prescribed or recommended by the School (Q1, p.11), 18 indicated units were included, compared to 3 who indicated they were not. Similarly, among the 45 respondents who selected the formula as their personally preferred calculation strategy (Q1, p.13), 40 indicated they would include units compared to 5 who indicated they would not Variants of the formula Question 1, p. 12 and Question 1, p. 18 asked participants to provide the version of the formula if they had nominated the formula either as the strategy prescribed or recommended by the School, or as their personally preferred calculation strategy, or both. Further, if the calculation method the participant had selected from the options provided was substantially different from the solution method the respondent actually used, the participant was asked to provide the preferred steps in setting out the solution (Q2, p.12 and Q2, p.14). Forty-one participants 87% of the 47 reporting the formula was taught provided at least one version of the formula they used. All versions of the formula provided by participants are included in Appendix

328 Chapter 7: The Teaching of Medicine Dose Calculation and Measurement Skills Participants who offered the version of the formula used were required to write it in prose form, following the instructions I provided. The reason for this was that the SurveyMonkey program did not allow participants to respond using mathematical expressions such as fractions. Then, based largely on my knowledge of how nursing educators and textbooks present formulae to students, I transcribed the prose format of each formula into mathematical format. There were few difficulties in making the transition. When ambiguities did occur, such as where the prose format could reasonably be interpreted in two different ways, I noted the ambiguity and listed both formats. Although almost every version of the formula provided was different, five major variations were identified (Q1, p. 12): (S28) (S35) (S8) (S54) (S6) Most differences between versions were minor and related to the wording of terms such as in the first and last versions above, offered by S28 and S6. No participant responded to the invitation to provide the preferred steps in setting out the solution if they differed substantially from the steps that appeared in the questionnaire. Dose ordered volume of stock strength Stock strength want vol got 1 what you want stock volume what you've got Stock required vol (mls) = Volume required (mls) Stock strength Prescribed dose volume or unit Stock dose In summary, the data indicated that the formula was the calculation strategy most often taught to students, sometimes supplemented by one or more non-formularelated calculation strategies. The data suggested that this was the case regardless of whether the School determined the calculation strategy to be taught, or whether it was left to the discretion of the teacher, most of whom reported a strong preference for the formula. Many different versions of the formula were reported to be in use, however when applying the formula staff were more likely than not to include units of measurement in the calculation steps. 315

329 Chapter 7: The Teaching of Medicine Dose Calculation and Measurement Skills 7.5 Methods used to assess dose calculation skills Approaches used to assess students medicine dose calculation skills were investigated through a series of questions focusing on different aspects of the assessment process. Question 1, p. 19 asked participants whether medicine dose calculation skills were assessed separately to other content in the unit (for example, by way of one or more distinct tests, or by way of an identifiable component within one or more tests). Separate assessment of students medicine dose calculation skills was reported by 46 (87%) of 53 respondents. Questions 2 and 3, p. 19 asked participants to select one or more of the options offered to indicate the methods used to assess students medicine dose calculation skills. The options included pen-and-paper test, practical assessment in a real clinical setting, practical assessment in a simulated clinical setting, online quiz or assessment, or other. Participants reported up to four different assessment methods being used. Employment of one or two assessment methods was by far the most frequently reported approach. Pen-and-paper tests were employed far more often than any other form of assessment, with online quizzes the second most frequently reported form of assessment. Of note was the fact that practical assessment in a real clinical setting was only ever used as one of several methods for assessing students medicine dose calculations, never as the sole method. Two respondents selected other as the primary assessment method to indicate that the methods used were of equal weighting. A further respondent indicated that students needed to achieve 100% in two quite different types of assessment. A single respondent reported that no assessment of dose calculation skills was undertaken. Minimum pass requirement Question 4, p. 19 asked participants to select from the options offered to indicate the minimum pass requirement for the medicine dose calculation component of the unit. The responses indicated widespread adoption of a 100% pass requirement. Forty-two of the 53 respondents (79%) said that 100% was required to pass the medicine dose calculation component. Five (9%) said that 50% correct was the minimum required to pass. Three participants (6%) said there was no minimum pass requirement. 316

330 Chapter 7: The Teaching of Medicine Dose Calculation and Measurement Skills Number of attempts permitted Question 5, p. 19 asked participants how many attempts students could have to pass the medicine dose calculation component of the unit. Table 7.13 summarises the responses. Table 7.13 Number of attempts permitted to pass medicine dose calculation component (n = 53) Number of attempts permitted No. of participants % of participants Must pass at first attempt 2 4% Two 12 23% Three 23 43% Four 2 4% As many as needed 7 13% At teacher s discretion 3 6% Other 4 8% The most frequent response was that students were permitted three attempts to pass the medicine dose calculation component of the unit. Participants who selected other described approaches to assessment that included allocating a P-plate mathematics licence (unrelated to their final grade) to students who achieved a minimum of 80% on each of four computer-marked assessments (S1). Another participant described a complex process over a 12-week period of allowing students repeated attempts until they achieved the required 100% to demonstrate competence (S22). Medicine dose calculations as a hurdle requirement Question 6, p. 20 asked participants whether it was possible to fail the medicine dose calculation component but still pass the unit. This question arose from concern that it might be possible for a student to progress through the course 317

331 Chapter 7: The Teaching of Medicine Dose Calculation and Measurement Skills successfully without having ever demonstrated competence in medicine dose calculations. Table 7.14 shows the results. Table 7.14 Is it possible to fail the dose calculation component but pass the unit? (n = 53 Response No. of participants % of participants No Unsure 3 6 Yes 9 17 Three participants (S5, S27 and S52) added that passing the medicine dose calculation component of the unit was a prerequisite for them progressing to the clinical component and clinical placements. On practicum they start to use [dose] calculation skills and intravenous/injection skills (S27). Additional information provided by participants The question about how students were prevented from passing the unit if they had failed the medicine dose calculation component brought forth valuable unsolicited information relating to learning and assessment of medicine dose calculations. This information related to (a) provisions for supporting student learning and providing remediation if a student failed an assessment, and (b) policies enabling students to appeal if they failed an assessment. Ten participants described provisions available to students to prepare them for assessments in medicine dose calculations or to provide remediation, usually after failing their first attempt. Descriptions of such provisions included the following. It is up to the student to do the study and pass the test. They have text, on-line resources and work books + tutor and lecturer support. (S4) Following the second attempt intensive tuition is undertaken with the students at risk of failing. (S28) 318

332 Chapter 7: The Teaching of Medicine Dose Calculation and Measurement Skills Student one-on-one sessions with tutors or lecturer in charge; exposure during clinical placement. (S18) Strategies are put in place for at risk students. Students are given a second chance if they don't achieve 100% on the first attempt. Practice questions are provided based on incorrect questions and individual student consultations are offered. (S30) Student is referred to maths learning & support for remedial work after the first attempt (early in semester); Tutor provides one-on-one feedback and some teaching to student. Practice quizzes that can be accessed as frequently as required (a large databank of questions). Basic maths calculations is tested in year one in preparation for drug calculations in Year 2. (S21) By giving the student a lot of support before the test. After first attempt the student is counselled and any issues/weak areas identified so that maximum support is given before the second attempt. (S45) Reminders, advice to go to maths learning centre and review of progress through [online learning program] IntelliLearn. (S22) Of particular note was the information provided by S21 concerning students being tested on basic maths calculations in year one. This practice reflects the similar practice found in many dose calculation text books of revising students abstract mathematical skills as a preparation for dose calculations. Skills typically included in a basic mathematics revision are: operations involving fractions (addition, subtraction, multiplication, and division); operations involving decimals; percentages; conversions between fractions, decimals, and percentages; multiplication and division of decimal numbers by powers of ten; and metric conversions. The fact that these skills are included in text books, and sometimes specifically tested in nursing programs, suggests these skills are considered essential for dose calculations. Three participants provided unsolicited information about provisions aimed at assisting students to pass the medicine dose calculation component and hence pass the unit. These provisions included supplementary assessments if this is the only component that was failed, and the right of appeal to the Head of School and a discretionary fourth attempt. In summary, students dose calculation skills were most often assessed using several types of assessment method, the most common being pen-and-paper tests and 319

333 Chapter 7: The Teaching of Medicine Dose Calculation and Measurement Skills online quizzes. Achieving 100% to pass the dose calculation component of the unit was a requirement reported by 79% of respondents, however students were usually permitted multiple attempts. 7.6 Student difficulties learning dose calculations Participants perceptions about the difficulties students experience in attaining competence in medicine dose calculations were explored through a series of four questions. Question 1, p. 23 employed a Likert scale to gauge participants endorsement that: Students often experience difficulties in attaining competence in medicine dose calculations. Table 7.15 provides a summary of the responses. Table 7.15 Staff endorsement of students experiencing difficulties learning dose calculations (n = 52) Level of agreement Coordinator n = 8 Number of participants by role Coordinator and teacher n = 24 Teacher n = 20 Total (%) n = 52 Strongly agree (25%) Agree (40%) Neither agree nor disagree (17%) Disagree (17%) Strongly disagree Sixty-five percent of participants strongly agreed or agreed with the statement that students often experience difficulties in attaining competence in medicine dose calculations, while only 17% of participants disagreed. 320

334 Chapter 7: The Teaching of Medicine Dose Calculation and Measurement Skills Areas of difficulty, contributing factors and solutions Questions 2 4, p. 23 were open-ended questions that sought participants perceptions about: the aspects of medicine dose calculations that students find most difficult; the factors that contribute to those difficulties; and suggested solutions. Up to six areas of difficulty were offered by each of 51 individual participants, resulting in a total of 80 suggested aspects of medicine dose calculations that students find difficult. Specific skill areas were identified, and these were then aggregated into seven broader areas of difficulty, on the basis of common characteristics. These areas of difficulty and the component skill areas that were seen to cause students most difficulty are shown in Table

335 Chapter 7: The Teaching of Medicine Dose Calculation and Measurement Skills Table 7.16 Aspects of medicine dose calculations students find most difficult (n = 51) Area of difficulty No. of responses (n = 80) Arithmetical skills 29 (36%) Numerical calculations 15 Fractions 7 Ratio, proportion 4 Rounding answers 3 Decimals 2 Long division 2 Metric units and conversions 13 (16%) Units of measure 4 Metric conversions 9 Formulae and their application 11 (14%) Rates 5 (6%) Affective factors 4 (5%) Problem set-up / assessing reasonableness of answer 4 (5%) Other 14 (18%) Responses in the category of arithmetical skills included the following: numerical calculations the actual working out arithmetic calculations; and applying the principles of mathematics. Responses in the category of formulae and their application were: 322

336 Chapter 7: The Teaching of Medicine Dose Calculation and Measurement Skills remembering formulas appropriate formulas to the scenarios; and the ability to apply the correct formula often if the student becomes confused they use the incorrect formula. Four responses were labelled as affective factors: bad experiences with maths in the past; frightened of maths; and 100% pass rate makes students more anxious. A total of 74 factors offered by 51 respondents that contribute to student difficulties were aggregated into nine categories on the basis of common characteristics. These contributory factors are listed in Table 7.17 together with the number and percentage of the 51 respondents offering each factor. 323

337 Chapter 7: The Teaching of Medicine Dose Calculation and Measurement Skills Table 7.17 Factors that contribute to student difficulties in dose calculations Suggested contributory factor No. of responses (n = 74) % of respondents offering response Poor entry-level mathematics skill Affective factors and bad prior mathematical experiences Lack of recent exposure to mathematics 8 16 Over-reliance on calculators affecting intuitive mathematical ability The methods used to teach medicine dose calculations Problems relating to formulae and their application Not reading the question properly, rushing, not taking enough care Medicine dose calculations not taken seriously: errors will not happen in the real world Other A total of 74 suggested solutions to student difficulties were offered by 49 participants, who suggested up to five remedies each. The solutions, grouped by common characteristics, are summarised in Table

338 Chapter 7: The Teaching of Medicine Dose Calculation and Measurement Skills Table 7.18 Suggested solutions to address student difficulties (n = 49) Suggested solution Change the way medicine dose calculations are taught No. of responses (n = 74) % of respondents making response Impose minimum entry requirements Provide support and remediation for students Practice 9 18 Change the way medicine dose calculations are tested 5 10 Utilise numeracy specialists in learning support unit 3 6 Change the teaching of mathematics in schools 3 6 Greater focus on revisiting basic mathematics 2 4 Other Some of the responses from participants are best viewed as a complete sequence comprising: the area of difficulty identified by the participant, contributing factors and suggested solutions. Appendix 9 provides examples of the complete sequence of participants responses for three skill areas: formulae, arithmetical skills and metric conversions. Responses of particular interest were those suggesting student difficulties might be resolved by changing the way medicine dose calculations are taught, and by changing the way student competence is tested. Key suggestions for change The methods used to teach and assess medicine dose calculations are of central interest to the thesis, so some verbatim examples of staff members suggestions concerning these two aspects of medicine dose calculations are included below. 325

339 Chapter 7: The Teaching of Medicine Dose Calculation and Measurement Skills Changing the methods used to teach and assess competence in dose calculations Create a more realistic setting (but it has to match the testing regime at university and in the clinical setting). There are a significant minority of students who do have a problem with mathematics (at about the year 9 level of understanding). For some this can be assisted with good quality contextual revisiting of the mathematics. There also needs to be a whole of program approach to ensuring students revise the skills every year and that it is embedded in the curriculum. (S1) Offer ratio method and formulas so students can choose what they use. Practice drug calcs in every class. (S2) Go back to basics with those students that are experiencing difficulty, relate material to what they already know, keep the questions reality based, practice, practice, more practice with support and positive reinforcement. (S3) Teaching differently and more applied teaching (S10) Combine the calculations with the practical measuring and giving (S26) I think to apply it to practice e.g. put the skill in a context. (S44) Multiple [calculation] strategies and context based (S60) More simulated exams (S18) Trial implementation of new drug calculation paper (format): questions are set out to replicate the clinical environment with a drug order and medication labels (S28) Ensure that [one is] testing more than calculations and test whether students know and understand the use of formulas for particular situations. Testing is often acontextual but with volume of students, difficult to incorporate more realistic situational testing (would be ultimate aim). Could be achieved with animation. (S33) Alternate testing regimes; avoid the 100% pass fail as the sole measure of competency (S35) We have used context-based paper tests but I think the simulated environment is the best they may be able to relate the numeracy to practice this way for it to make sense to them (S44). 326

340 Chapter 7: The Teaching of Medicine Dose Calculation and Measurement Skills A strong theme running through participants suggested changes to the methods used to teach and assess competence in dose calculations was that teaching, learning and assessment of medicine dose calculations should take place in authentic contexts, including in simulated clinical environments. Another theme concerned teachers offering students alternative calculation methods. In summary, 65% of respondents agreed that students often experience difficulty in learning to calculate medicine doses with staff reporting that basic numeracy skills was the most problematic area. Staff believed that poor mathematical preparation and affective factors such as lack of confidence and anxiety were the greatest contributory factors. Changing how calculation skills are taught, imposing entry requirements, and providing support and remediation for students were among the many solutions suggested by staff. 7.7 Staff difficulties teaching dose calculation skills Participants perceptions of the difficulties staff experience in teaching medicine dose calculations were explored through a series of four questions. Question 1, p. 24 employed a Likert scale to gauge the level of participant agreement with the statement: Staff sometimes experience difficulties in teaching medicine dose calculations to students. Table 7.19 provides a summary of the responses. 327

341 Chapter 7: The Teaching of Medicine Dose Calculation and Measurement Skills Table 7.19 Staff endorsement of difficulties experienced by staff teaching dose calculations (n = 52) Level of agreement Coordinator n = 8 Number of participants by role Coordinator and teacher n = 24 Teacher n = 20 Total (%) n = 52 Strongly agree (10%) Agree (46%) Neither agree nor disagree (23%) Disagree (13%) Strongly disagree (6%) Unsure (2%) Fifty-six percent of participants strongly agreed, or agreed, that staff sometimes experience difficulties in teaching medicine dose calculations, compared to 19% who disagreed, or strongly disagreed a ratio of almost three to one Problem areas, solutions and staff selection issues Questions 1 3, p. 25 were open-ended questions that sought participants perceptions about the types of problems staff experience in teaching medicine dose calculations, suggested solutions, and any issues surrounding the selection of staff for the task. Feedback from participants concerning staff difficulties was far more limited than it was in relation to student difficulties. In response to Question 1, 39 participants nominated 51 types of problems that staff may experience in teaching dose calculations. Individual participants offered up to three suggestions. Problem areas were grouped into categories on the basis of common characteristics and are summarised in Table

342 Chapter 7: The Teaching of Medicine Dose Calculation and Measurement Skills Table 7.20 Types of problems staff experience in teaching dose calculations (n = 39) Problem area Staff members feel ill-equipped to accommodate the diverse needs and learning styles of students No. (%) of respondents making response 15 (38%) Like students, staff members may not be strong in mathematics 11 (28%) Staff members, not being mathematics teachers, may be uncomfortable teaching mathematical skills 8 (21%) Lack of confidence for some, even mathematics phobia 6 (15%) Lack of recent application of mathematical skills in [clinical] practice 3 (8%) Lack of time allocated to covering content 3 (8%) Staff not having a uniform approach to teaching the content 3 (8%) Difficulties in combining expertise in mathematics pedagogy with expertise in the nursing context of application 2 (5%) Among the difficulties reported under the heading of staff members feel illequipped to accommodate the diverse needs of students were: staff not being able to appreciate the level of misunderstanding of some students (S2); generational differences in the way students are taught maths and the way academics were taught maths (S33); and teaching students who have difficulty in grasping maths concepts (S45). The category titled staff members, not being mathematics teachers, may be uncomfortable teaching mathematical skills included: staff may believe they should not be teaching mathematical skills (S36); staff may have difficulty translating mathematical principles (S6) and explaining how formulas work (S13); and some staff only know their way of performing dose calculations so they can t cope with students who use another correct way (S23). 329

343 Chapter 7: The Teaching of Medicine Dose Calculation and Measurement Skills Question 3, p. 25 asked participants what solutions participants could offer to the difficulties experience by staff in teaching of medicine dose calculations. Thirtyfive solutions were suggested by 30 participants. The suggested solutions are summarised in Table 7.21, grouped in categories according to common characteristics. Examples showing the full sequence of participant s responses in areas central to the thesis may be found in Appendix 10. Table 7.21 Solutions to staff difficulties in teaching dose calculations (n = 30) Suggested solution Increased focus on dose calculation in the curriculum and improved teaching methods Strengthen partnerships between content (maths) and context (nursing) experts Greater focus on student needs: entry pre-requisites, pretesting/mathematics preparation course, targeted remediation and support Increased staff development opportunities: more time and workshops with a focus on student needs No. (%) of responses (n = 35) 7 (23%) 6 (20%) 6 (20%) 6 (20%) Maintain currency of teachers skills through practice 3 (10%) Reassess how staff are selected to teach medicine dose calculations Greater collaboration with colleagues, more consistency in teaching approaches 3 (10%) 2 (7%) Other 2 (7%) Among specific suggestions for increasing the focus on dose calculation in the curriculum and improving teaching methods were recommendations to: strengthen the focus on clinically applicable scenarios (S40); gradually increase the level of difficulty of dose calculations throughout the nursing program (S28); pursue a goal of staff being able to teach numerous dose calculation methods (S48); and encourage students to demonstrate their calculation method if it is different from the teacher s (S64). 330

344 Chapter 7: The Teaching of Medicine Dose Calculation and Measurement Skills Other suggestions included: strengthening partnerships between content (mathematics) and context (nursing) experts in teaching dose calculations (S1, S21, S48 and S61); increasing the focus on student needs, including entry level prerequisites or preparation courses, and targeted remediation opportunities. Respondents suggested increasing staff development opportunities with a particular focus on addressing student needs, and more targeted selection of the staff teaching dose calculations. Recommendations included ensuring practices for selecting staff to teach units involve teaching medicine dose calculations: target staff who, knowing their own strengths, choose to teach the subject (S45), and those who are confident and have the ability to teach numerous calculation methods (S48); and avoid selecting staff who experience difficulty teaching units that require numeracy skills (S36). Ten participants added a comment about how staff members are selected for teaching units involving medicine dose calculations. Comments mostly centred on two areas: (a) what the participants believed were essential elements of effective teaching of medicine dose calculations, for example, the need for staff who can demonstrate more than one method and have a passion about the fact that this skill can be mastered (S22); and (b) flawed processes and expectations that result in staff difficulties and ineffective teaching, for example, As they are RNs I think it is assumed that they have that knowledge and the skills to teach (S44). In summary, over half of the respondents agreed that staff sometimes experience difficulties in teaching dose calculations. The areas that participants suggested were most problematic were that staff felt inadequately equipped to meet the diverse mathematical needs and learning styles of students and, like the students, some staff were not strong in mathematics and lacked basic mathematical skills. 7.8 Use of calculators Question 1, p. 27 asked participants to choose from the options provided to complete a statement indicating how they advised students regarding the use of calculators for calculating medicine doses and intravenous infusion rates. Table 7.22 summarises the frequency of the responses. 331

345 Chapter 7: The Teaching of Medicine Dose Calculation and Measurement Skills Table 7.22 Advice to students regarding calculator use (n = 49) Advice Use calculator in all aspects of medicine dose calculations Calculate first without a calculator, then use a calculator to check answers I do not indicate to students any particular policy about calculator use My personal teaching policy is to NOT permit the use of calculators I follow School policy by NOT permitting any use of calculators Coordinator n = 7 Number of participants by role Coordinator and teacher n = 23 Teacher n = 19 Total (%) n = (29%) (47%) (12%) (6%) (2%) Other (4%) A policy of actively encouraging students to use calculators was reported by 37 (76%) respondents, compared to 4 (8%) who did not permit calculator use, and 8 (16%) who neither encouraged nor discouraged calculator use. 7.9 The numeracy skills teachers routinely teach Question 1, p. 28 listed six specific numeracy skills and asked participants to indicate which of them they routinely taught. Table 7.23 provides a summary of the responses of the 50 participants who, between them, nominating a total of 179 numeracy skills they routinely taught. 332

346 Chapter 7: The Teaching of Medicine Dose Calculation and Measurement Skills Table 7.23 Specific numeracy skills routinely taught (n = 50) Numeracy skill No. of responses (n = 179) % of respondents making response Numerical processes Metric units and conversions Applying formulae General mathematical problem-solving techniques Estimation and checking techniques Effective use of a calculator Other 4 8 Applying formulae was the numeracy skill most frequently reported as being routinely taught, while Effective use of a calculator was least frequently reported. Among the skills listed by participants who selected other were: ratio proportions ; concentration ratios ; graphs, tables and charts (in a preparatory skill development unit); and rules of manipulation, the latter possibly referring to basic mathematical operations and algorithms. Individual participants reported routinely teaching between one and seven numeracy skills including those they identified themselves. Table 7.24 provides details of the number of skills participants selected. 333

347 Chapter 7: The Teaching of Medicine Dose Calculation and Measurement Skills Table 7.24 Number of numeracy skills routinely taught (n = 50) Number of specific No. of respondents % of respondents numeracy skills selected a One 8 16% Two 2 4% Three 9 18% Four 9 18% Five 13 26% Six 3 6% Seven 3 6% None b 3 6% a b May include additional numeracy skills identified by the participant Includes cases where online learning alone was used so there was no staff involvement in teaching. The most frequent response was that participants routinely incorporated five numeracy skills (including skills identified by the participant) into their teaching of medicine dose calculations The staff who provide instruction Questions 1 4, p. 29 sought information about: how confident staff were when teaching medicine dose calculations; their own mathematics backgrounds; and how they felt about teaching the mathematical skills associated with medicine dose calculations in the unit. Question 1, p. 29 asked participants whether they agreed with the statement: I feel confident teaching medicine dose calculations. Forty-three of the 50 respondents (86%) strongly agreed or agreed, five (10%) neither agreed nor disagreed, and two (4%) disagreed. 334

348 Chapter 7: The Teaching of Medicine Dose Calculation and Measurement Skills Question 2, p. 29 asked participants the highest level of mathematics study they had successfully completed at school. Of the 50 respondents, 33 (66%) had successfully completed Year 12 mathematics, 7 (14%) had completed Year 11, and 10 (20%) had completed Year 10. Question 3, p. 29 asked participants what post-school study of mathematics or statistics they had completed. 26 of the 50 respondents (52%) said they had successfully completed mathematics or statistics at university. The majority reported studying statistics (for example epidemiology, biostatistics, SPSS statistical analysis, and a statistics course for PhD). Courses studied included approximately equal numbers of undergraduate/honours courses and postgraduate courses. No participant indicated that they had completed a TAFE course, and 24 participants said they had completed no post-school study of mathematics or statistics. Question 4, p. 29 asked participants to complete a statement to indicate their feelings about teaching the mathematical skills associated with medicine dose calculations by selecting from the options offered. Table 7.25 summarises the responses. 335

349 Chapter 7: The Teaching of Medicine Dose Calculation and Measurement Skills Table 7.25 Participants feelings about teaching mathematical skills (n = 49) Feelings about teaching mathematical skills I have a strong interest in, and enjoy, teaching mathematical skills I feel quite comfortable and like teaching mathematical skills n = 7 Number of participants by role Coordinator Coordinator and teacher n = 23 Teacher n = 19 Total (%) n = (29%) (45%) I have no particular interest in, or aptitude for, teaching mathematical skills I feel quite uncomfortable and dislike teaching mathematical skills I make no attempt to teach mathematical skills (14%) (6%) Other (6%) Approximately three-quarters (74%) of participants responded positively to the statement, compared to just three participants (6%) responding negatively, and seven participants (14%) adopting a neutral stance. Participants selecting other expressed feelings such as being comfortable teaching the mathematical skills, but it not being their most favourite subject (S4), having a strong interest and enjoying teaching mathematical skills but feeling uncomfortable at times because of their limited knowledge of teaching basic numeracy (S49). Another respondent indicated they no longer taught the topic since we went online (S5) Question 1, p. 30 asked participants to nominate from the options provided which mathematical techniques associated with the calculation of medicine doses they would like to learn more about. Table 7.26 summarises their responses. 336

350 Chapter 7: The Teaching of Medicine Dose Calculation and Measurement Skills Table 7.26 Mathematical techniques participants wish to learn more about (n = 63) Mathematical technique Number of responses by role of participant n = 7 Coordinator Coordinator and teacher n = 27 Teacher n = 29 Total (%) Numerical processes (17%) Metric units and conversions (11%) Applying formulae (14%) General mathematicsteaching techniques appropriate to the topic Estimation and checking techniques (32%) (11%) Effective use of a calculator (6%) General mathematical problem-solving techniques (17%) None of the above (29%) Other (3%) There was a strong response from participants that they had no wish to learn more about the mathematical techniques associated with the calculation of medicine doses. Among those who responded in the affirmative, learning more about mathematics teaching techniques for the topic was the area of greatest demand. The high number of respondents who indicated they had no wish to learn more may be partly explained by the fact that there was a strong association between participants who had completed a university level mathematics or statistics course, who felt quite comfortable and liked teaching mathematical skills or had a strong interest in, and enjoyed teaching mathematical skills, and who either said that they did not wish to learn more about the listed mathematical techniques or who nominated a higher order area for professional development. 337

351 Chapter 7: The Teaching of Medicine Dose Calculation and Measurement Skills Two topic areas participants themselves nominated as areas they would like to learn more about by selecting other were: understanding more about students difficulties with numeracy (S36), and up-to-date examples of what is being tested in clinical and university settings (S1 Mathematics staff teaching in preparatory skill development unit). These two participants had not nominated any of the specific topic areas listed. Question 1, p. 31 sought participants preferred means of accessing professional development opportunities relating to the mathematical techniques associated with calculation of medicine doses. Twenty-eight participants nominated their preferences as follows: in-service workshops or seminars: 12 participants (43%) printed resources: 1 participant (4%) online resources: 15 participants (54%) Question 2, p. 31 sought comments from participants about how staff might best be supported in their teaching of medicine dose calculations. Five categories of response emerged from the responses. Participants indicated their teaching would be best supported through a focus on the following areas. The contexts in which learning occurs: for example, embedding application in real-world clinically-based situations (S3); making learning fun for students through team-based activities that promote active learning (S54); incorporating simulation into learning for the benefit of students and staff (S44); and using online mastery learning [as a way of unburdening teaching staff] (S59). The importance of the theory-practice relationship: for example, ensuring the curriculum is aligned with industry requirements, expectations and standards, and that nursing practice informs nursing theory and vice versa (S15). Addressing issues and difficulties surrounding the teaching of medicine dose calculations: for example, ensuring staff have sufficient time for the topic in their workload (S1); collaborating with mathematics learning skills staff to support students who need more help (S45); and improving the confidence of staff so they are better able to teach mathematically able students, thus enabling them to add value to all students (S23). The need to broaden the calculation strategies taught to permit student choice: for example, introducing more mathematics so students have a choice, rather than 338

352 Chapter 7: The Teaching of Medicine Dose Calculation and Measurement Skills just providing formulae which confuse many students (S2); addressing the problem of staff often having only one way to solve a problem: if the student is used to a different process, the staff member can struggle to adjust and accommodate the student s preferred calculation method (S53). The importance of support for ill-equipped students: some students will not have the background numeracy skills, so appropriate resources are needed to help this cohort (S49). In summary, 86% of respondents said they felt confident teaching medicine dose calculations. Two-thirds of respondents had completed mathematics at Year 12 level at high school and over half had successfully completed some study of mathematics or statistics at university. Almost three-quarters responded positively when asked how they felt about teaching the mathematical skills associated with medicine dose calculations. Participants expressed limited interest in learning more about the suggested mathematical skills required for dose calculations, with general mathematics-teaching techniques appropriate to the topic being the area of greatest demand Teaching and assessing measurement skills As well as investigating the teaching and assessment of calculation skills, the questionnaire sought information about teaching and assessment practices relating to the ability to accurately measure medicine doses. Question 1, p. 22 asked participants to select the statement that best described the approach taken to teaching measurement skills in the unit of study they were reporting on. Table 7.27 summarises the results. 339

353 Chapter 7: The Teaching of Medicine Dose Calculation and Measurement Skills Table 7.27 Approaches taken to teaching measurement skills (n = 52) Approach taken Measurement skills are specifically listed in the content for the unit and teachers are required to teach them In this unit, students are routinely exposed to exercises and/or activities specifically aimed at developing measurement skills There is no requirement for staff to teach measurement skills; the teaching of such skills is entirely at the discretion of the teacher No teaching of measurement skills is undertaken; rather students are assumed to be competent in accurately measuring doses No. of respondents (n = 52) % of respondents making response Unsure 1 2 Other 2 4 Thirty-nine respondents (75%) reported either that teachers were required to teach measurement skills or that students were routinely exposed to exercises and/or activities specifically aimed at developing measurement skills. By contrast, 10 respondents (20%) reported either that no teaching of measurement skills was undertaken or that it was discretionary. The reason one participant gave to explain their selection of other was that the question was not applicable as staff do not teach. Student learning [is] done [via] online learning packages. The second participant who selected other explained that: In the skills labs associated with the course students do this Approaches to assessing dose measurement skills Question 2, p. 22 asked participants whether students medicine dose calculation skills were assessed separately to other content in the unit. Of the

354 Chapter 7: The Teaching of Medicine Dose Calculation and Measurement Skills respondents 19 (37%) said that they were assessed separately, 31 (60%) said they were not, and two (4%) were unsure. Question 3, p. 22 asked participants to select at least one of the suggested assessment methods to indicate how students skills in measuring medicine doses were assessed (p. 22, Q3). Ninety-two percent of the 51 respondents reported some form of assessment of students measurement skills was undertaken. Individual respondents reported variously that one, two or three different assessment methods were used in the unit they were reporting on. Employment of a single form of assessment was reported by 26 participants (51%). Two forms of assessment were reported by fifteen participants (29%) and three forms by six (12%). Two participants (4%) reported that assessment of measurement skills is rarely included in formal assessment tasks. The number of times each suggested assessment method was selected is shown in Table

355 Chapter 7: The Teaching of Medicine Dose Calculation and Measurement Skills Table 7.28 Methods used to assess measurement skills (n = 52) Assessment method No. of responses (n = 77) % of respondents making response Pen-and-paper test Observing students administering medicines in actual clinical settings Observing students administering medicines in simulated clinical settings Not a requirement, but often included in formal assessment tasks Assessment of measurement skills is rarely included in formal assessment tasks Unsure 2 4 Other 4 8 Observing students in simulated clinical settings was the most frequently reported assessment method, whether singly or in combination with other assessment methods. Most frequently it was combined with observation of students in actual clinical settings a combination reported by 9 of the 52 respondents. Pen-and-paper testing was the second most frequently employed method for assessing measurement skills. Most frequently it was combined with observation of students in simulated clinical settings a combination reported by three participants. Assessment through observing students administering medicines in actual clinical settings was only ever used in combination with other assessment methods. Participants selecting other reported one or more additional methods used to assess measurement skills, such as online quizzes (2 respondents) and Objective Structured Clinical Assessment (OSCA) (3 respondents). In summary, three-quarters of respondents reported that dose measurement skills were either specifically listed as part of the unit, or that students were routinely given opportunities to develop dose measurement skills. Almost all participants reported that measurement skills were assessed, most often in combination with other 342

356 Chapter 7: The Teaching of Medicine Dose Calculation and Measurement Skills content in the unit. The most common assessment methods were observing students administering medicines in simulated clinical settings and pen-and-paper tests Participants final comments Question 2, p. 59 sought participants final comments concerning students skills in calculating and measuring medicine doses, or the teaching or assessment of those skills. Comments from seven participants, focusing on five different areas, are reproduced below. Student-related issues The problem of female students with socially ingrained beliefs of their inability to solve mathematical problems is a hurdle to be overcome before they can successfully and positively continue to apply their calculation skills. (S40) Students appear to look for the complex solution and have difficulty identifying the basic information and converting that into the formulas that they are taught back in first year. (S18) Teaching focus Drug calculations is the easy part of this unit to teach; the vast number of drugs/ interactions etc. to learn is harder for teacher and learner. So make the calcs fun and then the student will enjoy the learning. Also remind students that as nurses they are responsible for the calculations there is no shifting the blame if things go wrong. Remind them that what they are learning saves lives or destroys lives it s not just what they need to learn in order to pass a test at uni. (S54) Value of checking strategies based on proportional reasoning The value of using checking methods based on proportional reasoning (e.g. 4 mg = 2 ml, 8 mg = 4 ml, 2 mg = 1 ml ) for students not comfortable with maths (S27). They can use this checking method with most of the calcs after they have used one of the seven formulas [they learn]. It provides a lateral view of the question as some students get uncomfortable with lots of numbers and formulas on the page. I was taught this method and it works well. (S27) Assessment issues The crux of the issue for teachers is How do we assess real medication dosage calculations? Simulated clinical calculation tests are difficult to achieve 343

357 Chapter 7: The Teaching of Medicine Dose Calculation and Measurement Skills efficiently and effectively with large student numbers and different types of medicine administrations (IV, tablets, [and] pump rate). Online assessment is fraught as the potential for collaboration is high, although a good option for [formative assessment]. (S55) The scale of the problem and the need for research I think there is a growing problem in this area of nursing education. Thank you for researching and I look forward to the outcomes. (S28) 7.12 Summary of the teaching of medicine dose calculation and measurement skills This chapter addressed Research Question 3 and presented the results of the University Phase of the study. It reported on the data concerning teaching practices relating to the calculation and measurement of medicine doses in Australian nurse education programs, collected via an online questionnaire. Data concerning assessment practices, numeracy skills routinely taught, and teachers advice to students concerning their use of calculators were described. Staff perceptions concerning difficulties experienced by students learning dose calculation and measurement and by staff teaching these aspects of the nursing curriculum were discussed. 344

358 8 Discussion The most important single factor influencing learning is what the learner already knows. Ausubel (1968, p. vi) This chapter summarises the findings of the two phases of the study the Hospital Phase of the study in which nurses were observed administering medicines as part of their routine duties and the University Phase of the study in which academic staff across Australia were surveyed to determine current teaching approaches to dose calculation and measurement. An emerging theory relating to the determinants of nurses dose calculation strategies is presented and the methods nurses use to calculate and measure doses in clinical practice are compared with current teaching practice relating to these essential skills for the safe administration of medicines. 8.1 The strategies nurses use to calculate medicine doses Naturalistic observation of nurses in the wards of three Australian hospitals was used to investigate nurses dose calculation practices. Nurses explanations of the methods they used to calculate doses were the primary means of classifying their calculation strategies The strategies nurses use to calculate medicine doses in clinical practice Informal proportional reasoning strategies were dominant amongst the strategies nurses used; they were used to calculate 212 (88%) of the 240 medicine doses requiring a dose calculation for which the nurse s calculation strategy was known. The traditionally-taught formula method was the only other calculation method nurses used during observation sessions. Nurses used the formula for only 28 (12%) of these calculations. identified: Four broad categories of proportional reasoning strategy, all scalar 35, were 35 See Figure 2.1, for a model of proportional reasoning strategies after Vergnaud (1983). 345

359 Chapter 8: Discussion multiplicative reasoning or repeated addition; fraction operation or division process; halving combined with addition; and complex proportional reasoning. Nurses used multiplicative reasoning and repeated addition to scale up from the stock mass to the prescribed mass by applying an integral scalar factor (e.g. 2, 3, 4, etc.). They used fraction operations and division processes to scale down to the prescribed dose by dividing by an integer. The processes I termed halving combined with addition, and complex proportional reasoning, were used to apply non-integral scalar factors to the stock mass. A fifth category of non-formula-related calculation strategy identified simple addition was associated with the administration of medicines using two pharmaceutical products rather than one. For other two-product medicine administrations involving proportionality, nurses showed the same preference for proportional reasoning strategies, specifically scalar strategies, as they had when they performed dose calculations for single-product medicine administrations. A striking characteristic of calculations performed using non-formula-related methods, regardless of whether one or two pharmaceutical products were administered, was that without exception nurses carried out all necessary computations using mental arithmetic procedures without recourse to pen and paper or calculators. By contrast, when nurses used the formula, they frequently performed the associated calculations using a calculator. Nurses made no use of the formula or calculators when calculating doses administered using two products. The rejection by nurses of the commonly-taught formula in favour of proportional reasoning calculation strategies resonates with the findings of the only similar study found in the literature a study in which the researchers observed just 12 nurses administering 30 medicines in a single specialist paediatric hospital in the UK (Hoyles et al., 2001). One of the key findings of both studies was that nurses made limited use of the formula just 12% of dose calculations in my study and 20% in Hoyles et al. s study. The exclusive use nurses made of mental arithmetic procedures in association with proportional reasoning strategies was also reported by Hoyles et al. 346

360 Chapter 8: Discussion The findings of my study also accord with research from the broader domain of mathematical problem-solving, particularly that relating to problems of proportionality. Previous research suggests that in everyday problem situations and in professions where mathematics is used, formal calculation processes are rejected in favour of quick and efficient informal processes adapted to the problem context (Coben, 2010; Hoyles et al., 2010; Nunes et al., 1993; Pozzi et al., 1998). The rejection of formal solution methods and the dominance of informal proportional reasoning approaches, specifically scalar strategies, among nurses dose calculation strategies in my study are consistent with findings from the wider domain of mathematics research concerning the preferred methods of adults and children for solving problems of proportion in everyday contexts. Empirical studies by Karplus et al. (1983), Schliemann and Nunes (1990), Vergnaud (1983), together with that of Hoyles et al. (2001) all concluded that when finding the missing value in problems of proportionality, problem solvers make little use of the rule of three or the unitary method. Further, when proportional reasoning strategies are used, scalar procedures are strongly favoured over functional procedures. It is not surprising that the unitary method has little appeal to nurses. Its use typically involves finding the volume or fraction of a tablet corresponding to 1 mg of mass, a quantity nurses are unlikely to relate to meaningfully. Rather than using one unit of mass as a useful portion to work with, nurses prefer to use the stock mass as the unit they work with. Nurses scale the unit of stock mass up or down until they reach the prescribed mass. They then perform parallel transformations on the stock volume or vehicle (e.g. one tablet) to obtain the corresponding dose to administer. Nurses occasionally used the unitary method to find the mass corresponding to a volume of 1 ml. This approach was only fruitful if the corresponding mass could be easily related to the prescribed mass for example, a multiple or simple fraction of it. Research in the mathematics domain has almost exclusively described processes used to scale up from a base quantity, such as finding the cost of several items, given the unit cost. Vergnaud used a single umbrella descriptor scalar operator (1983, p. 130) for such processes, possibly because they related to a single direction of scaling, namely upwards, and primarily involved integer scalar factors. Hoyles et al. (2001, pp. 21; 22) used the single descriptor chunking to describe nurses use of integer scalar factors to scale up from the stock mass, although they did identify both multiplicative and additive variations of chunking. Hoyles et al, 347

361 Chapter 8: Discussion gave no specific name to strategies used to scale down from the stock mass, instead describing the technique as comparing the dose directly with the package mass (p. 21). In my study, the direction of scaling was more frequently up than down, however one third of scaling procedures were used to scale down from the stock mass to the prescribed mass. Multiplicative reasoning and repeated addition involving integer scalar factors were used to scale up from the stock mass. Fraction operations and division processes involving integer scalar factors were used to scale down from the stock mass. Further, nurses used both integer and non-integer scalar factors. Nurses used the multi-step technique of halving combined with addition when the scalar multiplier was one-and-a half, two-and-a half, three-and-a half 36, etc. Using a technique of halving combined with addition was equivalent to Vergnaud s (1983) scalar decomposition (p. 146) (see Table 2.2, 2.5.3) and Wright s (2013) relational methods (p. 454). This procedure was not observed by Hoyles et al. (2001). The term complex proportional reasoning was used to describe two multi-step processes. One process involved nurses expressing the stock concentration as a series of equivalent forms until they arrived at an expression involving the prescribed mass. Hoyles et al. (2001) identified this technique but did not give it a name. The second process, sometimes used in conjunction with the first, involved nurses using a syringe scale as a measure of mass (mg) as well as volume (ml). This technique was also identified by Wright (2013) The invisible nature of nurses dose calculations This study used a technique of asking nurses to explain their dose calculation methods. Involving nurses in the data collection and analysis in this way proved crucial in exposing the nature of the mathematics nurses use when they calculate medicine doses in clinical practice. One of the likely reasons nurses strategies for dose calculation have for so long lacked rigorous investigation is that the routine and predictable nature of dose 36 Half was the only fraction involved is this process in my study. Other fractions, such as one quarter, could equally be involved. 348

362 Chapter 8: Discussion calculation renders it invisible to both the user and outside observers. Nurses use of the formula is often signalled when they pick up a calculator and key in the three numerical values that characterise the medicine administration. However, nurses use of informal scalar strategies to calculate doses is rarely visible, primarily because they perform routine calculations with ease using mental arithmetic processes. Nurses in the study were dismissive of simple computational processes they used to calculate doses. This was particularly evident during focus group discussions when nurses dismissed their mathematical processes with comments such as: I can do that one off the top of my head ; Well, that s a no brainer ; It s just embedded: I don t have to think about it ; I don t have to work it out ; It s automatic ; Some things are patently obvious ; I wouldn t bother working that out. Such comments suggest many nurses did not regard the mental arithmetic processes they used as constituting a calculation. Comments such as these have come to be recognised as signposts for invisible mathematics in the workplace, and are also described in the nursing literature (Coben, 2000, 2010; Hoyles et al., 2001; Hutton, 1998b; Sabin, 2013). When nurses claimed in focus groups to always adhere to the formula methods they had learnt as students, it became clear they were referring only to those medicine administrations that required a formal calculation procedure involving the formula, usually supported by a calculator. These two components seemed to imply mathematics to nurses. The embedding of workplace knowledge, including mathematics, in the tools, artefacts, and processes of professional practice has been reported by many authors (Coben, 2010; Hoyles et al., 2010; Hutton, 1998b; Marks et al., 2016; Sabin, 2013). Nurses in Hoyles et al. s study (2001) confirmed this phenomenon. Dose calculations were the only examples they offered when they were asked to nominate examples of mathematics in their practice. Further, in interviews with nurses and senior staff, it became clear that the dose calculations they were referring to were those involving the use of the formula. The association of calculator use with the formula no doubt further reinforced they were using mathematics Factors influencing the need for a dose calculation The relatively small proportion of medicine administrations requiring a dose calculation 27% of 1571 medicine administrations raised the question of what factors influence the need for nurses to calculate doses. Statistically significant 349

363 Chapter 8: Discussion results from Chi-squared tests of goodness of fit (p < 0.05) revealed several factors that influenced the need for a dose calculation. These factors were: the type of ward in which the medicine was administered; the administration route; and the type of packaging of the medicine. Nurses administering medicines to paediatric patients were more than twice as likely to need to perform a dose calculation as nurses administering medicines to adult patients. This finding reflects Hughes and Edgerton s claim (Hughes & Edgerton, 2005) that almost all paediatric doses require calculation. The heavy concentration of dose calculations in paediatric wards in my study can be explained largely by the fact that 40% of medicines administered to paediatric patients required nurses to perform a prior calculation to determine (or confirm) the prescribed dose on the basis of the child s weight. When this occurred, the resultant prescribed mass was usually a decimal value, and one that almost inevitably differed from the stock mass. A prescribed mass different from the stock mass was a trigger for a dose calculation one most often involving a decimal manipulation. The subcutaneous route was associated with a lower need for dose calculation compared to other routes, such as oral and intravenous. This lower need stemmed largely from nurses use of single-dose medicines, mostly administered subcutaneously. These included prefilled syringes of the anticoagulant, enoxaparin, available in a range of volumes that allowed administration of exactly the doses doctors generally prescribed Factors influencing nurses choice of strategies for calculating medicine doses The data were interrogated to investigate possible associations between nurses calculation strategies and a range of factors relating to the clinical context of the medicine administration, factors in the personal backgrounds of nurses, and environmental factors present in the ward at the time of the administration. The numerical relationship between two key quantities that defined the medicine administration the prescribed mass and the stock mass emerged as the preeminent factor in determining nurses dose calculation strategies. The link between dose-to-stock ratio and calculation strategy The dose-to-stock ratio, was defined in 5.8 as the ratio of the prescribed mass to the stock mass, the latter quantity being the first-named quantity in the stock 350

364 Chapter 8: Discussion formulation of the pharmaceutical product used to administer the medicine. I adopted the term (DSR) as its value proved critical in determining nurses dose calculation strategies. A major finding of the study was the identification of strong associations between particular dose calculation strategies nurses used and particular DSRs. Five DSRs 2:1, 1:2, 3:2, 3:1, and 4:1 accounted for 81% of the calculations for which the nurse s calculation strategy was known. Each of the three most frequently occurring DSRs, 2:1, 1:2, and 3:2, was strongly linked to a particular calculation strategy: multiplicative reasoning or repeated addition was used for 92% of medicine administrations with a DSR of 2:1; a fraction operation or division process was used for 93% of medicine administrations with a DSR of 1:2; and halving combined with addition was used for 93% of medicine administrations with a DSR of 3:2. Nurses eschewed the traditionally-taught formula method for calculating doses for medicine administrations with these three DSRs, using it for less than 3% of them. The data suggested the associations between DSR and calculation strategy extended to the broader class of DSR n:1 for n 4, multiplicative reasoning or repeated addition being the dominant strategy. The limited amount of data relating to medicine administrations with a DSR of 1:n for n>2 precluded more than limited confirmation that nurses use of a fraction operation or division process, identified in relation to a DSR of 1:2, carried over to the broader class of DSR, 1:n for n 4. For medicine administrations with a DSR of n:2, even fewer data were available, making investigation relating to the broader class of DSR unjustified. DSRs outside these three classes were, for convenience, grouped together under the term complex DSRs. Complex DSRs included values such as 2:5, 3:4, 1:25, 13:20, 3:50, 63:10, and 73:120. A striking observation concerning the dose calculation strategies nurses used was that the nurses showed no evidence of consciously mathematising the dose calculation task. They appeared to be unaware of any concept of a mathematical ratio, nor of its influence in determining their dose calculation strategies. 351

365 Chapter 8: Discussion Nurses appeared to cognitively process the significant numerical relationships in medicine administrations without being consciously aware of it. They then responded to these relationships in predictable ways, without thinking about their responses in mathematical terms. The association between paediatric doses and formula use Nurses use of the formula was generally limited to medicine administrations with complex DSRs. Complex DSRs and use of the formula were also strongly linked to the administration of medicines for paediatric patients, an association that can be explained in terms of the DSR. Medicine doses for paediatric patients are generally fractions of adult doses (Hughes & Edgerton, 2005). Often the prescribed dose is determined on the basis of the child s weight using a milligram (or microgram) per kilogram value (Hughes & Edgerton, 2005; Starkings & Krause, 2015). Consequently, prescribed doses for paediatric patients are seldom simple integral multiples or simple fractions of the stock mass, as explained earlier in this chapter. The relationship between the stock mass and prescribed mass usually does not allow accurate mental calculation of the dose to administer. One of the features of nurses use of proportional reasoning strategies was the associated use of mental computations. The corollary is that when a medicine administration has a complex DSR, making mental computation difficult or impossible, nurses are more likely to use the formula and a calculator. During observation sessions, medicines prescribed for paediatric patients had a far higher proportion of complex DSRs than medicines for adult patients. Thus in my study, the level of calculation difficulty associated with paediatric dose calculations was reflected in the fact that over two-thirds of the 28 dose calculations for which nurses used the formula were for medicines administered to paediatric patients. Further, of the 45 medicine administrations with a complex DSR, 27 (60%) occurred in paediatric wards. Viewed slightly differently, of 65 paediatric dose calculations, 27 (42%) had a complex DSR. This proportion is even higher than the proportion of over 30% of paediatric calculations Cartwright (1996) classified as complex the highest level of difficulty in the rating system she devised. As occurred in my study, Cartwright s classification system placed paediatric dose calculations as the most difficult category of calculation, a fact reflected in reports of higher error rates for paediatric 352

366 Chapter 8: Discussion medicines than for medicines administered to adult patients (Cartwright, 1996; Scharnweber et al., 2013). The dose-to-stock ratio in relation to previous research During the literature search, no study was found that comprehensively investigated the relationship between the dose calculation strategies nurses use and the numerical characteristics of the medicine administrations, with only the study by Hoyles et al. (2001) touching on the notion of this relationship. In their study, Hoyles et al. (2001) referred to the ratio I called the dose-tostock ratio as a scalar ratio, listing the scalar ratio for each of the 26 medicine administrations needing a dose calculation. Other names used by Hoyles et al. to describe this ratio were scalar ratio of mass-of-drug-prescribed to mass-in-package (p. 15) and mass prescribed: packaged dose (Table 3, p. 15). Applying a mathematical lens to describe the characteristics of the medicine administrations they observed, Hoyles et al. (2001) noted the involvement of 18 distinct scalar ratios and 26 different combinations of the prescribed mass and stock concentration in the 30 doses administered (p. 15). Although Hoyles et al. stated they had tried to map each calculation strategy to features of the practice, such as the ratios in the problem (2001, p. 16), they attached no further significance to the scalar ratios they recorded. This was not surprising because there were too few occurrences of each ratio for any patterns to emerge between dose calculation strategies and scalar ratios The strategies nurses use to solve written medicine dose calculations Nurse participants in my study were asked to respond in writing to calculation tasks posed in narrative form in a questionnaire. The pattern of nurses dose calculation strategies in relation to the written word problems in the questionnaire was strikingly different from the pattern of nurses responses to authentic calculation problems encountered in clinical practice. The formula dominated the calculation strategies of the 44 nurses who completed the questionnaire in relation to the five items selected for inclusion in this thesis. Items 1 to 5 were selected because they were most similar to the authentic dose calculation tasks nurses performed during observation sessions. Overall, nurses 353

367 Chapter 8: Discussion used the formula for 61% of the 220 dose calculations performed, a stark contrast to 12% of the 240 calculations performed in clinical practice. Although nurses made far less use of scalar strategies than they did in relation to the authentic dose calculation problems they encountered in the ward, they used similar proportional reasoning strategies for the written tasks. Nurses used proportional reasoning for 35% of the 220 written tasks, compared to 88% of the problems encountered in clinical practice. One additional scalar strategy not observed during observation sessions that of the ratio form of the rule of three was used by one nurse for all five questionnaire tasks. The study findings are consistent with the results of the only other study identified (Wright, 2013) that examined the calculation strategies of qualified nurses in response to dose calculation tasks posed as written word problems. In that study, eight experienced nurse educators used the formula for 43% of problems. In light of the evidence from Hoyles et al. (2001) that nurses rarely use the formula in practice, Wright (2013) was surprised by nurses higher rate of formula use in her study. However, a different view of the comparison is that nurses use of the formula in Wright s study was surprisingly low given the nurses studied were concurrently engaged in teaching dose calculations to student nurses. In that role one might expect they would frequently be demonstrating application of the formula, the method taught in the UK (Hoyles et al., 2001). The corresponding facility of these nurses with the formula method, resulting from their teaching role, would arguably make them more likely to use the formula themselves to solve dose calculation problems posed in written, test-like conditions Comparison between nurses strategies in different contexts The radical difference between little use of the formula in clinical practice and the formula being the dominant strategy for all tasks posed in written format in the questionnaire suggests that nurses vary their calculation strategies according to the setting in which they encounter problems and the way in which problems are posed. The finding that the same nurses responded so differently in the two different settings resonates with the findings of Nunes et al. (1993), who concluded that adults and children responded to school-like written proportionality problems by using the formal school-taught rule of three. When they encountered problems in everyday or 354

368 Chapter 8: Discussion out-of-school contexts and were unconstrained by formal conventions they responded quite differently, using invented proportional reasoning strategies. This proposition provides another possible explanation for the inconsistency that puzzled Wright (2013) concerning the relatively high rate (43%) of formula use in her study compared to the 20% rate in the Hoyles et al. study (2001). In Wright s study, the problems were posed in narrative form, eliciting the formal solution method of nurses the formula. In the Hoyles et al. study the problems were encountered in authentic clinical practice environments, eliciting informal proportional reasoning strategies. When my study, those of Wright (Wright, 2013), and Hoyles et al. (2001) are considered together, the evidence suggests that nurses problem-solving methods are consistent with those used by problem solvers in the study by Nunes et al. (1993). That is, nurses respond differently to dose calculation problems depending on the setting in which the problem is encountered and the format in which it is posed. An alternative explanation for nurses greater use of the formula in response to the questionnaire tasks is one proposed by Wright (2013) in relation to similar findings in her study. Wright suggested that, when nurses are familiar with medicine administrations, they feel more confident to use invented, scalar calculation methods. By contrast, when nurses are required to calculate doses for unfamiliar medicine administrations, they are less confident in their use of scalar strategies, with the result that they tend to default to the safe option of using the formula. In my study, one might postulate that the dose calculations nurses performed in clinical practice were for familiar administrations performed routinely in their home ward. Thus, in accordance with Wright s (2013) hypothesis, nurses greater familiarity with the task resulted in more confident application of proportional reasoning strategies. By contrast, the medicine administrations in the questionnaire were likely to be less familiar, resulting in nurses feeling less confident in their calculations and therefore more inclined to choose the formula as the safe option. In support of her proposition, Wright (2013) identified nurses who used proportional reasoning methods as being among those with broad clinical backgrounds, including experience in acute areas and intensive care. In these areas Wright postulated they would have gained confidence by routinely performing more complex calculations. Lack of familiarity and lower levels of confidence were confirmed as triggers for formula use by nurses during focus groups. Nurses indicated that, in addition to 355

369 Chapter 8: Discussion using the formula to calculate doses for paediatric patients, they used it for new medicines, medicines they were not familiar with or were not part of their normal routine, and medicines that were only available in a strength they had not previously used on a regular basis. Another factor of relevance in considering differences in nurses responses to dose calculation problems posed in different contexts is the amount, nature and location of information nurses use in their calculations. In authentic practice contexts, nurses are surrounded by the tools and artefacts of medicine administration (Wright, 2009b). These include the patient chart providing details of the prescribed dose and medicine packaging showing the concentration of the medicine. The numerical information on the package provides the critical link between the dose prescribed and the quantity of medicine given to the patient. The assistance provided to nurses in their dose calculations in the clinical setting by the tools and artefacts of medicine administration was highlighted during focus groups. Nurses described how they progressively added a number of milligrams to correspond to each pill popped out of a medicine package, and in administering a 37.5 mg dose from 25 mg tablets, how they thought in terms of whole and half tablets, rather than numbers, as they viewed the tablets inside the medicine bottle. By contrast, the information critical to nurses solution processes is provided in a far less graphic and meaningful way when problems are posed in written word form. Further, nurses are robbed of the subtle visual, tactile, and kinesthetic experiences of clinical practice that contribute in valuable ways to the calculation process, adding to the basic numerical information provided in word problems. The antithesis of the value of the cues available to nurses in the practice environment is suggested by the evidence from my study and that of Wright (2013). Notwithstanding other likely influences, it is possible that the absence of real-world cues in my study contributed to the poorer calculation performances of nurses on written tasks than in clinical practice. When nurses drew up a volume of medicine into a syringe in clinical practice, the visual image of the quantity appeared to trigger an assessment of whether it was a reasonable quantity to administer to the particular patient via a particular route orally, intravenously, or by injection. This type of link with clinical reality was often not present when nurses performed pen-and-paper dose calculations in the questionnaire, leading to nurses shading five doses that were only one-tenth of the 356

370 Chapter 8: Discussion intended dose. Similarly, failure of the narrative problems to adequately provide the visual and other cues of authentic practice in Wright s (2013) study may have contributed to the poor success rate of 67% achieved by the eight experienced nurse educators on the 64 calculations attempted. Using words in an attempt to provide context to dose calculation problems has been criticised as an inadequate substitute for the richness of authentic problem contexts and realistic simulations of authentic contexts (Weeks, 2001). Growing recognition of the contribution of the artefacts and visual cues of authentic medicine administration to nurses success in calculating doses has led to recent attempts to facilitate contextualisation and conceptualisation of problems. These have included attempts by several authors to emulate the features of real-world medicine administration in online and simulated, authentic learning environments (Grandell- Niemi et al., 2003; Macdonald et al., 2013; McMullan et al., 2010; Weeks, Clochesy et al., 2013; Wright, 2012a). The impact of problem setting and calculation method on accuracy Another point of agreement between the findings of my study and existing research concerns the relationship between problem setting and calculation errors. Problem solvers tend to make more errors when they encounter problems in formal school-like settings than when they encounter them in out-of-school settings (Lave, 1988; Nasir et al., 2008; Nunes et al., 1993). No calculation errors were detected in the 431 dose calculations nurses performed in the natural clinical environment of my study. Nor did nurses make any errors in calculations such as metric conversions, mg/kg calculation of the prescribed dose, and infusion rates that nurses performed prior, or subsequent, to determining the dose to administer. When the same nurses performed calculations in response to written word problems in the questionnaire, however, 8 (18%) of the 44 nurses made a total of 11 calculation errors on the 220 tasks analysed. Two of the items (Tasks 4 and 5) each attracted four calculation errors. The most frequently occurring types of error associated with the written medicine administration tasks involved nurses correctly setting up the formula for calculation but failing to obtain the correct answer because of computation errors, and nurses applying an incorrect conversion factor in a prior conversion of a mass from milligrams to micrograms. 357

371 Chapter 8: Discussion The nature and difficulty level of the dose calculation tasks performed in the two settings were examined to look for possible reasons for the higher error rate on the written tasks. Critical examination of the questionnaire tasks revealed that they may have been more difficult in several respects compared to the majority of the authentic practice problems. All five questionnaire tasks required decimal manipulation or resulted in a decimal answer, compared to only 17% of the 431 authentic medicines that required decimal manipulation. Despite the expectation that decimal numbers may be a trigger for nurses to use the formula and calculator, there was insufficient evidence to confirm this in either setting. The two tasks attracting the greatest numbers of errors, Tasks 4 and 5, possessed features identified in the literature with increased levels of difficulty in solving proportionality problems. In addition to both these tasks requiring decimal manipulation, a known area of weakness among nurses (Pierce et al., 2008), Task 4 involved large numbers (both the prescribed dose and stock mass were four-digit integers), a factor known to increase the difficulty level of proportionality problems (Karplus et al., 1983). Task 5 required a metric conversion, a known source of difficulty and errors (Hicks, Becker, & Cousins, 2006; NPSA, 2009; Pierce et al., 2008; Wright, 2012b). The factors that increased the difficulty of the questionnaire tasks were, however, offset by three of the five items, Items 3 to 5, having simple DSRs of 2:1, 1:2, and 3:2 respectively. These three most commonly occurring DSRs were associated with easy mental computation, making proportional reasoning solutions a viable option for nurses. Differences in the accuracy of problem solving relating to the two different problem-solving settings may be explained by the conclusions reached by Nunes et al. (Nunes et al., 1993), who found that when problem solvers used formal schooltaught algorithmic solution methods they were more likely to make errors than when they used informal scalar strategies. On the one hand, this conclusion, together with the lack of contextual cues associated with the questionnaire tasks, are possible explanations for why nurses made more errors when they used the formula on questionnaire problems than in clinical practice, where they used predominantly proportional reasoning methods. On the other hand, my study provides little support for the conclusions reached by Nunes et al. (1993). In the natural setting of the ward nurses made no calculation 358

372 Chapter 8: Discussion errors, regardless of the calculation method they used, nor did their performance on the questionnaire tasks point to calculation method being a factor contributing to error. Indeed, several of the errors resulted quite clearly from causes independent of the calculation method used. These errors involved applying an incorrect metric conversion and incorrectly transcribing numbers. It is possible, however, to argue that nurses transcription errors were the result of requiring them to give their answers in a written format in the questionnaire booklet. Nurses applying scalar strategies in clinical practice would normally have no need to transcribe numbers because they performed all computations mentally. Thus, in clinical practice, any risk of incorrect transcription leading to calculation error is eliminated. The risk of misreading numbers still remains, however, regardless of calculation strategy. The impact of solution strategy on direction of calculation and magnitude of errors A phenomenon observed by Nunes et al. (1993) and confirmed by Wright (2013) concerns the relationship between the problem solving approach applied, the direction of the calculation, and the magnitude of errors made. When nurses in my study used scalar methods to calculate doses, the direction of their calculation processes corroborated the findings of Wright (2013, p. 456). Having initially mentally noted the prescribed mass, nurses commenced the calculation process with the stock formulation and worked backwards from known to unknown until they reached the prescribed dose. By contrast, in both my study and Wright s study (2013) when nurses used the formula to calculate doses, the direction of the calculation was reversed: nurses commenced the calculation process with the prescribed dose, the unknown. They commenced the calculation process by first substituting the value of the prescribed mass into the formula, then the stock mass, and finally the stock volume or vehicle 37. In the next step their focus returned to the prescribed dose, which they divided by the stock mass. Wright likened this phenomenon to that proposed by Mayer (1992), where problem solvers who are more confident work backwards from the known to the unknown, and those less confident work forwards from the unknown to the known. 37 When the vehicle was one tablet or capsule, this part of the calculation was often omitted. 359

373 Chapter 8: Discussion Hoyles et al. (2001) remarked that when nurses apply the formula, the order of operations always follows the sequence of actions carried out by nurses. According to Hoyles et al. (p. 22), the fact that rule matches action explains why the formula has never been presented in any other order. However, Hoyles et al. did concede that the reverse may be true. That is, nurses actions follow the rule because the structure of the formula effectively imposes a prescribed order on their actions. The latter explanation seems to better accord with the evidence from my study and that of Wright (2013). Nunes et al. (1993) reported that directional differences associated with the problem-solving method applied affected the accuracy of calculations and the magnitude of errors. When Brazilian children working as street vendors used informal mental processes to calculate the cost to customers of several items, Nunes et al. observed they added the larger numbers first, then the smaller numbers. By contrast, when these children performed the same additions using formal school algorithms, the direction of their problem solving was reversed. Children started with the smaller numbers and progressed to the larger numbers. Further, the errors they made were of greater magnitude. Nunes et al. (1993) concluded that when mental processes are used to solve problems, the direction of calculation proceeds in ways that preserve the relative value of the numbers, believed to be an important factor in detecting errors. As a consequence, errors of smaller magnitude were more likely to result when children used informal mental strategies, working from larger to smaller numbers, the direction that better preserved the relative value of numbers. By contrast, when formal written processes are used and the direction of calculation is reversed, the relative value of numbers is often lost, making detection of errors less likely. As a consequence, errors of greater magnitude were likely to result when the children used the formal school-taught methods, working from smaller to larger numbers, the direction less likely to preserve the relative value of numbers. The fact that use of particular solution methods dictates the direction of calculation, which in turn influences accuracy, suggests this is an area warranting further investigation in relation to nurses calculation of medicine doses, where finding ways to minimise error is a priority. 360

374 Chapter 8: Discussion 8.2 The strategies nurses use to measure medicine doses Nurses measured medicine doses in preparing medicines for administration during observation sessions and also in response to questionnaire tasks. At its simplest, dose measurement involved little more than counting the correct number of tablets or capsules in the case of solid medicines, and occasionally vials, bags, drops, and puffs in the case of liquid and atomised medicines. Syringes were the most commonly used device for measuring liquid medicines. Frequently, however, the dose measurement task was considerably more complex, sometimes involving several measurement processes, several measuring instruments, and possibly calculation processes specific to the measurement process. Measurement requirements were dictated by factors such as the form of the medicine (solid or liquid), patient characteristics (including adult or child, conscious or not, ability to swallow), and the route of administration nominated by the prescribing officer. As part of the process of measuring medicine doses, nurses also set up intravenous infusion pumps, entering appropriate values into the digital settings to administer the prescribed volume of medicine at a constant rate over an appropriate period of time. A vast amount of research has focused on the calculation aspect of accurate medicine administration and the adequacy of nurses calculation skills. Accuracy in nurses measurement of medicine doses has failed to gain a similar level of recognition in the literature. Relating the dose measurement practices of nurses in my study to existing literature is therefore limited to a small number of reports. Among the few authors to address this aspect of medicine administration are Weeks, Hutton, Young et al. (2013), who viewed technical measurement competence ( dosage-measurement ; p. e23) as an essential aspect of competence in medicine administration. In their measurement of medicine doses, nurses demonstrated the types of skill in using measuring equipment described in the literature, such as measuring devices involving different calibration systems. (Cartwright, 1996; Coben et al., 2010; Hoyles et al., 2001; Macdonald et al., 2013; Nicholls, 2006; Weeks, Hutton, Coben, et al. 2013). Measurement issues of concern Several issues of concern relating to nurses practices in measuring medicine doses emerged from the Hospital Phase of the study. Some of these issues have been 361

375 Chapter 8: Discussion raised in the nursing literature, but others appear not to have been previously identified. The issues concern the phenomenon of excess volume in ampoules of medicine and how nurses respond to overages, and nurses selection of syringe type and capacity for measuring small volumes of liquid in preparation for administration. Nurses responses to overages in ampoules Evidence of overages in ampoules emerged initially in relation to frequently prescribed 5000 international unit doses of heparin, administered mostly by subcutaneous injection from stock labelled 5000 IU in 0.2 ml. My decision to gain nurses cooperation in monitoring the volume contained in the small glass ampoules used to administer heparin during observation sessions also provided an opportunity to monitor nurses responses to overages. Nurses responses were divided roughly in the ratio 2:1, where for every two nurses who measured the volume before administering the dose, discarding any excess volume beyond the 0.2 ml prescribed, one nurse claimed to always administer the entire contents of the ampoule in the belief that it contained exactly 0.2 ml, as they interpreted the information of the label to mean. All 19 heparin ampoules monitored exceeded the 0.2 ml indicated on the label. This confirmed the information provided by several manufacturers I consulted, that excess fluid is always included in ampoules to ensure the labelled 0.2 ml is available to nurses to administer. The overage in the volume able to be withdrawn from the ampoule ranged from 10% to 70%, the average overage being 41%. Overages evident in other medicines available in small ampoules included morphine, clonidine, iloprost and milrone, some of which were also monitored. Assessment of whether administration of the full contents of ampoules posed a potential threat to patient safety was beyond the scope of my study. However, the fact that a significant minority of nurses whose opinions were canvassed expressed the belief that it was appropriate to administer the full contents of the ampoule flags a need to address nurses misconceptions regarding the labelling of pharmaceutical products, particularly small ampoules of medicine containing high-risk medicines such as heparin and morphine. The beliefs expressed by these nurses revealed a widespread misconception that the label on the ampoule conveys information about the total volume of the contents of the ampoule, rather than the concentration of the liquid contained within 362

376 Chapter 8: Discussion it. In nurses defence, however, is the fact that the messages they receive from labels are confused and confusing. On the one hand, nurses correctly assume the volume of liquid contained in a prefilled syringe (e.g. enoxaparin) is the exact volume shown on the label. Consequently, there is no need to measure the volume prior to administration. On the other hand nurses are expected to know that they must measure liquids withdrawn from ampoules and discard excess liquid if the volume exceeds the volume printed on the label. Nurses should not assume the volume contained in the ampoule is that stated on the label in the concentration information. Clearly, the assumptions nurses make concerning the volumes contained in pre-packaged pharmaceutical products have the potential to lead to inaccuracies in the quantity of medicine administered to patients. The phenomenon of manufacturers including excess volume in sealed, single-dose ampoules of medicine, in contrast to prefilled syringes, and nurses responses to overages in ampoules in their measurement of liquid doses are issues that appear to be previously unreported in the literature. Selection of syringe type and capacity Nurses use of insulin syringes, calibrated in international units (IU) of insulin, to measure and administer volumes of liquid medicine, stated in millilitres was another area of concern that emerged from my study. Instances of this occurred in both observation sessions and measurement tasks in the questionnaire. During observation sessions, nurses measured most heparin doses, usually 5000 IU, using insulin syringes marked in insulin units instead of 1 ml syringes. Heparin was usually administered from stock ampoules labelled 5000 IU in 0.2 ml. Nurses appeared to have memorised, possibly with little understanding of the mathematical underpinnings of the equivalence, that a 0.2 ml dose of heparin could be prepared by drawing the liquid up to the 20-unit mark on the international unit scale of an insulin syringe. The only legitimate equivalence nurses can rely on concerning the two medicines, heparin and insulin, is that 20 international units of insulin and 5000 international units of heparin are each contained in 0.2 ml of liquid, provided the stock concentration of heparin is 5000 IU in 0.2 ml and the insulin is 100-unit per 1 ml. The anomaly concerning the apparent equivalence of these two unlike 363

377 Chapter 8: Discussion quantities expressed in international units is explained by the fact that international units are defined differently for different substances. The fact that heparin stock is available and used in concentrations other than 5000 IU in 0.2 ml, thus increasing the risk of error, was confirmed during observation sessions. For a small number of medicine administrations, nurses accessed heparin stock in concentrations of 5000 IU per 1mL and IU per 5mL. In the questionnaire, nurses again demonstrated their practice of using insulin syringes to measure doses expressed in millilitres. On Item 4, five (11%) of the 44 nurses who completed the task selected an insulin syringe to measure the 0.1 ml dose of heparin they had calculated. The issue of whether the type of syringe selected by the nurse is appropriate for the medicine being prepared is not so much a matter of whether 0.2 ml of heparin can be accurately measured on an insulin syringe calibrated in international units of insulin. Rather, the issue relates to the potential for measurement error when a syringe designed specifically for measuring and administering one type of pharmaceutical product is used to measure an entirely different type of product calibrated in a different unit of measurement. The inherent risk is that encouraging or simply condoning the practice of using insulin syringes for non-insulin medicines signals approval of a potentially dangerous practice. To reduce the risk of measurement errors, the safe policy is surely to always use a syringe calibrated in the same unit of measure as the quantity being measured. The potential for measurement error when nurses do not make a clear distinction between insulin and non-insulin syringes has been highlighted by medication errors reported in the UK. Unaware of the differences between a 1 ml syringe (referred to also as an intravenous, tubercular or hypodermic syringe) and an insulin syringe, errors have resulted when health professionals have inappropriately used non-insulin syringes, calibrated in ml, to measure and administer insulin products, rather than using insulin syringes, marked in insulin units (NPSA, 2010a). Ten-fold errors in the amount of insulin administered, some resulting in the death of the patient, have resulted from confusion between the two types of syringe. Examples have included administering 0.8 ml of Novomix instead of 8 units, and administering 1.2 ml of insulin instead of 12 units (NPSA, 2010b, p. 5). 364

378 Chapter 8: Discussion Aware of the fact that insulin is frequently listed among the top ten high-alert medicines worldwide, the National Patient Safety Agency (NPSA, 2010b, p. 2) has warned that the use of intravenous syringes to measure insulin doses in units is an error prone practice as the graduations are in volume, not units of activity. Accordingly the Agency has advised that intravenous syringes must never be used for insulin administration, [and] an insulin syringe must always be used to measure and prepare insulin for an intravenous infusion (NPSA, 2010a, p. 1). The UK history of sometimes fatal errors highlights the risks associated with use of a syringe not intended for the measurement task. Nurses did not always exercise the best judgement in their selection of syringe capacity. For as many as one-quarter of the observed doses that nurses measured using syringe scales, the accuracy of the measurement could have been improved by selecting a syringe of smaller capacity that had a more finely graduated scale. Similar evidence of nurses choosing syringes without a view to achieving optimal measurement accuracy was found in relation to medicine administration tasks in the questionnaire. However, the likely impact on patient safety and clinical efficacy of small inaccuracies in nurses volume measurements is unknown and beyond the scope of this study. 8.3 The strategies nurses are taught to calculate and measure medicine doses Using an online questionnaire, data were collected from 64 academic staff employed at 43 campuses of 28 Australian universities offering pre-registration nursing programs. Every state and territory in Australia was represented in the participants who volunteered as a result of inviting the participation of 35 universities known to offer nursing programs. Participants described over 50 units of study involving calculation of medicine doses in pre-registration nursing programs. In these units, calculation of doses was typically a relatively small component of a much broader unit. Academic staff from the School of Nursing were most often responsible for delivering instruction in medicine dose calculations, usually supported by clinical facilitators, or staff from a student learning or academic support unit. Staff were most commonly selected to teach the unit for reasons unrelated to their ability to teach the associated mathematical skills. 365

379 Chapter 8: Discussion Strategies taught to calculate medicine doses The calculation strategy or strategies taught were more likely to be determined by the School than by the individual teacher. Regardless of who determined the calculation strategies taught, the formula was clearly the dominant calculation strategy taught in these Australian universities, sometimes in combination with one or more non-formula-related strategies so that students could exercise choice in the calculation method they used. Alternative methods cited were proportional reasoning and ratio-proportions (rule-of-three) methods. Several participants reported that learning and assessment of dose calculation and measurement skills were conducted entirely through the use of online learning programs. Further confirmation of the dominance of the formula as a teaching strategy came in the form of participants responses to a question about skills taught. Applying formulae was the numeracy skill most frequently reported as being routinely taught to develop students dose calculation skills. Other skills routinely taught were metric units and conversions, and numerical processes 38. Effective use of a calculator was the least frequently reported numeracy skill routinely taught. In the option of other, two respondents reported ratio proportions and concentration ratios as skills they routinely taught. It is likely the former referred to the rule of three. The latter may have referred to manipulation of concentrations (e.g. 10 mg in 2 ml) to produce equivalent concentrations (e.g. 5 mg in 1 ml), or application of the unitary method to reduce the concentration to 1 mg or 1 ml. The single reference to concentration ratios was the only suggestion of teachers routinely instructing students in the scalar approaches nurses were observed using in practice, or the numeracy skills most useful in supporting those scalar approaches. Pen-and-paper tests and online quizzes were the most frequent forms of assessment used. Almost 80% of respondents indicated a requirement for students to achieve 100% accuracy in tests; three attempts were most commonly permitted. The prospect of students progressing through nursing education programs without ever demonstrating competence in dose calculations against the criteria applied was confirmed by 17% of respondents. They indicated it was possible for students to fail the dose calculation component but still pass the unit. A further 6% of respondents were unsure. 38 The question included the following examples of numerical processes: cancelling fractions, multiplying fractions, division operations, operations involving decimals, e.g. ½ =

380 Chapter 8: Discussion The continuing practice of teaching students in Australian universities the formula to calculate medicine doses corroborates the little evidence available, mainly from the UK, suggesting that the formula is the commonly taught method for calculating medicine doses (Macdonald et al., 2013; Weeks, Hutton, Coben et al., 2013; Wright, 2009a, 2013). The single exception is the USA where ratioproportions and dimensional analysis methods are widely taught (Cookson, 2013; Greenfield et al., 2006; Hunter Revell & McCurry, 2013; Olsen, Giangrasso, & Shrimpton, 2012). The data collected via the online questionnaire from academic staff suggest little change from the strong emphasis on teaching the formula reported approximately two decades ago (Gillies, 1994) in the only investigation identified examining dose calculation policy and teaching practice in Australian universities (n = 58). A small, but possibly important, change from the results of the earlier survey is a shift in policy reported by a few respondents, to one of exposing students to one or more non-formula-related calculation strategies to give students choice in their calculation methods. In the current study, there was widespread agreement that students experience difficulties in gaining competence in medicine dose calculations and staff experience difficulty in teaching the topic. Basic numeracy skills, metric units and conversions, and formulae and their application reported to be the areas of greatest difficulty for students. Recommended solutions for these difficulties included imposing minimum student entry requirements, providing support and remediation opportunities and practice opportunities. In regard to difficulties experienced by staff in teaching dose calculations, the findings of my study are little different from those of my earlier study (Gillies, 1994) in which the majority of respondents (n = 58) believed staff experienced difficulties. In the earlier survey, one in five respondents indicated either they personally did not feel comfortable teaching the mathematical aspects of the topic or that they made no attempt to do so. In line with Coben s (2010) prediction, the adequacy of educators skills for teaching mathematical concepts was called into question by the fact that approximately one-third of respondents had not studied mathematics to the end of secondary school. The academic staff who participated in the current survey reported feeling comfortable and well-equipped to teach medicine dose calculations. However, they 367

381 Chapter 8: Discussion reported that nurse educators sometimes have difficulties in teaching this aspect of the nursing curriculum, confirming the findings of the earlier survey. Difficulties experienced by staff in teaching dose calculations were reported to be most often the result of staff members: feeling ill-equipped to accommodate the diverse mathematical needs and learning styles of students, especially those who experience difficulties; not being strong in mathematics and possibly lacking basic mathematical skills; and, not being mathematics teachers, feeling uncomfortable teaching mathematical skills. Changing the way dose calculations are taught and finding ways to support staff in meeting the demands of teaching the associated mathematical skills, and in dealing with the diverse mathematical needs and learning styles of students, were uppermost among the solutions participants suggested. The findings of the current study also confirm the suggestion by Wright (2005, 2009a) that some nurse educators struggle to find effective ways to teach the mathematical skills required for medicine administration and to deal with the needs of students who experience difficulties. This suggestion was supported by Coben (2010) who noted that the lack of proficiency among some qualified nurses suggests some nurse educators may also have an inadequate understanding of numeracy, or be unable to communicate their knowledge to student nurses, even if they are able to perform calculations expertly themselves Strategies taught to measure medicine doses Approaches to teaching measurement skills for medicine administration varied greatly between universities. Three-quarters of respondents reported that measurement skills for medicine administration were either specifically listed in the content for the unit or students were routinely exposed to exercises and/or activities specifically aimed at developing measurement skills. By contrast, ten respondents (20%) reported that no teaching of measurement skills was undertaken or that it was discretionary. Assessment of students dose measurement skills was most commonly conducted by observing students administering medicines, either in simulated clinical settings or in actual clinical settings, or via pen-and-paper tests. The questions posed in the questionnaire were not designed to gather information about the degree of rigour associated with efforts to develop and assess students dose measurement skills in Australian nurse education programs. The apparently sound approaches suggested by participants responses are not, however, 368

382 Chapter 8: Discussion consistent with the absence of measurement skills evident in commonly used text books, where the main measurement focus is instruction in converting between different units of measurement. Student difficulties and mathematical inadequacies have been the subject of much research (Coben et al., 2010; Fleming et al., 2014; Kohtz & Gowda, 2010; Macdonald et al., 2013; Pierce et al., 2008). However, the little known about the teaching of strategies for calculating medicine doses has focused largely on interventions to remediate students poor results in tests of dose calculation competence and numeracy skill. The mixed responses of participants concerning approaches to teaching dose measurement skills provide some justification for Cartwright s conjecture (1996) that the lack of recognition in the literature of the potential for the measurement aspect of medicine administration to contribute to dosing errors may indicate measurement skills are not taught in nursing programs, perhaps because educators assume nurses are able to accurately measure doses. Information about teaching practices relating to dose measurement skills is largely restricted to an outline of how Weeks, Hutton, Young et al. (2013) have incorporated technical measurement competence ( dosage-measurement ; p. e23) into their computer-based teaching, learning and assessment program (Coben et al., 2010; Macdonald et al., 2013; Weeks, Hutton, Young et al., 2013). Weeks et al. viewed technical measurement competence as one of three essential sub-elements of competence in medicine administration. They observed that an error in any one of these areas may result in a medication error. 8.4 Calculating medicine doses: The theory practice divide This study has exposed a far-reaching theory practice divide in relation to the calculation of medicine doses. This divide manifested itself in relation to: the calculation methods nurses are taught to use versus the methods they actually use; the calculation methods nurses use in response to written word problems versus the methods they use to solve authentic practice problems; 369

383 Chapter 8: Discussion the computational skills needed in conjunction with the formula versus those needed in conjunction with scalar strategies; and the conceptual difficulties associated with formula use versus the absence of such conceptual difficulties when scalar approaches are used. Each of these manifestations of the theory practice divide will now be discussed in more detail Nurses dose calculation methods The study revealed a marked disjunction between the dose calculation strategies nurses are taught as students and the strategies they use most often in clinical practice. In the university setting, instruction in dose calculation methods places a heavy emphasis on the formula as a universal method for calculating medicine doses, usually in combination with a calculator. By contrast, in clinical practice, nurses reject the formula method for all but the most difficult dose calculations, preferring instead to use their own invented scalar strategies, applied mentally. This disjunction underscores the inadequacies of the formula teaching model as a preparation for calculating medicine doses in clinical practice. Nurses rejection of the formula supports research findings indicating that formal processes are also rejected in favour of quick and efficient informal processes adapted to the problem context in other professions where mathematics is used, as well as in everyday problem situations (Coben, 2010; Hoyles et al., 2010; Nunes et al., 1993; Pozzi et al., 1998). The literature identifies many reasons why problem solvers both adults and children reject formal school-taught methods, such as the rule of three, from which the formula is derived. Formal methods compete with problem solvers natural schema for conceptualising and solving proportions (Schliemann & Nunes, 1990). Formal methods remove the problem solver from the problem context and often involve written algorithms that are often poorly remembered and applied. The result is often unrealistic answers that remain undetected (Nunes et al., 1993). When nurses use the formula, they calculate across measures (for example, multiplying milligrams by millilitres). Whereas multiplying and dividing numbers is meaningful to students, it is unnatural for them to perform these operations on quantities, with the result that the intermediary products or quotients so formed 370

384 Chapter 8: Discussion generally have no meaning to them, (Cramer et al., 1993; Hoyles et al., 2001; Vergnaud, 1983, p. 149). Problem solvers consistently show a strong preference for scalar methods to solve everyday problems of proportionality. Many of the reasons for this preference also appear to apply to nurses in clinical practice when they solve similar proportionality problems in the form of dose calculations. Scalar methods accord with nurses natural schema of proportionality. By using scalar strategies, nurses remain connected to the problem and its meaning. They can also perform the associated computations mentally, without support from pen and paper or a calculator. The theory practice divide in relation to the methods used to calculate doses was further highlighted by the comments of students and their nurse mentors in a study by Marks et al. (2016). Students, when describing their experiences during clinical placements, reported seeing little evidence of the formulaic methods they learnt at university being used in the practice environment. One nurse mentor declared their student s university mathematics (p. 50) was not something nurses did on a daily basis. Another mentor expressed the view that nurses did not do calculations, seemingly because formal calculations requiring algorithmic methods were seldom performed. The formula is typically applied as a rote-learned, poorly understood and remembered, procedural process. Scalar methods, by contrast: accord with the universally-held schema for understanding proportional relationships and solving proportionality problems; keep the variables separate as parallel transformations are carried out, first in one measure space (e.g. mass), then the other (e.g. volume); can be performed mentally in a series of simple parallel transformations, without tools such as calculator or pen-and paper, thus leaving nurses hands free to perform the physical actions associated with preparing and administering medicines; allow the problem solver to remain focused on the problem situation and retain its meaning at each step; preserve the meaning and relative values of the numbers involved, an important component of error detection; and 371

385 Chapter 8: Discussion are associated with fewer errors than formal school-taught procedures Written word problems versus authentic practice problems The theory practice divide relating to dose calculations was further demonstrated when nurses responses to written word problems in the questionnaire were compared to their responses to authentic problems encountered in clinical practice. The same nurses who used scalar dose calculation processes for all but 12% of the authentic medicine administrations requiring calculation in clinical practice exhibited quite different calculation responses when confronted with the need to respond in writing to test-like word problems in the questionnaire. The theoretical problem scenarios in the questionnaire drew formula methods from nurses for 61% of the 220 tasks performed. Further, nurses made errors on the questionnaire tasks, whereas their calculations in clinical practice were error-free. The identified theory practice divide is consistent with existing research suggesting that the contexts in which problems are situated and the manner in which they are posed influence the way problem solvers respond. When problem solvers encounter real-world problems in authentic contexts, they respond by using informal solution methods. By contrast, when problem solvers encounter word problems or context-free computations, they are more likely to respond using school-taught algorithms, which are associated with a greater risk of error. The propensity for error when nurses use the formula was confirmed by Hoyles et al. (2001), who observed that on the rare occasions nurses used the formula: it seemed to inhibit a sense of connection either with straightforward arithmetic that would have simplified the task of with the meanings of the quantities, derived from nursing practice. (p. 18) Other studies have also found a theory practice divide in relation to dose calculations (Macdonald et al., 2013; Weeks et al., 2000). However, the gap identified has not extended beyond the difference between the traditional word problem format used in didactic teaching approaches and the authentic presentation of dose calculation problems in clinical practice. 372

386 Chapter 8: Discussion Computational skills needed for formula use versus scalar strategies The existence of two vastly different dose calculation models the theoretical formula model and the practice scalar model exposed two further aspects of the theory practice divide. Nurses computational methods in the study highlighted differences in the nature of the computational skill needed for each of the calculation approaches, a conjecture also made by Wright (Wright, 2009b). When nurses used scalar approaches, the emphasis was on simple processes such as doubling and halving, sometimes in combination with addition or repeated addition, always performed mentally. By contrast, when nurses used the formula, the entire calculation process was incorporated into one complex calculation. A combination of cancelling operations, a multiplication operation, and a division process is frequently required to resolve what Macdonald et al. (2013, 50 2 p. e71) described as multiple computations e.g. ). Multiple computations have been associated with a high error rate and a high proportion of student nurses admit to not knowing how to carry out these calculations (Macdonald et al., 2013). In focus groups, nurses indicated they switch between the two different dose calculation models according to the circumstances. In clinical practice where no constraints are imposed on their calculation methods, they use scalar strategies and mental computations. In test situations, where they are likely to be given the formula and may be required to show their working, they use the formula because that is what is expected. Nurses indicated that in formal situations they show their working in conventional ways in order to legitimise their answers. They perform computations using written algorithms to cancel fractions and perform multiplication and division operations, rather than using their preferred scalar strategies and mental computations. If nurses were to use scalar processes in tests, their attempts to express in writing the reasoning they performed mentally would be counterproductive. Nurses would most likely find it difficult to express in mathematical terms that could be understood and considered acceptable by educators the reasoning they view as common sense. Attempts to achieve this would also impose an extra layer of complexity to their task

387 Chapter 8: Discussion Conceptual difficulties: A formula problem Differences in the computational skills required for the two approaches also revealed factors contributing to the problem of conceptual difficulties, a major cause of calculation error. Conceptual difficulties have been linked to didactic teaching methods and formula use (Fleming et al., 2014; Gillies, 1994; Hutton et al., 2010; Weeks et al., 2000; Wright, 2006). Conceptual difficulties result from teaching practices in which students learn to calculate doses by solving word problems that attempt to depict dose calculation scenarios nurses might encounter in clinical practice. The common description of conceptual difficulties as inability to correctly link the information in the problem statement to the terms in the formula (Blais & Bath, 1992; Gillham & Chu, 1995; Hutton, 1998a; Weeks et al., 2000; Weeks, Hutton, Young et al., 2013) reveals that this problem stems directly from formula use. The use of words to depict medicine administration scenarios provides inadequate context for dose calculation problems, with the result that students often struggle to make semantic connections between the words and numbers in the problem description and the different parts of the formula (Weeks et al., 2000; Weeks, Hutton, Young et al., 2013). Constructed through words alone, students conceptual models for dose calculation scenarios are inadequate. Without access to the visual and tactile cues provided by the patient chart, ampoules, product labels, syringes, and other artefacts associated with medicine administration, students struggle to correctly locate numerical information in place of words in the formula (Cartwright, 1996; Weeks et al., 2001). The result is conceptual error, incorrect medicine doses and the potential to harm patients. My study has highlighted the fact that when nurses use scalar calculation methods they have no need to match words with the symbols in a formula. Thus, when nurses use their preferred scalar methods rather than the formula to calculate doses, the issue of conceptual difficulty vanishes. However, enabling students to learn dose calculations in the ideal learning environment of clinical practice presents logistical difficulties, and is unlikely to offer an appropriate range of different medicine administration situations. Therefore authentic simulation of the clinical environment possibly provides the best option for successful learning. 374

388 Chapter 8: Discussion 8.5 Determinants of nurses dose calculation strategies: An emerging theory A previously unreported phenomenon that emerged from the study was the strong association between nurses dose calculation strategies and the numerical characteristics of the medicine administration task. The dose-to-stock ratio (DSR) is a novel concept, not previously explored in any comprehensive way in relation to how nurses calculate medicine doses. Calculating the DSR for every medicine administration recorded during the observation sessions for which it was relevant proved to be pivotal in teasing out why, for particular medicine administrations, nurses chose to use one particular strategy, and for others, a different strategy. An emerging theory is proposed, based on the evidence from the study. The theory encapsulates the pattern of nurses calculation strategies in clinical practice and provides a rationale for the particular calculation strategies nurses use and when they use them. The theory explains nurses choice of dose calculation strategies in terms of the DSR for each medicine administration. The theory identifies: two distinct types of dose calculation strategy nurses use in clinical practice the formula and proportional reasoning; the conditions that determine which of these two types of strategy nurses are most likely to use; and the numerical characteristics that determine which specific scalar strategy nurses are most likely to use when they use proportional reasoning. The following criteria determined the dose calculation strategy nurses were most likely to use according to the DSR for the medicine administration task. For a DSR of 1:1, no calculations were required (27% of all observed medicine administrations). For the most commonly occurring DSRs those in the classes of DSR n:1, 1:n, and n:2 when n 4 nurses were most likely to use proportional reasoning to calculate the dose to administer. Of 193 such medicine administrations, nurses used proportional reasoning for 186 (96%). These three groups of medicine administrations accounted for 385 (25%) of all 375

389 Chapter 8: Discussion 1571medicine administrations observed and 89% of the 432 medicine administrations requiring a dose calculation. For more complex DSR, nurses were most likely to use the formula. In my study these medicine administrations were mostly required for paediatric patients. Of 23 such medicine administrations, nurses used the formula for 18 (78%). When nurses used proportional reasoning strategies to calculate medicine doses, the particular scalar strategy they were most likely to use was determined by the specific value of the DSR. The theory is summarised in Table 8.1. The table shows the dominant strategy for each class of DSR and the number and percentage of dose calculations in that class for which the dominant strategy was used when n 4. Table 8.1 Dominant calculation strategies for different DSR classes Class of DSR Values of DSR (n 4) Dominant calculation strategy n:1 2:1, 3:1, 4:1 Multiplicative reasoning or repeated addition 1:n 1:2, 1:3, 1:4 Fraction operation or division process n:2 3:2 Halving combined with addition No. (%) of calculations in DSR class for which strategy was used 113 (91%) 49 (89%) 13 (93%) Complex 2:5, 3:4, 1:25, DSR a 13:20, 3:50, 73:120 Formula 18 (78%) a Examples only of DSR values are provided; the constraint n 4 does not apply. In this study, there was insufficient data for DSRs with n > 4 for the three most commonly occurring classes to investigate whether this theory can be extended beyond this value. Further research involving a larger data sample is needed to determine this. 376

390 9 Conclusion There is a crack, a crack in everything That s how the light gets in That s how the light gets in. Anthem, Leonard Cohen ( ) Accuracy in calculating and measuring medicine doses is critical for the safety of patients and the clinical efficacy of medicine therapies. As discussed in Chapter 8, this study identified the calculation and measurement strategies Australian nurses use in clinical practice and compared them to the strategies taught in Australian universities relating to these aspects of medicines management. 9.1 Significance of the study This study provides new insights into an aspect of nursing practice that has long been the subject of concern among nurse educators, employers of nurses, and the broader nursing profession nurses accuracy in calculating medicine doses. The study also exposes several issues of concern relating to the other key aspect of accurate administration of medicines the measurement of medicine doses. My study is the only known Australian study of its kind, and possibly the first comprehensive study of its type worldwide. It extends the work of Hoyles et al. (2001), which, although limited in scope, was a seminal work as it was the first study to reveal the methods nurses use to calculate medicine doses in practice. The consistency of nurses use of particular calculation strategies in response to the numerical characteristics of the medicine administration, represented by the dose-to-stock ratio, resulted in the formulation of a theory explaining why nurses choose one calculation strategy for a particular medicine administration and a different strategy for another. My study adds to the growing body of evidence concerning the ways in which people use mathematics in the workplace and other out-of-school settings. It confirms existing research suggesting that for problems of proportionality, which include nurses dose calculations, problem solvers reject formal calculation strategies such as the rule of three (Karplus et al., 1983); (Nunes et al., 1993); (A.D. Schliemann & Carraher, 1993); (Vergnaud, 1983). Instead, they prefer to use 377

391 Chapter 9: Conclusion informal proportional reasoning methods, tailored to the particular problem, that bear little relationship to the formal methods problem solvers are taught to use. The invented processes nurses use, which are almost exclusively scalar in nature, accord with the everyday schema of proportionality people use to interpret and solve proportionality problems (Analucia Dias Schliemann & Nunes, 1990). The survey of university educators revealed a strong emphasis on teaching of the formula, with the School or Faculty most often determining the calculation strategies taught rather than individual educators. There was little evidence of students being taught proportional reasoning methods or the computational strategies to support such methods, highlighting a theory practice divide in relation to nurses dose calculation strategies. 9.2 Implications for practice The disconnect between the calculation methods taught to students in university programs and the calculation methods nurses actually use in practice has wide-ranging implications for nurse education and practice. These implications include a need to review: the approaches used for teaching, learning and assessing dose calculations in the nursing curriculum; the approaches used by employers of nurses in the continuing education and competency testing of nurses relating to dose calculation; and nurses and nurse employers perceptions of the legitimacy of the dose calculation methods nurses use in practice. The divide between theory and practice highlights the fallacy of the assumption implicit in the continued emphasis placed on the formula in current nursing education programs. That assumption is that by instructing students in the formula method alone, they are adequately equipped for professional practice. The theory practice divide exposes the myth that as nurses move from university into professional practice they continue to use the formula they learnt as students. Rather than providing a fail-safe, one-size-fits-all method for calculating medicine doses, the formula may instead interfere with students existing schema of 378

392 Chapter 9: Conclusion proportionality and their already well-developed approaches to solving proportional problems. Evidence-based teaching practice would advise that the dose calculation methods nurses are taught reflect methods nurses use successfully in clinical practice. This goal is dependent, however, on identifying what those methods are, an important outcome of this study. Educators and employers of nurses need accurate and reliable information about effective calculation approaches and computational skills used by practising nurses so that they can design effective, achievable learning goals (Ermeling, Hiebert, & Gallimore, 2015) and create valid assessments (Wright, 2012). To date, attempts to ascertain the critical skills for dose calculation have largely focused on analysing nurses written responses to dose calculation tasks posed as word problems, underpinned by a belief that the only legitimate method for calculating doses is to use the formula. Prior to this study, there has been little attempt to analyse and understand the cognitive processes of nurses as they engage in dose calculation behaviours in clinical practice. Nurses in my study demonstrated well-formed concepts of proportionality, a sound appreciation of the invariance of medicine concentration, and the ability to successfully draw on these concepts and skills to calculate a wide variety of dose calculations. Nurses provided abundant evidence that they are capable of applying and adapting their existing proportional reasoning skills to the calculation of medicine doses; they prefer to use these methods rather than the formula. This study adds to a growing body of evidence pointing to the need for reassessment of the current model for teaching and assessing dose calculations ((Best & Moore, 1988); (Cartwright, 1996); (Coben, Hodgen, Hutton, & Ogston-Tuck, 2008); (Hoyles et al., 2001); (Wright, 2007); (Wright, 2009); (Wright, 2012)). Almost 30 years ago, New Zealand authors, Best and Moore (Best & Moore, 1988), called on nurse educators to adopt an holistic approach (p. 28), encouraging students to develop more effective reasoning processes, and in so doing, motivating students. The proportional reasoning approaches nurses used in my study and the computational skills they used to support these approaches provide a blueprint for educators in the design of effective learning goals and the creation of valid and reliable assessments. The fact that these nurses were able to employ proportional reasoning concepts and skills with little or no apparent instruction in them highlights 379

393 Chapter 9: Conclusion the potential for all nurses to succeed in dose calculation and become safe practitioners in the administration of medicines. However, realising this latent capability is contingent upon educators designing instruction and assessment that acknowledges, values, and accommodates nurses innate problem-solving methods. The online questionnaire of Australian university staff provided abundant evidence that students are instructed in applying the formula and the skills needed to support its use. However, respondents provided little evidence to suggest that proportional reasoning methods are currently recognised as important or that nurses are instructed in computational skills to support such methods, including simple skills such as doubling, halving, and expressing solution concentrations in equivalent forms. The literature suggests this may be the case worldwide. Ideally, learning and assessment of dose calculations should take place in authentic settings with all the tools of practice available to student nurses. A goal of formal assessment of dose calculation skills should be to present problems in ways that mimic as closely as possible authentic clinical practice environments, and allow students the freedom to respond without the constraints of written answers and the need to show their working in a written format. Common requirements such as these do not reflect nurses natural ways of performing dose calculations in the practice environment and may interfere with their cognitive processes. It is important that students feel unconstrained in the solution methods and free to use their preferred scalar strategies and mental computations, as they do when they calculate medicine doses in clinical practice. The extent of nurses rejection of the traditional formula for calculating doses in favour of scalar strategies has implications for employers of nurses also. Many hospitals endeavour to protect the safety of patients by testing the dose calculation skills of newly employed nurses, providing continuous professional development focused on medicine calculations and requiring nurses to meet mandatory annual testing requirements. These measures, the last of which was practised at two of the three research sites, are aimed at assisting nurses to retain their dose calculation skills so they remain competent to administer medicines, thereby reducing medication errors. Information gathered in focus groups and from materials such as tests provided by senior hospital staff, indicated a strong focus on the formula method in tests and professional development programs. This focus is reinforced by hospitals routinely providing the formula in tests to assist nurses in their calculations. 380

394 Chapter 9: Conclusion Reconsideration of the continued heavy emphasis placed on the formula in efforts by hospitals to protect patients from calculation error is warranted in light of the fact that nurses make so little use of the formula in practice. Subtle indications emerged during observation sessions and focus groups that the formula is perceived by nurses to be the proper method they should use. It also became clear in focus group discussions that nurses have adapted their practices to meet different circumstances and expectations. They use one approach scalar strategies in practice, and a different approach the formula when they perceive that the situation calls for a formal approach. In practice, nurses are unconstrained in their calculation methods and choose the most expedient method that achieves the correct dose while minimising the risk of harm to their patient. These methods usually involve scalar approaches and mental computations. In mandatory tests and possibly interactions with colleagues to check each other s medicine administration processes, nurses use the formula and written processes or a calculator. Validation of student and graduate nurses scalar calculation approaches by educators and employers is vital for a number of reasons. Nurses need assurance that their informal, often invented, methods are natural and legitimate responses to problems of proportionality and are used by most competent problem solvers. Legitimising nurses informal methods supports their attempts to take control of their own learning, and facilitates the development of confidence, self-awareness and selfesteem (Best & Moore, 1988). It is also important to reset public opinion among nursing and allied healthcare professionals concerning student and graduate nurses mathematical capabilities. New, valid benchmarks for dose calculation competence need to be constructed and standardised within the profession so that nurses are judged not on spurious skills deemed to be critical for dose calculation competence, but against legitimate evidence-based criteria reflecting expert clinical practice. 9.3 Limitations of the study Limitations of the study result from the fact that: convenience sampling was used in both phases of the study, rather than random sampling; 381

395 Chapter 9: Conclusion no independent verification of data was conducted; and focus group participants were not given an opportunity to comment on and verify my interpretation of discussions. Convenience sampling may have resulted in sampling bias. Although a representative mix of hospitals was studied and all universities offering preregistration nursing programs were invited to participate, within the research sites, the fact that participants volunteered may have introduced bias. Participating nurses may have been more confident in their dose calculation skills that others who declined. Similarly, academics who participated may have had a particular interest or expertise in the topic under investigation, and those with no interest and possibly a perception they were less competent than others in the topic area may have chosen not to participate. In the conduct of the study, the pragmatic design of the study allowed the flexibility to employ methods best able to help me answer my research questions (Cherryholmes, 1992) by responding to issues as they unfolded (Johnson & Christensen, 2012), including pursuing the issue of excess volume in single-dose ampoules. However, this flexibility came at a cost in terms of intervening in nurses routine medicine rounds to collect data monitoring overfill in single-dose ampoules. During these brief periods of time, my role changed from that of passive observer conducting naturistic observation to active researcher. In this respect, the pragmatic design of the study design may be viewed as a limitation. My role as an outsider observing nurses brought advantages as well as disadvantages. I was able to identify aspects of nurses practice that those more intimately connected with it may have overlooked. However the need to quickly acclimatise to the unfamiliar environment of nursing practice meant there may have been some aspects of nurses mathematical practice that I missed. It is likely that participants perceived me as less threatening than a fellow nurse might have been. Rather that the researcher participant relationship placing me in a position of power or authority, the nurse participants were the experts the teachers demonstrating their practice and sharing their expertise. I was the learner, a novice. Accessing a wealth of information concerning nurses dose calculation and measurement practices was only possible because I was able to immerse myself in the practical experience itself (Sabin, 2013). 382

396 Chapter 9: Conclusion 9.4 Implications for future research Considerable work remains to be done in the quest for a comprehensive understanding of how nurses calculate medicine doses in clinical practice and the factors influencing those methods. The validity of the theory proposed on the basis of my findings needs to be thoroughly tested with different samples of nurses, in different clinical settings, and in different countries. A significant research challenge is to investigate how best to implement the knowledge gained from this study. Research is needed to explore the impact on the learning outcomes of students and graduate nurses of a changed approach to the teaching, learning and assessment of dose calculation and measurement skills, in line with the findings of this study. Research is also needed to monitor the effects of efforts to create valid benchmarks against which to judge nurses competence, and changes in the risks to patients associated with calculation and measurement of medicine doses. Future research efforts might also be directed towards investigating: nurse educators beliefs in relation to instruction and assessment of the dose calculation aspects of medicine administration, with a particular focus on the role of the formula, its advantages and disadvantages, and the extent of educators awareness of alternative calculation methods; the benefits of introducing students to simple functional strategies for those medicine administrations to which this type of proportional reasoning is most suited; and the impact on student learning of employing only computer-based teaching and assessment of dose calculations. Research is needed in the measurement aspects of medicine administration identified in this study as areas of concern. Future research might be directed towards investigating: the knowledge and understandings of both students and nurse educators concerning optimising accuracy in the measurement of medicine doses, particularly in relation to the choice of syringe capacity; industry standards and practices relating to the volumes contained in singledose pharmaceutical products, specifically prefilled syringes and ampoules, 383

397 Chapter 9: Conclusion the labelling conventions for such products, and the implications of these practices for safe use of such products by health professionals, particularly nurses; and student and graduate nurses understandings concerning the information displayed on the labels of single-dose ampoules and prefilled syringes, and how their interpretation of this information translates into dose measurement practices that potentially impact on patient safety. 9.5 Concluding remarks Nurses need more than one method to calculate doses. At the very least, nurses need one method to calculate the dose and another method to check it. Educators should take courage from the knowledge that, given appropriate support, students are capable of finding their own methods for calculating medicine doses. They should resist the temptation to over-mathematise dose calculation in the mistaken belief they are assisting students. The capacity of nurses to find their own error-free solution methods was evidenced by the clever and flexible methods they used in this study. Nurses were masterful in demonstrating their mathematical knowledge and skills relating to proportionality, acquired as a natural part of everyday living (Nunes et al., 1993; Vergnaud, 1983; Schliemann & Nunes, 1990; Schliemann & Carraher, 1993). Mathematics is, in essence, about discovering patterns. Nurses found patterns in the numerical characteristics of medicine administrations, responding flexibly to them by using different approaches for different DSRs. Moreover, nurses responded with remarkable consistency to the patterns they discerned, despite almost certainly having received no formal instruction during their professional education to guide them. My study provides support for contemporary beliefs within the mathematics education community concerning the robust knowledge students construct when they are free to explore and invent their own problem-solving methods. These beliefs stand in stark contrast to the long-standing practices in nurse education of using didactic pedagogical methods, rote-learned formulae and word-based portrayals of real-world practice situations. Such methods have resulted in student difficulties, failure to master dose calculations, and calculation errors. 384

398 Chapter 9: Conclusion Current and future approaches to teaching dose calculations may be viewed as the result of social and cultural influences. From this viewpoint, nurse educators have the opportunity, as all educators do, to contribute to the culture inherited by the next generation (Vygotsky, 1978); (Gredler, 1992). Viewed through Vygotsky s lens on the sociohistorical factors that shape the development of cultures, each generation contributes to the culture inherited by the next generation. Therefore, if the present generation does not acquire the complex cognitive skills viewed as important, subsequent generations run the risk of being deficient as well (Gredler, 1992), (p. 402). Educators who accept this challenge may be guided by the following recommendations from Ermeling (Ermeling et al., 2015). Effectively implementing new practices requires extended practice-based professional learning, as well as continual study and refinement of teaching. Teachers need time to learn new practices; time to help students respond to them; and time to configure, adapt, and incorporate these practices into classroom instruction. (Ermeling et al., 2015) (p. 50) Improvements in student learning will be dependent on improving the knowledge of teachers, and providing the resources and opportunities to support teachers in reflecting on their teaching, student learning and the inter-relationship between the two (Ermeling et al., 2015). This calls for a research and development process involving both practitioners and researchers. It requires first, a clear definition of learning goals, and then development of a knowledge base of empirically tested teaching methods for specific learning goals and particular students. Ermeling et al. (Ermeling et al., 2015) advised that such an approach is more likely to be successful in achieving lasting results than short-lived attempts to copy a few best practice exemplars. The findings from my study significantly expand knowledge of the strategies nurses use to calculate doses in practice and provide an evidence-based foundation on which to develop more effective teaching, learning, and assessment practices in relation to dose calculations in the nursing curriculum. Rather than adding to an already large volume of literature purporting to demonstrate nurses conceptual difficulties, failure on dose calculation tests, and poor mathematical skills, this thesis provides positive evidence of nurses sound skills in solving problems of proportionality in the nursing context. The nurses 385

399 Chapter 9: Conclusion solved dose calculation problems in their own intuitive, yet remarkably uniform, ways, using methods based on their existing schema of proportionality methods that bear little resemblance to the formula method they were taught. Nurses invent their own methods to calculate medicine doses that match the numerical characteristics of the medicine administration task. To nurses, these methods are logical and safe because they understand what they are doing. 386

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414 Appendices Appendices Appendix 1: Nurses invitation to participate 401

415 Appendices Appendix 2: Sample of completed observation schedule 402

416 Appendices Appendix 3: Sample page from questionnaire for nurses 403

417 Appendices Appendix 4: Discussion points for focus groups 1. Tell me about the Calculation Methods you use in your Clinical Practice and how they relate to what you learnt as a student Were you taught specific methods to use for dosage calculations? What were these methods? Do you still use them? Have the calculation processes you use changed over time? How have they changed? Why? In what situations would you use different methods now? What are these methods? Can you show me how you use these using the following examples? If participant suggests applying a formula: Can you explain why you find this method works well for you? Would you be able to do it any other way? If participant suggests an alternative method not involving a formula (e.g. proportional reasoning): Can you explain why you find this method easiest? If participant suggests a different method to what they used in an earlier problem: Can you explain why you are using a different method for this one? What determines the method you select? 2. I ve seen nurses in this Hospital using methods other than the formula method for calculating their doses. For example in calculating doses such as those on the sheet here. 404

418 Appendices (a) Order: Paracetamol 1 g; PO Stock available: 500 mg tablets (b) Order: Digoxin 125 micrograms; IV Stock available: 500 mcg / 2 ml In (a) how would YOU work out how many tablets to give? In (b) how would YOU work out the volume of liquid you need to give? What factors determine the method you choose to use? 3. Here is an example about administering a dose of heparin (Present Medication Order on butcher s paper) Order: Heparin 5000 IU; IV Stock available: 5000 IU in 0.2 ml When you re preparing this medication, if you draw out the entire contents from the vial can you comment on what you might find? Participant may suggest that it s very likely to find there is more than 0.2 ml in the syringe. How do you deal with this situation? Can you explain the thinking behind you taking that action? What are the factors that determine how accurate you feel you should be when you are giving a volume of liquid drawn from an ampoule? 4. While I ve been observing medication administration in the hospital, I ve been interested in the type and size of syringe you select for administering for different volumes of fluid, particularly small volumes Tell me about the size and type of syringe you would use to measure a volume less than 1 ml, for example the heparin order we ve just discussed. What factors influence your choice of syringe? 405

419 Appendices Discuss issues of scale, and advantages and disadvantages of different syringe types (these may include insulin syringes and 1 ml syringes). Are there any additional other factors that influence your choice of syringe? (eg needle size; route of administration eg Subcutaneous vs IM) 5. I ve noted the hospital pharmacists often record notes in green biro on the patient charts. What do you understand to be the purpose of these notes? Do the pharmacist s notes play any role in guiding your medication administration practice? If yes: in what way/s do the pharmacy notes assist you? in what circumstances are the pharmacy notes MOST valuable to you? when are they LEAST valuable to you? 6. During the time I ve spent in the Hospital observing nurses I ve been interested in how much use you make of calculators for working out the amount of medication to give? In what situations do you use a calculator, and why is that? Are there situations where you choose NOT to use a calculator? What are these and why is a calculator not required? When you use a calculator, do you then perform some sort of check on the answer you get on the calculator? If so, what sort of check or checks might you use? 7. Nurses have traditionally learnt how to calculate drip rates in drops per minute for IV infusions. the calculations relate to IV administrations where the order is a volume in litres or ml and the time for the infusion to run is stated in hours. The calculation also involves use of the drop factor (macro: 20 drops per ml, and micro: 60 drops per ml). What was the method you were taught in your training course for calculating drip rates such as these? How likely is it in this hospital that you would use a giving set such as the macro/micro giving sets I've described? 406

420 Appendices Given the infrequent use of this type of apparatus in this hospital, would it be a problem for you if you found yourself in another hospital where you were required to use a giving set, or for some reason didn t have access to a pump? How successful would you be calculating a drip rate if it s been a while since you had to do this sort of calculation? How successful were you (or would you be) in recalling the formula and applying it in the questionnaire drip rate question? 8. What factors operating in the clinical environment are likely to impact on your ability to administer the correct dose of medicine? Give me an example of what might be going on around you in the ward or medication room that is likely to affect your ability to correctly calculate and administer medicines? What are the major factors stemming from the clinical environment that impact on you positively and negatively? 9. Is there anything else you would like to tell me about your nursing practice as it relates to calculating and measuring medicine doses? Or about what nurses learn as students in this area? Supplementary Questions (if time permits) 10. Are there calculations that you find particularly difficult to do in your current clinical area? What types of medication calculation cause you most difficulty? What is it about this type of calculation that causes you difficulty? 11. How would you know if you had made a gross error in calculating a medication? For example, how would you know if you had made an error large enough to potentially cause harm to the patient? 407

421 Appendices Do you use any methods to routinely estimate or check your calculations? Describe any estimation and checking methods you use and the situations in which you use them. 12. Are the calculation methods you would use in a written test situation different from the methods you use routinely on your ward rounds? How are they different and why? An example of the type of written test situation I m thinking of is the annual medication calculation test you are required to sit as an employee of the hospital. 13. Are there situations where you find measurement of the dose causes you particular difficulty? What types of medication cause you most difficulty in terms of measuring the quantity you will administer? What is it about this type of measurement task that causes you difficulty? Thank participants for participating in the focus group and for their contribution to the project. 408

422 Appendices Appendix 5: Extract from spreadsheet recording observations Includes Observation Session 156 (see Appendix 2) 409