- Email: [email protected]
The assessment and development of drug calculation skills in nurse education – A critical debate
Nurse Education Today 29 (2009) 544–548
Contents lists available at ScienceDirect
Nurse Education Today journal homepage: www.elsevier.com/nedt
The assessment and development of drug calculation skills in nurse education – A critical debate Kerri Wright * University of Greenwich, Avery Hill Road, Eltham, London SE9 2UG, United Kingdom
a r t i c l e
i n f o
Article history: Accepted 26 August 2008
Keywords: Drug calculations Assessments Clinical practice skills Numeracy
s u m m a r y The drug calculation skill of nurses continues to be a national concern. The continued concern has led to the introduction of mandatory drug calculation skills tests which students must pass in order to go on to the nursing register. However, there is little evidence to demonstrate that nurses are poor at solving drug calculation in practice. This paper argues that nurse educationalists have inadvertently created a problem that arguably does not exist in practice through use of invalid written drug assessment tests and have introduced their own pedagogical practice of solving written drug calculations. This paper will draw on literature across mathematics, philosophy, psychology and nurse education to demonstrate why written drug assessments are invalid, why learning must take place predominantly in the clinical area and why the key focus on numeracy and formal mathematical skills as essential knowledge for nurses is potentially unnecessary. Crown Copyright Ó 2009 Published by Elsevier Ltd. All rights reserved.
In nurse education at present we have a problem. Nurses have poor drug calculation skills. We know this because research has demonstrated that nurses perform poorly on drug calculation tests with studies implying that nurses are making between 10% and 20% errors in their practice (Kapborg, 1994; Hutton, 1998; Weeks et al., 2000; Wilson, 2003; Wright, 2004, 2005). These studies, along with high profile media cases, have led to increasing concern regarding this key nursing skill (Daily Mail, 2006; The Telegraph, 2006). In the United Kingdom (UK) the Department of Health have released guidance regarding drug errors in practice and recommended increased focus on nurses’ drug calculation skills education (DH, 2004) and the UK’s Nursing and Midwifery Council (NMC) have responded by making competency at drug calculations a key requirement before student nurses can register as a qualified nurse (NMC, 2007). The NMC has stipulated that all student nurses must pass an assessment of their drug calculation skills competency before qualifying and have further endorsed the increasingly popular practice of potential student nurses being required to pass a numeracy test before being accepted onto pre registration nursing programmes. With these changes it is hoped that nurses will qualify with better calculation skills and we will no longer have this particular problem in nurse education. But are drug calculation skills of nurses really a problem? The Department of Health paper was responding to the drug error rate in hospitals and the huge financial burden this was placing on the National Health Service (NHS) with 25% of its litigation bill due to * Tel.: +44 (0) 20 8331 8965. E-mail address: [email protected]
cases involving drug errors (DH, 2000). Most research into drug errors accepts that reducing drug error rates needs to be a whole system approach and study the complexity of the drug administration system in particular in hospitals and possible amendments to vulnerable points in these systems. The system from prescribing, to eventual administration of the drug to a patient is complex and involves doctors, pharmacists and nurses at different stages. The calculation to determine the dosage to administer to the patient is usually the final step in this system. The majority of drug errors are as a result of prescribing errors by doctors, many in connection with prescribing wrong dosages due to incorrect interpretation of blood results and therapeutic needs (Bates, 1999; Kaushal et al., 2001; Winterstein et al., 2004). In all of the large drug error studies undertaken there has never been a category for wrong calculation during administration of the drug (Bates, 1999; Santell et al., 2003; Winterstein et al., 2004). The closest category is usually wrong dosage administered. The fact that there is not a separate category for calculation errors suggests to me that this is not a significant cause of drug error in practice. Many of the large drug error studies used self reporting as a data collection method to ascertain drug errors. Clearly, self report has obvious limitations. One of the arguments relating to nurse’s drug calculation skills is that nurses are not aware that they are making the errors and are oblivious to their poor practice. This skill deficit is only picked up and prevented by nurse educationalists when nurses attend study days or through Trust drug calculation tests, thereby preventing patient’s lives being put at further risk. Some studies have used an observation method and focussed on the nurses’ administration of medication alone. These studies have
0260-6917/$ - see front matter Crown Copyright Ó 2009 Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.nedt.2008.08.019
K. Wright / Nurse Education Today 29 (2009) 544–548
observed nurses administering intravenous medication and fluids in the hospital ward (Ho et al., 1997; Taxis and Barber, 2003; Han et al., 2005). Taxis and Barber was a well published study with calculation errors observed in 1 in 10 medications administered. However, when this study and others similar to this are examined the definition of calculation error is found to include infusions where nurses have used their clinical judgement to alter the rate of the infusion or intravenous injections that are administered too quickly (Ho et al., 1997; Han et al., 2005). The calculation errors in these studies refer to the nurses’ medication administration practice as opposed to their actual calculation ability. If nurses’ drug calculation skills really were a problem then we would expect studies observing and studying the causes of drug errors to indicate that a large number of drug errors are attributable to calculation errors. This is not the case. Even without these studies in clinical practice, however, other research studies have indicated that nurses make between 10% and 20% errors on written drug assessments and the assumption is made that they would be making similar numbers of errors in their practice. But where are these errors? You would expect that if up to a fifth of all nurses’ calculations are incorrect then there would be some implications for practice and patients’ health. The fact that there are not calculation errors being reported, observed or causing harm to patients on a significant scale places doubt on the assumption that the current changes in pre registration education and selection are based. Nurses are not poor at calculating drug dosages. We have, however, still got a problem in nurse education. The problem is not really that nurses have poor calculation skills where the solution would be to focus on the education of student nurses by nurse educationalists. Rather, the problem is the method of assessment that we use to assess competency in this skill (Wright, 2007). Most research studies looking at drug calculation skills of nurses or student nurses use written drug calculation assessments as their measure of skill (Kapborg, 1994; Hutton, 1998; Weeks et al., 2000; Wilson, 2003; Wright, 2004, 2005). Nurses who perform poorly on the written tests are assumed to have poor skills in practice. But if studies using written tests demonstrate poor skills, yet there is little evidence of this in the practice setting, this does point to the invalidity of written drug calculation tests. The written drug assessments do not represent the reality of practice and are therefore not a valid measure of drug calculation skills in practice. This is not a new phenomenon and the differences between practice and formal tests have been studied by various psychological researchers in relation to mathematical knowledge and situated cognition. Studies have looked at the skills of different unschooled adults in the workplace, for example foremen (Nunes et al., 1986), fishermen (Schliemann and Nunes, 1990), carpenters (Schliemann, 1984), farmers (Grando, 1988 in Nunes et al., 1993) and shoppers (Lave and Wenger, 1991) and examined their mathematical skills displayed during their everyday practice and then tested in formal tests. In all studies the participants demonstrated complex mathematical skills in practice and scored much higher on these tests compared to the formal tests. The difference between formal and ‘everyday’ mathematics is complex, but is thought to involve, amongst other things, the social practice of the community, the meaning and solution of the problem and the physical setting and artefacts. Drug calculations do not take place in isolation from nursing practice. A calculation is ‘dilemma driven’ (Lave, 1992, p. 80), it is a means to determine a correct dosage to administer to a specific patient for a specific reason or outcome; be it reducing pain, correction of chemical imbalances or eradication of a bacterial infection. The calculation is one small part of the administration process. In order to gain the required patient outcome the nurse is required to use the prescribed medication alongside information about the patient, for example weight, have they got a cannula
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in situ, are they able to swallow? In addition, nurses use their pharmacology knowledge by appraising the dosage required, whether this is appropriate, using the standard medication available in the practice unit, e.g. ampoules, tablets. Using all this knowledge and information the nurse determines the appropriateness of the prescription and the problem that requires solving. For example, if Jay is vomiting and requires 50 mg cyclizine intravenously, the nurse will need to check that Jay has a patent IV line, the prescription chart to see what is prescribed, that Jay agrees to the injection, the stock ampoules available and then determine the problem. If the ampoules in this case were 100 mg/2 ml then the problem is Jay requires 50 mg and the ampoules are 100 mg/2 ml, so how many millilitres would give 50 mg? Asking the problem alone takes it from its social context and possibly removes cues which nurses rely on to conceptualise, visualise and solve the problem. In a practice setting the nurse has a number of tools and artefacts such as the prescription chart, ampoules and syringes or other measuring devices which are used to help solve the problem (Pozzi et al., 1998). In addition it is recognised that the use of cues, practice environment and other people are often so integrally woven that it is difficult to separate out the influence of each to the process (Rogoff and Lave, 1984). For this reason purely ensuring nurses have access to syringes, ampoules and prescription charts while solving written drug assessments will not ensure that the test is completely valid. Some nurses use the ampoule or syringe as a cue to be able to visualise the problem. For example, some student nurses I teach have actually sat and shut their eyes so they can visualise what the written question is asking them. This would not be necessary if they were in clinical practice with the problem and equipment visible in front of them. Some nurses also use the syringe to calculate the dosage required. Using the example previously the measurements on the side of the syringe could be used to see that 2 ml gives 100 mg, so half of that would be 1 ml to give 50 mg. This is an example of ‘whole person enactment’ ( Lave, 1992) where the nurse can physically engage in an activity that helps to quantify and solve the problem. Another example of this is if you were required to administer 50,000 units heparin in a 50 ml infusion over 24 h. If the ampoules were 25,000 units/ml you would draw up two ampoules into your 50 ml syringe and then draw up sodium chloride until you had 50 ml. You would not calculate that you would need to draw up 48 ml to make 50 ml you would enact this using the syringe. Therefore written test questions asking how much sodium chloride you would use to make up to 50 ml are irrelevant as nurses would not actually calculate this in practice. One of the common difficulties with written drug assessment tests is that the questions do not always relate to the reality of what nurses are asked to do in practice. In the studies with fisherman they also had difficulties with questions posed which were not found in their everyday practice (Schliemann and Nunes, 1990). For example in my university we have a 10 item intravenous (IV) additive test in which nurses must achieved 100% before NHS Trusts will allow nurses to administer IV medications in practice. Some of these questions ask nurses to solve problems which they would not be required to do in practice. For example how many grams of glucose would be in a 1000 ml infusion bag of 5% glucose? If you had a 1 ml ampoule of adrenaline of 1:1000 how many millilitres would you draw up to administer 0.01 g? How many micrograms are there in 0.128 g? The other common difficulty is that many institutions still ask that nurses complete the tests without using a calculator, which many nurses would normally use in practice. This again makes the written assessment unreal and invalid. For example a local hospital recently made all nurses and midwives complete a written drug assessment without using a calculator. One staff member who has been practising for 35 years and is nearing retirement has failed this test and is facing
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possible loss of her job if she is unable to pass the test. The test is being used as a valid representation of this staff member’s skill in practice. In nursing the social practice of administering medication is mainly oral and through reading. The drug and dosage required is read from the prescription chart and from the ampoule/tablet bottle. Written calculations remove the oral practice from the calculation and reproduce the practice setting in an unfamiliar written form. There is a variety of written questions used by institutions. On the one extreme are questions which involve only numbers and mathematical symbols such as 500 4 =?, or those which have minimal contextual information such as you need to give 120 mg of a drug, the tablets are 60 mg how many would you administer?, to more elaborate problems which attempt to contextualise the whole practice of drug administration by describing the patient being in pain, the analgesia prescribed and the walk to the drug cupboard, for example. With all of the problems they do not represent the reality of practice. Reading and interpreting a word problem is a skill in itself; to extract the correct information and interpret the scenario. Just as in clinical practice it is a skill to extract the required information to formulate the problem and how to solve it. A concept such as ‘draw up’ only has meaning through the interpretation of the reader through experience and the context of the sentence in which the word is found (Wittgenstein, 1939 in Dimond, 1976). For example, an architect can draw up plans for a new house or a nurse can draw up a drug to be administered. Similarly 500 has no meaning on its own except as a numerical figure. Five hundred only gains meaning when we put it in a sentence such as 500 mg tablets. Even then though, we rely on social practice knowledge of language to know that it does not mean 500 lots of milligram tablets, but 500 lots of milligram weight. I give these examples only to illustrate the complexities of written language and the necessity to interpret this before a solution to a problem can be found; a different skill from solving calculations in practice. Most teaching and learning strategies in relation to drug calculations use written tests in a pre and post test design to determine the effectiveness of strategies implemented (Hutton, 1998; Weeks et al., 2000; Wright, 2004, 2005; Rice and Bell, 2005). Significant increases to the scores on post test results usually result in the assumption that the teaching and learning strategy is effective at improving drug calculation skills. These strategies, however, only demonstrate that they are successful in increasing the skills of student nurses performing a written drug calculation test. There is no way of knowing whether the strategies improve drug calculation skills in practice. Unwittingly nurse educationalists are implementing teaching and learning strategies that create competent students at solving calculations presented in a written drug calculation assessment. Through didactic instruction we have created an unintended practice; the skill of solving written calculation problems. Evidence from this is apparent during the instruction of nursing students who become confused when ‘extra’ numbers are present in the written word problem, for example 0.9% sodium chloride and who then believe that I am trying to ‘trick’ them by including an extra number from those they have learnt to expect. Through our attempts to situate mathematics in the real world of practice we end up with ‘an artificial world created purely for pedagogical purposes’ (Brown, 2001, p. 257). In order to develop effective teaching and learning strategies which improve the drug calculation skills for nurses in practice we need to be able to talk about the practice of drug calculations from ‘within’ rather than ‘talking about calculation from the outside’ (Lave and Wenger, 1991, p. 109). This involves studying calculations from within the complexities of the social context in which they occur ( Brown, 2001; Ernest, 1991; Lave, 1992; Lave and Wenger, 1991; Pozzi et al., 1998).
Studies investigating formal mathematics found in a classroom and informal mathematics found in everyday life or ‘street mathematics’ have shown that adults will always keep their calculations close to the meaning of the problem they are solving (Schliemann and Nunes, 1990; Grandos, 1998 in Nunes et al., 1993). In order to do this the adults and children in the studies would choose a problem solving strategy which ensured the numbers were always close to the meaning rather than use formally taught strategies which could have offered a simpler route to a solution (Vergnaud, 1983; Nunes et al., 1993). This is similar to a study by Hoyles et al. (2001) which studied the mathematical skills of 12 paediatric nurses in practice. The study found that although the nurses often quoted the nursing formula ‘like a mantra’ as their method of solving drug calculations they did not in fact use this strategy, but similar strategies to the children and adults in Schliemann and Nunes (1990) studies. One of the most common drug calculations in practice involves proportional reasoning. Proportional problems occur when one variable varies in relation to another variable. There are three main types of proportional problems: isomorphism of measures, product of measures and multiple proportions ( Vergnaud, 1983). The simplest problem type which is found in drug calculation problems is the Isomorphism of measures. The isomorphism of measures consists of simple direct proportion between two variables. For example if one tablet is 125 mg then using proportional reasoning you can solve how many milligrams you would have if you had four tablets. Vergnaud identifies five strategies which can be correctly used to solve isomorphism of measure problems (Fig. 1). The formal method taught in school to solve these types of problems is known as the rule of three. The rule of three is also the same as the nursing formula which is commonly taught in nurse education. The rule of three gives a method of using the numbers of the variables in a formula, which can then be solved. For the nursing formula the variables are the amount of drug required by the patient, the amount of drug available in the ampoule and the volume that it is dissolved in. Nurses need only place the numbers in the formula and calculate the answer to arrive at the dosage to administer the patient. When Vergnaud studied the methods children used correctly to solve isomorphism of measures problem types he found that the most common approaches were the scalar strategies. This study was replicated by Schliemann and Nunes (1990) who studied fishermen and children and Hoyles et al. who studied nurses. Both of these additional studies also found that scalar methods were the most commonly used strategies by participants in the studies. The scalar approach focuses on the relationship between the variables being constant and uses this to manipulate both variables until the desired dosage or figure is ascertained. The scalar approaches are thought to be used most often as it always keeps the numbers close to their meaning. If we consider the nursing formula, once the required information is extracted from its context, nurses are left with a numerical problem involving multiplication of fractions. The numbers are stripped of their meaning. In addition we are also asking nurses to ignore previously learnt mathematical rules and ask them to multiply a weight by a volume and include decimals as fractions (Wright, 2008). Preliminary research exploring how nurses solve drug calculation in depth indicates that the nursing formula takes nurses cognitively further away from the meaning of the problem they are solving, especially if they are not allowed to use a calculator (Wright, in preparation) (see Fig. 2) . In contrast scalar approaches which were also common in my preliminary study manipulates the numbers within the context. For example if a patient was prescribed 0.6 mcg/kg and weighed 15 kg and the ampoules available are 10 mcg/1 ml the nurse would first need to solve 0.6 mcg for every 1 kg so how many mcg for 15 kg. This could be done on a calculator, multiplying 0.6 by 15
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K. Wright / Nurse Education Today 29 (2009) 544–548
Strategy
Solution example
Functional Operator
÷ 10 50mg
5ml ÷ 10
125 mg Scalar Operator
12.5ml X2.5
50 mg
125mg X2.5
5ml
12.5ml
Unitary Method (variant of scalar)
÷ 50
X125
50mg
1mg ÷ 50
5ml Scalar Decomposition
125mg X125
0.1mg
12.5ml
50mg +50mg +½ (50mg) = 125mg 5ml+5ml+½ (5ml) = 12.5ml
Rule of three
125 = 50 = 125 x 2 = 12.5ml
×
5
50
Fig. 1. Clinical example. A patient requires 125 mg of a drug. The elixir available is 50 mg/5 ml.
Fig. 2. Diagrammatic representation of strategies in relation to cognitive distance from context and meaning.
or multiplying 0.6 by 10 kg and 0.6 by 5 kg and added to give 9 mcg. If 10 mcg is in every 1 ml then how many millilitres would give 9 mcg? The answer could be worked out using one of the scalar approaches by dividing both by 10 to get 1 mcg in 0.1 ml and then multiplying by 9 to get 9 mcg in 0.9 ml. At no point did the numbers ever become devoid of their meaning. In addition this scalar approach did not use any formal mathematical operations such as long division or multiplication of fractions which the NMC has recently advocated is included in the nursing curriculum and numeracy tests (NMC, 2008). The scalar approach is commonly used by adults and nurses in their practice to solve proportional problems, and is actively sought as a solution even when other approaches would be quicker to use in order to keep the numbers close to the meaning and context. Yet nurse educationalists persist
in teaching the nursing formula as the key method for solving proportional problems. This demonstrates that we are not within the practice of drug calculations, but are on the outside looking in; placing our own interpretations on how to solve calculations and using this to teach and assess drug calculations. In nurse education we have created a problem that potentially does not exist in practice. Written drug calculation assessments used in research demonstrate poor skills that are not found in clinical practice. In creating the problem we have spent a great deal of time and effort in seeking effective solutions to this problem. However, our solutions are meaningless. We have unwittingly created an unintended practice and skill; that of solving written drug calculation assessments. There is no problem with the drug calculation skills of nurses; the problem is with the way that we assess
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this skill. Drug calculations need to be examined and studied in clinical practice where it is immersed in the social practice of nursing and is relevant and meaningful. Until we examine how nurses become competent in practice we cannot devise effective teaching and learning strategies to support and facilitate student nurses to learn this skill. As a starting point though, literature from psychology, education and philosophy points towards student nurses needing to learn calculations in clinical practice environments with real problems. Only then will they be able to participate in drug administration practice, learn the social language of nursing and gain the meaning and context required to understand the numbers in the calculation problems and how to solve. References Bates, D., 1999. Frequency, consequences and prevention in adverse drug events. Journal of Quality Clinical Practice 19, 13–17. Brown, T., 2001. Mathematics Education and Language. Interpreting Hermeneutics and Post Structuralism, second ed. Kluwer Academic Publishers. Hall, C., 2006. A third of new nurses fail simple English and Maths test. The Telegraph 5th August 2006. (accessed 22.04.08). Department of Health, 2000. An Organisation with a Memory, Report of an Expert Group on Learning from Adverse Events in the NHS. Stationary Office, London. Department of Health, 2004. Building a Safer NHS for Patients: Improving Medication Safety. DoH, London. Dimond, C., 1976. Wittgenstein’s Lectures on the Foundations of Mathematics Cambridge 1936. The Harvester Press Limited. Ernest, P., 1991. The Philosophy of Mathematics Education. The Falmer Press, London. Han, P., Combes, I., Green, B., 2005. Factors predictive of intravneous fluid administration errors in Austrian surgical care wards. Quality and Safety in Health Care 14, 179–184. Ho, C., Dean, B., Barber, N., 1997. When do medication administration errors happen to hospital inpatients. The International Journal of Pharmacy Practice 5, 91–96. Hoyles, C., Noss, R., Pozzi, S., 2001. Proportional reasoning in nursing practice. Journal for Research in Mathematics Education 32 (1), 4–27. Hutton, M., 1998. Nursing mathematics: the importance of application. Nursing Standard 13 (11), 35–38. Kapborg, I., 1994. Calculation and administration of drug dosage by swedish nurses, student nurses and physicians. International Journal for Quality in Health Care 6 (4), 389–395. Kaushal, R., Bates, D., Landrigan, C., McKenna, K., Clapp, M., Federico, F., Goldmann, D., 2001. Medication errors and adverse drug events in pediatric hospitals. Journal of the American Medication Association 285, 2114–2120. Lave, J., Wenger, E., 1991. Situated Learning Legitimate Peripheral Participation. Cambridge University Press, Cambridge.
Lave, J., 1992. Word problems: a microcosm of theories of learning. In: Light, P., Butterworth, G. (Eds.), Context and Cognition Ways of Learning and Knowing. Lawrence Erlbaum Associates, pp. 74–92. Nunes, T., Schliemann, A., Carraher, D., 1993. Street Mathematics and School Mathematics. Cambridge University Press. Nunes, T., Schliemann, A., Carraher, D., 1986. From drawings to buildings. International Journal of Behavioural Development 9, 527–544. Nursing and Midwifery Council, 2007. Guidance for the introduction of the essential skills clusters for pre-registration nursing programmes. NMC Circular. (accessed 21.06.07). Nursing and Midwifery Council, 2008. Evidence of literacy and numeracy required for entry to pre-registration nursing and midwifery programmes. NMC Circular. (accessed 01.05.08). Pozzi, S., Noss, R., Hoyles, C., 1998. Tools in practice, mathematics in use. Educational Studies in Mathematics 36, 105–122. Rice, J., Bell, M., 2005. Using dimensional analysis to improve drug dosage calculation ability. Journal of Nursing Education 44 (7), 315–318. Rogoff, B., Lave, J., 1984. Everyday Cognition. Harvard University Press. Santell, J., Hicks, R., McMeekin, J., Cousins, D., 2003. Medication errors: experience of the United States pharmacopeia (USP) MEDMARK Reporting System. Journal of Clinical Pharmacology 43, 760–767. Schliemann, A., Nunes, T., 1990. A situated schema of proportionality. British Journal of Developmental Psychology 8, 259–268. Schliemann, A., 1984. Mathematics among carpenters and apprentices. In: Damerow, P., Dunckley, M., Nebres, B.,Werry, B. (Eds.), Mathematics for all UNESCO, pp. 92–95. Taxis, K., Barber, N., 2003. Ethnographic study of incidence and severity of intravenous drug errors. British Medical Journal 326, 684–688. The Daily Mail, 2006. Parents blame ‘devastating failures’ for baby’s death. The Daily Mail Newspaper. (accessed 22.04.08). Vergnaud, G., 1983. Multiplicative structures. In: Lesh, R., Landau, M. (Eds.), Acquisition of Mathematics Concepts and Processes. Academic Press, pp. 127– 174. Weeks, K., Lynne, P., Torrance, C., 2000. Written drug dosage errors made by students: the threat to clinical effectiveness and the need for a new approach. Clinical Effectiveness in Nursing 4, 20–29. Wilson, A., 2003. Nurses maths: researching a practical approach. Nursing Standard 17 (47), 33–36. Winterstein, A., Johns, T., Rosenberg, E., Hatton, R., Gonzalez-Rothi, R., Kanjanarat, P., 2004. Nature and causes of clinically significant medication errors in a tertiary care hospital. American Journal Health – System Pharm 61, 1908–1916. Wright, K., 2004. Investigation to find strategies to improve student nurses’ maths skills. British Journal of Nursing 13 (21), 1280–1287. Wright, K., 2005. An exploration into the most effective way to teach drug calculation skills to nursing students. Nurse Education Today 25, 430–436. Wright, K., 2007. A written assessment is an invalid test of numeracy skills. British Journal of Nursing 16 (13), 828–831. Wright, K., 2008. Drug calculations part 1: a critique of the formula. Nursing Standard 22 (36), 40–42.
Contents lists available at ScienceDirect
Nurse Education Today journal homepage: www.elsevier.com/nedt
The assessment and development of drug calculation skills in nurse education – A critical debate Kerri Wright * University of Greenwich, Avery Hill Road, Eltham, London SE9 2UG, United Kingdom
a r t i c l e
i n f o
Article history: Accepted 26 August 2008
Keywords: Drug calculations Assessments Clinical practice skills Numeracy
s u m m a r y The drug calculation skill of nurses continues to be a national concern. The continued concern has led to the introduction of mandatory drug calculation skills tests which students must pass in order to go on to the nursing register. However, there is little evidence to demonstrate that nurses are poor at solving drug calculation in practice. This paper argues that nurse educationalists have inadvertently created a problem that arguably does not exist in practice through use of invalid written drug assessment tests and have introduced their own pedagogical practice of solving written drug calculations. This paper will draw on literature across mathematics, philosophy, psychology and nurse education to demonstrate why written drug assessments are invalid, why learning must take place predominantly in the clinical area and why the key focus on numeracy and formal mathematical skills as essential knowledge for nurses is potentially unnecessary. Crown Copyright Ó 2009 Published by Elsevier Ltd. All rights reserved.
In nurse education at present we have a problem. Nurses have poor drug calculation skills. We know this because research has demonstrated that nurses perform poorly on drug calculation tests with studies implying that nurses are making between 10% and 20% errors in their practice (Kapborg, 1994; Hutton, 1998; Weeks et al., 2000; Wilson, 2003; Wright, 2004, 2005). These studies, along with high profile media cases, have led to increasing concern regarding this key nursing skill (Daily Mail, 2006; The Telegraph, 2006). In the United Kingdom (UK) the Department of Health have released guidance regarding drug errors in practice and recommended increased focus on nurses’ drug calculation skills education (DH, 2004) and the UK’s Nursing and Midwifery Council (NMC) have responded by making competency at drug calculations a key requirement before student nurses can register as a qualified nurse (NMC, 2007). The NMC has stipulated that all student nurses must pass an assessment of their drug calculation skills competency before qualifying and have further endorsed the increasingly popular practice of potential student nurses being required to pass a numeracy test before being accepted onto pre registration nursing programmes. With these changes it is hoped that nurses will qualify with better calculation skills and we will no longer have this particular problem in nurse education. But are drug calculation skills of nurses really a problem? The Department of Health paper was responding to the drug error rate in hospitals and the huge financial burden this was placing on the National Health Service (NHS) with 25% of its litigation bill due to * Tel.: +44 (0) 20 8331 8965. E-mail address: [email protected]
cases involving drug errors (DH, 2000). Most research into drug errors accepts that reducing drug error rates needs to be a whole system approach and study the complexity of the drug administration system in particular in hospitals and possible amendments to vulnerable points in these systems. The system from prescribing, to eventual administration of the drug to a patient is complex and involves doctors, pharmacists and nurses at different stages. The calculation to determine the dosage to administer to the patient is usually the final step in this system. The majority of drug errors are as a result of prescribing errors by doctors, many in connection with prescribing wrong dosages due to incorrect interpretation of blood results and therapeutic needs (Bates, 1999; Kaushal et al., 2001; Winterstein et al., 2004). In all of the large drug error studies undertaken there has never been a category for wrong calculation during administration of the drug (Bates, 1999; Santell et al., 2003; Winterstein et al., 2004). The closest category is usually wrong dosage administered. The fact that there is not a separate category for calculation errors suggests to me that this is not a significant cause of drug error in practice. Many of the large drug error studies used self reporting as a data collection method to ascertain drug errors. Clearly, self report has obvious limitations. One of the arguments relating to nurse’s drug calculation skills is that nurses are not aware that they are making the errors and are oblivious to their poor practice. This skill deficit is only picked up and prevented by nurse educationalists when nurses attend study days or through Trust drug calculation tests, thereby preventing patient’s lives being put at further risk. Some studies have used an observation method and focussed on the nurses’ administration of medication alone. These studies have
0260-6917/$ - see front matter Crown Copyright Ó 2009 Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.nedt.2008.08.019
K. Wright / Nurse Education Today 29 (2009) 544–548
observed nurses administering intravenous medication and fluids in the hospital ward (Ho et al., 1997; Taxis and Barber, 2003; Han et al., 2005). Taxis and Barber was a well published study with calculation errors observed in 1 in 10 medications administered. However, when this study and others similar to this are examined the definition of calculation error is found to include infusions where nurses have used their clinical judgement to alter the rate of the infusion or intravenous injections that are administered too quickly (Ho et al., 1997; Han et al., 2005). The calculation errors in these studies refer to the nurses’ medication administration practice as opposed to their actual calculation ability. If nurses’ drug calculation skills really were a problem then we would expect studies observing and studying the causes of drug errors to indicate that a large number of drug errors are attributable to calculation errors. This is not the case. Even without these studies in clinical practice, however, other research studies have indicated that nurses make between 10% and 20% errors on written drug assessments and the assumption is made that they would be making similar numbers of errors in their practice. But where are these errors? You would expect that if up to a fifth of all nurses’ calculations are incorrect then there would be some implications for practice and patients’ health. The fact that there are not calculation errors being reported, observed or causing harm to patients on a significant scale places doubt on the assumption that the current changes in pre registration education and selection are based. Nurses are not poor at calculating drug dosages. We have, however, still got a problem in nurse education. The problem is not really that nurses have poor calculation skills where the solution would be to focus on the education of student nurses by nurse educationalists. Rather, the problem is the method of assessment that we use to assess competency in this skill (Wright, 2007). Most research studies looking at drug calculation skills of nurses or student nurses use written drug calculation assessments as their measure of skill (Kapborg, 1994; Hutton, 1998; Weeks et al., 2000; Wilson, 2003; Wright, 2004, 2005). Nurses who perform poorly on the written tests are assumed to have poor skills in practice. But if studies using written tests demonstrate poor skills, yet there is little evidence of this in the practice setting, this does point to the invalidity of written drug calculation tests. The written drug assessments do not represent the reality of practice and are therefore not a valid measure of drug calculation skills in practice. This is not a new phenomenon and the differences between practice and formal tests have been studied by various psychological researchers in relation to mathematical knowledge and situated cognition. Studies have looked at the skills of different unschooled adults in the workplace, for example foremen (Nunes et al., 1986), fishermen (Schliemann and Nunes, 1990), carpenters (Schliemann, 1984), farmers (Grando, 1988 in Nunes et al., 1993) and shoppers (Lave and Wenger, 1991) and examined their mathematical skills displayed during their everyday practice and then tested in formal tests. In all studies the participants demonstrated complex mathematical skills in practice and scored much higher on these tests compared to the formal tests. The difference between formal and ‘everyday’ mathematics is complex, but is thought to involve, amongst other things, the social practice of the community, the meaning and solution of the problem and the physical setting and artefacts. Drug calculations do not take place in isolation from nursing practice. A calculation is ‘dilemma driven’ (Lave, 1992, p. 80), it is a means to determine a correct dosage to administer to a specific patient for a specific reason or outcome; be it reducing pain, correction of chemical imbalances or eradication of a bacterial infection. The calculation is one small part of the administration process. In order to gain the required patient outcome the nurse is required to use the prescribed medication alongside information about the patient, for example weight, have they got a cannula
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in situ, are they able to swallow? In addition, nurses use their pharmacology knowledge by appraising the dosage required, whether this is appropriate, using the standard medication available in the practice unit, e.g. ampoules, tablets. Using all this knowledge and information the nurse determines the appropriateness of the prescription and the problem that requires solving. For example, if Jay is vomiting and requires 50 mg cyclizine intravenously, the nurse will need to check that Jay has a patent IV line, the prescription chart to see what is prescribed, that Jay agrees to the injection, the stock ampoules available and then determine the problem. If the ampoules in this case were 100 mg/2 ml then the problem is Jay requires 50 mg and the ampoules are 100 mg/2 ml, so how many millilitres would give 50 mg? Asking the problem alone takes it from its social context and possibly removes cues which nurses rely on to conceptualise, visualise and solve the problem. In a practice setting the nurse has a number of tools and artefacts such as the prescription chart, ampoules and syringes or other measuring devices which are used to help solve the problem (Pozzi et al., 1998). In addition it is recognised that the use of cues, practice environment and other people are often so integrally woven that it is difficult to separate out the influence of each to the process (Rogoff and Lave, 1984). For this reason purely ensuring nurses have access to syringes, ampoules and prescription charts while solving written drug assessments will not ensure that the test is completely valid. Some nurses use the ampoule or syringe as a cue to be able to visualise the problem. For example, some student nurses I teach have actually sat and shut their eyes so they can visualise what the written question is asking them. This would not be necessary if they were in clinical practice with the problem and equipment visible in front of them. Some nurses also use the syringe to calculate the dosage required. Using the example previously the measurements on the side of the syringe could be used to see that 2 ml gives 100 mg, so half of that would be 1 ml to give 50 mg. This is an example of ‘whole person enactment’ ( Lave, 1992) where the nurse can physically engage in an activity that helps to quantify and solve the problem. Another example of this is if you were required to administer 50,000 units heparin in a 50 ml infusion over 24 h. If the ampoules were 25,000 units/ml you would draw up two ampoules into your 50 ml syringe and then draw up sodium chloride until you had 50 ml. You would not calculate that you would need to draw up 48 ml to make 50 ml you would enact this using the syringe. Therefore written test questions asking how much sodium chloride you would use to make up to 50 ml are irrelevant as nurses would not actually calculate this in practice. One of the common difficulties with written drug assessment tests is that the questions do not always relate to the reality of what nurses are asked to do in practice. In the studies with fisherman they also had difficulties with questions posed which were not found in their everyday practice (Schliemann and Nunes, 1990). For example in my university we have a 10 item intravenous (IV) additive test in which nurses must achieved 100% before NHS Trusts will allow nurses to administer IV medications in practice. Some of these questions ask nurses to solve problems which they would not be required to do in practice. For example how many grams of glucose would be in a 1000 ml infusion bag of 5% glucose? If you had a 1 ml ampoule of adrenaline of 1:1000 how many millilitres would you draw up to administer 0.01 g? How many micrograms are there in 0.128 g? The other common difficulty is that many institutions still ask that nurses complete the tests without using a calculator, which many nurses would normally use in practice. This again makes the written assessment unreal and invalid. For example a local hospital recently made all nurses and midwives complete a written drug assessment without using a calculator. One staff member who has been practising for 35 years and is nearing retirement has failed this test and is facing
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possible loss of her job if she is unable to pass the test. The test is being used as a valid representation of this staff member’s skill in practice. In nursing the social practice of administering medication is mainly oral and through reading. The drug and dosage required is read from the prescription chart and from the ampoule/tablet bottle. Written calculations remove the oral practice from the calculation and reproduce the practice setting in an unfamiliar written form. There is a variety of written questions used by institutions. On the one extreme are questions which involve only numbers and mathematical symbols such as 500 4 =?, or those which have minimal contextual information such as you need to give 120 mg of a drug, the tablets are 60 mg how many would you administer?, to more elaborate problems which attempt to contextualise the whole practice of drug administration by describing the patient being in pain, the analgesia prescribed and the walk to the drug cupboard, for example. With all of the problems they do not represent the reality of practice. Reading and interpreting a word problem is a skill in itself; to extract the correct information and interpret the scenario. Just as in clinical practice it is a skill to extract the required information to formulate the problem and how to solve it. A concept such as ‘draw up’ only has meaning through the interpretation of the reader through experience and the context of the sentence in which the word is found (Wittgenstein, 1939 in Dimond, 1976). For example, an architect can draw up plans for a new house or a nurse can draw up a drug to be administered. Similarly 500 has no meaning on its own except as a numerical figure. Five hundred only gains meaning when we put it in a sentence such as 500 mg tablets. Even then though, we rely on social practice knowledge of language to know that it does not mean 500 lots of milligram tablets, but 500 lots of milligram weight. I give these examples only to illustrate the complexities of written language and the necessity to interpret this before a solution to a problem can be found; a different skill from solving calculations in practice. Most teaching and learning strategies in relation to drug calculations use written tests in a pre and post test design to determine the effectiveness of strategies implemented (Hutton, 1998; Weeks et al., 2000; Wright, 2004, 2005; Rice and Bell, 2005). Significant increases to the scores on post test results usually result in the assumption that the teaching and learning strategy is effective at improving drug calculation skills. These strategies, however, only demonstrate that they are successful in increasing the skills of student nurses performing a written drug calculation test. There is no way of knowing whether the strategies improve drug calculation skills in practice. Unwittingly nurse educationalists are implementing teaching and learning strategies that create competent students at solving calculations presented in a written drug calculation assessment. Through didactic instruction we have created an unintended practice; the skill of solving written calculation problems. Evidence from this is apparent during the instruction of nursing students who become confused when ‘extra’ numbers are present in the written word problem, for example 0.9% sodium chloride and who then believe that I am trying to ‘trick’ them by including an extra number from those they have learnt to expect. Through our attempts to situate mathematics in the real world of practice we end up with ‘an artificial world created purely for pedagogical purposes’ (Brown, 2001, p. 257). In order to develop effective teaching and learning strategies which improve the drug calculation skills for nurses in practice we need to be able to talk about the practice of drug calculations from ‘within’ rather than ‘talking about calculation from the outside’ (Lave and Wenger, 1991, p. 109). This involves studying calculations from within the complexities of the social context in which they occur ( Brown, 2001; Ernest, 1991; Lave, 1992; Lave and Wenger, 1991; Pozzi et al., 1998).
Studies investigating formal mathematics found in a classroom and informal mathematics found in everyday life or ‘street mathematics’ have shown that adults will always keep their calculations close to the meaning of the problem they are solving (Schliemann and Nunes, 1990; Grandos, 1998 in Nunes et al., 1993). In order to do this the adults and children in the studies would choose a problem solving strategy which ensured the numbers were always close to the meaning rather than use formally taught strategies which could have offered a simpler route to a solution (Vergnaud, 1983; Nunes et al., 1993). This is similar to a study by Hoyles et al. (2001) which studied the mathematical skills of 12 paediatric nurses in practice. The study found that although the nurses often quoted the nursing formula ‘like a mantra’ as their method of solving drug calculations they did not in fact use this strategy, but similar strategies to the children and adults in Schliemann and Nunes (1990) studies. One of the most common drug calculations in practice involves proportional reasoning. Proportional problems occur when one variable varies in relation to another variable. There are three main types of proportional problems: isomorphism of measures, product of measures and multiple proportions ( Vergnaud, 1983). The simplest problem type which is found in drug calculation problems is the Isomorphism of measures. The isomorphism of measures consists of simple direct proportion between two variables. For example if one tablet is 125 mg then using proportional reasoning you can solve how many milligrams you would have if you had four tablets. Vergnaud identifies five strategies which can be correctly used to solve isomorphism of measure problems (Fig. 1). The formal method taught in school to solve these types of problems is known as the rule of three. The rule of three is also the same as the nursing formula which is commonly taught in nurse education. The rule of three gives a method of using the numbers of the variables in a formula, which can then be solved. For the nursing formula the variables are the amount of drug required by the patient, the amount of drug available in the ampoule and the volume that it is dissolved in. Nurses need only place the numbers in the formula and calculate the answer to arrive at the dosage to administer the patient. When Vergnaud studied the methods children used correctly to solve isomorphism of measures problem types he found that the most common approaches were the scalar strategies. This study was replicated by Schliemann and Nunes (1990) who studied fishermen and children and Hoyles et al. who studied nurses. Both of these additional studies also found that scalar methods were the most commonly used strategies by participants in the studies. The scalar approach focuses on the relationship between the variables being constant and uses this to manipulate both variables until the desired dosage or figure is ascertained. The scalar approaches are thought to be used most often as it always keeps the numbers close to their meaning. If we consider the nursing formula, once the required information is extracted from its context, nurses are left with a numerical problem involving multiplication of fractions. The numbers are stripped of their meaning. In addition we are also asking nurses to ignore previously learnt mathematical rules and ask them to multiply a weight by a volume and include decimals as fractions (Wright, 2008). Preliminary research exploring how nurses solve drug calculation in depth indicates that the nursing formula takes nurses cognitively further away from the meaning of the problem they are solving, especially if they are not allowed to use a calculator (Wright, in preparation) (see Fig. 2) . In contrast scalar approaches which were also common in my preliminary study manipulates the numbers within the context. For example if a patient was prescribed 0.6 mcg/kg and weighed 15 kg and the ampoules available are 10 mcg/1 ml the nurse would first need to solve 0.6 mcg for every 1 kg so how many mcg for 15 kg. This could be done on a calculator, multiplying 0.6 by 15
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Strategy
Solution example
Functional Operator
÷ 10 50mg
5ml ÷ 10
125 mg Scalar Operator
12.5ml X2.5
50 mg
125mg X2.5
5ml
12.5ml
Unitary Method (variant of scalar)
÷ 50
X125
50mg
1mg ÷ 50
5ml Scalar Decomposition
125mg X125
0.1mg
12.5ml
50mg +50mg +½ (50mg) = 125mg 5ml+5ml+½ (5ml) = 12.5ml
Rule of three
125 = 50 = 125 x 2 = 12.5ml
×
5
50
Fig. 1. Clinical example. A patient requires 125 mg of a drug. The elixir available is 50 mg/5 ml.
Fig. 2. Diagrammatic representation of strategies in relation to cognitive distance from context and meaning.
or multiplying 0.6 by 10 kg and 0.6 by 5 kg and added to give 9 mcg. If 10 mcg is in every 1 ml then how many millilitres would give 9 mcg? The answer could be worked out using one of the scalar approaches by dividing both by 10 to get 1 mcg in 0.1 ml and then multiplying by 9 to get 9 mcg in 0.9 ml. At no point did the numbers ever become devoid of their meaning. In addition this scalar approach did not use any formal mathematical operations such as long division or multiplication of fractions which the NMC has recently advocated is included in the nursing curriculum and numeracy tests (NMC, 2008). The scalar approach is commonly used by adults and nurses in their practice to solve proportional problems, and is actively sought as a solution even when other approaches would be quicker to use in order to keep the numbers close to the meaning and context. Yet nurse educationalists persist
in teaching the nursing formula as the key method for solving proportional problems. This demonstrates that we are not within the practice of drug calculations, but are on the outside looking in; placing our own interpretations on how to solve calculations and using this to teach and assess drug calculations. In nurse education we have created a problem that potentially does not exist in practice. Written drug calculation assessments used in research demonstrate poor skills that are not found in clinical practice. In creating the problem we have spent a great deal of time and effort in seeking effective solutions to this problem. However, our solutions are meaningless. We have unwittingly created an unintended practice and skill; that of solving written drug calculation assessments. There is no problem with the drug calculation skills of nurses; the problem is with the way that we assess
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this skill. Drug calculations need to be examined and studied in clinical practice where it is immersed in the social practice of nursing and is relevant and meaningful. Until we examine how nurses become competent in practice we cannot devise effective teaching and learning strategies to support and facilitate student nurses to learn this skill. As a starting point though, literature from psychology, education and philosophy points towards student nurses needing to learn calculations in clinical practice environments with real problems. Only then will they be able to participate in drug administration practice, learn the social language of nursing and gain the meaning and context required to understand the numbers in the calculation problems and how to solve. References Bates, D., 1999. Frequency, consequences and prevention in adverse drug events. Journal of Quality Clinical Practice 19, 13–17. Brown, T., 2001. Mathematics Education and Language. Interpreting Hermeneutics and Post Structuralism, second ed. Kluwer Academic Publishers. Hall, C., 2006. A third of new nurses fail simple English and Maths test. The Telegraph 5th August 2006.
Lave, J., 1992. Word problems: a microcosm of theories of learning. In: Light, P., Butterworth, G. (Eds.), Context and Cognition Ways of Learning and Knowing. Lawrence Erlbaum Associates, pp. 74–92. Nunes, T., Schliemann, A., Carraher, D., 1993. Street Mathematics and School Mathematics. Cambridge University Press. Nunes, T., Schliemann, A., Carraher, D., 1986. From drawings to buildings. International Journal of Behavioural Development 9, 527–544. Nursing and Midwifery Council, 2007. Guidance for the introduction of the essential skills clusters for pre-registration nursing programmes. NMC Circular.