Where do nursing students make mistakes when calculating drug doses? A retrospective study

Dosage calculation errors can have serious consequences when administering medicines, and hence numeracy skills are crucial for ensuring safe medication management [1]. A study by Ross et al. [2] in a pediatric teaching hospital found that 8% of medication incidents involved a tenfold error in the dose administered. More recently, a systematic review of intravenous admixture drug preparation errors found that the reported incidence of wrong doses across the studies reviewed ranged from 0 to 32.6%, while for wrong diluent volume the range was 0.06 to 49.0%. The authors highlighted the need in future research to develop standardized definitions for these types of errors so as to facilitate a better understanding of where they happen within the drug preparation process and to devise ways of avoiding them [3]. This underlines an issue raised by other authors, namely that it is difficult to know whether an error in the final dose administered is due solely or primarily to miscalculation, insofar as it may be the result of an error further back in the process, such as pharmacy mislabeling or incorrect or unclear prescribing [2].

Research focusing on nursing students suggests they often have poor drug calculation skills, due especially to difficulties with understanding mathematical principles [4]. Accordingly, although they are usually able to perform simple calculations, they struggle with tasks involving multiple steps and which require a higher level of conceptual knowledge [5]. A further issue concerns the extent to which nursing students are aware of their errors. In this regard, a recent study in which students were asked to indicate their level of certainty about answers given to a pharmacology knowledge questionnaire concluded that there was a high risk of medication administration error in 14% of the students who rated incorrect answers with high certainty [6].

Aside from their arithmetic skills, there are a number of other factors that may contribute to nursing students’ difficulties with dose calculation. One of these is math anxiety, which can undermine their ability to understand and complete tasks involving mathematics [7]. A fear of math, resulting in resistance to learning math for medication administration, has also been noted in research using focus groups to explore students’ own perspectives on learning math for medication calculation [8]. Other themes that emerged in the same study were: resentment among students towards what they perceive as ‘complicated’ math; lack of confidence among students leading to a fear of error in clinical practice; a recognition among students that they need to be more self-directed in developing their math skills; and the need for clinical instructors to be consistent in giving students the opportunity to practice calculations in the clinical setting [8].

Notwithstanding the difficulties that students experience with dose calculation, the literature suggests that the problem is far from unsurmountable. Indeed, various studies have reported the effectiveness of workshops or web-based platforms designed to support students’ learning and improve their medication calculation skills [9‐13].

Another issue to consider, and one highlighted in a recent comparative study of six European countries [5], concerns cross-national differences in medication education regulations and practices and the competences that graduating nurses are expected to have acquired. For instance, some professional bodies such as the UK Nursing & Midwifery Council recommend that nurse education institutions should require students to achieve a 100% pass on a health numeracy assessment including calculation of medicines [14]. In our country, Spain, a strict criterion such as this is not applied within nurse education programs, although safe medication management is considered a key competence for students to acquire during their pre-registration university training [15].

Whatever the requirements and approach to training, it is vital that nursing students acquire adequate numeracy skills, as once they enter professional practice they will be responsible for administering medication. The importance of their becoming proficient in this respect by the time they graduate is underlined by research suggesting that difficulties with drug calculation often persist among registered nurses [16‐18]. From the perspective of nurse education, therefore, it is crucial to identify where students struggle the most when it comes to dosage calculation. Despite this, few studies have examined in detail the specific aspects of the drug calculation process where students make mistakes [7, 19‐21].

Given that the dose calculation skills of both student and registered nurses is an issue of international concern, and one that has implications for patient safety, our aim in the present study was to conduct an in-depth analysis of the kinds of errors that undergraduate nursing students make when performing dose calculation exercises. Identifying the specific aspects or steps in the process they find most difficult would enable nurse educators to target teaching where it is most needed.

We reviewed 285 examination papers that included 1034 calculation exercises. After excluding those exercises that had been left blank (n = 171), a total of 863 exercises were analyzed. Table 2 shows the number of exercises reviewed and analyzed for each of the three course years.

Of the exercises analyzed, 455 (52.7%) were answered correctly. Table 3 shows the number of each type of exercise that were attempted and the number that were correct. Overall, a correct answer was given in 28.4% of the clinical case exercises in year 1, in 50.9% of the exercises in year 2 (mean score of 5.2 (SD 2.2) out of 10), and in 41.8% of those in year 3. The mean score across the three pediatric exercises in year 3 (final three rows in Table 3) was 4.6 (SD 3.2) out of 10.

Regarding the method used to solve the calculation problems (not including the 69 exercises corresponding to theoretical unit equivalences), in 67.1% (n = 533) of cases the student used the rule-of-three method, in 18.0% (n = 143) a conversion factor (i.e. a number for changing given units to desired units), and in 3.1% (n = 25) both these methods. In 93 exercises (11.7%), the student gave an answer directly without using either of these methods. Overall, 90% of the exercises analyzed were considered complete as the student indicated a final answer to the problem, although the result was only correct in 52.7% of cases.

This article presents a detailed analysis of the errors made by nursing undergraduates when performing written dose calculation exercises. The results add to existing evidence regarding the kinds of problems that nursing students have with calculation exercises [21]. Our analysis suggests that students’ overall level of calculation skills is limited, although they are generally able to perform basic dose calculations. The proportion of students who correctly answered the exercises set was slightly below that reported in some studies [19, 23, 24], but similar to that observed by Bagnasco et al. [4]. However, our results should be interpreted with caution as a small number of the year 2 exercises we analyzed included questions that went beyond the level of knowledge that students were expected to have at this point in their studies; as noted above in Method (sub-section Examination Papers Reviewed), these more difficult problems were deliberately included as a way of enabling us to track the progress of individual students in subsequent years of the degree program. If we omit these three questions from the analysis, the mean grade obtained by students on this exam increases from 5.2 (SD 2.2) to 6.3 (SD 2.5) out of 10, a figure consistent with pass rates reported in the aforementioned literature. Given that these year 2 students also have two more years of their degree ahead of them, it would obviously be interesting to follow them up and compare their level of achievement on the same kinds of dose calculation problems in years 3 and 4, thus providing an indication of the level they have reached by the time they transition to professional practice.

One of the errors we observed, which was also discussed by Bagnasco et al. [4], reflected students’ difficulty with converting units. In Spain, this concept is taught during secondary education (with the exception of % = mg/ml and drops – ml), and hence students should be able to perform this operation by the time they enter university. More specifically, we found that students had greater difficulty moving up the scale of units (e.g., from mcg to mg) rather than down, and also that some students correctly converted units in the clinical case exercise but not in the unit equivalences theory test, and vice-versa. Given their importance in clinical practice, greater attention needs to be paid to these concepts during students’ training.

Our analysis also showed that students were more likely to produce a correct answer when they applied a structured approach to the problem (e.g., extract all the key information from the question, use the correct units, and follow the correct calculation steps). This structured approach is taught at earlier stages of education in our country, although it may not be adequately assimilated by all students. If this is the case, then it could have a negative impact on their ability to perform medication calculations, which tend to be more complex in content than the purely arithmetic problems they will have been set during secondary education [21, 25].

Obviously, students would most likely find calculation exercises easier if they involved a single task expressed in clear and concise terms. However, this would not reflect clinical reality, because in practice a dose calculation is made in the context of a specific patient and other variables that may affect the final result must also be taken into account. Setting students contextualized case exercises therefore helps to reduce the theory-practice gap [26]. Accordingly, the exercises analyzed in this study involved clinical scenarios of varying complexity, and it was noticeable that the easier questions (those with just one or two calculation steps) were more likely to be answered correctly than were the more complex multi-step problems. This is reflected in the proportion of exercises where the student had clearly not understood the question (16.9%), which tended to be the more difficult problems involving more than one calculation [25]. In those exercises (n = 328) where it was possible to analyze whether the student had contextualized their result and checked whether it was realistic and made sense, we found that 45.5% failed to do so. In order to solve problems of this kind, students must understand precisely what they are being asked to do and extract from the question the key information they need to perform the calculation correctly [21]. In this context, Grunetti et al. [19] found that while students may find it helpful to use a calculator, this can also produce a false sense of security, such that they do not then consider whether the result makes sense or not. This kind of error is much more common among students who do not have a good grasp of the principles of mathematical calculation or who struggle with logical reasoning [27]. An example from our analysis was a student who did not question a final result giving a drug dose of 10^− 6 mg, even though it should be obvious that it is impossible to administer such a small amount to a patient. In our view, clinical simulation with manikins is a highly useful tool for helping students develop their skills in this respect [27, 28], insofar as it allows them to see the practical result of their calculations (i.e., the drug volume to administer), in addition to providing them with an opportunity to improve their critical thinking [29] and to learn from mistakes and their peers [30]. It should also be noted that simulation is not a stress-free experience for students, as they will be observed and be set a time limit for performing the task, and in this respect it more closely resembles the realities of clinical practice [31]. As an alternative or complement to simulation, one might also use more active learning strategies or those in which students can see the material they need or visualize what is being explained to them, rather than it being presented in abstract or purely theoretical terms [1, 26].

Another important difficulty that students had, regardless of the course year they were in, concerned calculation of the IV infusion rate. In our view, this suggests a gap between theory and practice in this respect, because although students are taught in class how to calculate the infusion rate, they are unlikely to see clinical nurses calculate the drip rate in drops/minute as this is usually estimated by the nurse when setting up a manual IV set [32]. By contrast, students do gain practical experience of calculating the rate in ml/h, because these are the units used with infusion pumps. In accordance with Hedlund et al. [3], we also found that students had difficulties in calculations involving the total administration time or the volume of diluent, both of which are more theoretical pharmacological concepts. A task for future research would be to examine in more detail the possible relationship between students’ exposure to these kinds of calculations while on clinical placement and their performance in written examinations.

The present study has several limitations that derive from the retrospective design and the fact that the analysis is based solely on written dose calculation exercises. One is that we do not know why some exercises were left blank, that is to say, whether it was because the student did not know how to solve the problem or simply ran out of time during the exam. Neither is it clear whether the number of correct answers would have been greater if students had been allowed more time or did not feel the pressure of an exam situation. On a related issue, we have no way of knowing whether those students who gave a correct answer were confident about their calculations or got there more by luck than judgment. It would therefore be useful in future studies to complement an analysis of this kind with qualitative feedback from students themselves regarding the difficulties they experienced and their level of confidence in their answers. Our approach here also provides no insight into students’ thought process or reasoning, which would be necessary in order to understand more about why precisely they made the errors they did. This would also be an interesting topic for future research. As noted earlier, three of the exercises set during year 2 imply a knowledge level above that expected of students at this stage of their training, the rationale being that this allows us to track the progress of individual students over subsequent years of their studies. We acknowledge, however, that in the context of the present analysis the inclusion of these exercises may bias the results obtained for year 2 students, which must therefore be interpreted with caution. A final limitation to consider is that we have no comparative data among the years of nursing degree regarding the dose calculation skills. Moreover, students spend year 4 almost entirely on placement, making it difficult to schedule a classroom-based test their ability in this respect. In order to build on the present results, it would be useful to introduce a final written examination (such as that used with year 2 students) at the end of every year so as to explore the evolution of the knowledge and level that our students reach by the time they graduate.

Notwithstanding these limitations, our study also has two important strengths: One is the large number and variety of dose calculation exercises analyzed, while the other is the detailed analysis of the aspects that students find most difficult.

Nursing students have adequate skills when it comes to basic dose calculations, but struggle with more complex problems, although they tend to improve as they progress through their studies. The most common errors we observed were related to not understanding or not extracting the key information from the question, not following the correct steps in their calculations, and a lack of basic knowledge such as how to convert units. The fact that some students did not consider whether their answer was realistic and made sense in a clinical context is problematic from the point of view of safe medication management. The use of high-fidelity simulation scenarios during their training could play an important role in helping them improve their skills in this respect.

In order to ensure that nursing students are proficient in medication calculation by the time they graduate, nurse educators need to identify the specific aspects and steps in the process that students find most difficult, thus enabling instruction to be targeted where it is most needed. The present analysis of students’ answers to a series of dose calculation exercises of varying levels of complexity shows that their errors cannot be attributed solely to poor calculation skills, insofar as they involved different aspects and stages of the problem-solving process. Notably, students often struggled to understand key concepts associated with dose calculation and failed to follow the correct steps when performing the exercises set. Nurse education programs must, in addition to developing students’ mathematical competence, ensure they acquire an adequate understanding of the key concepts (both numerical and clinical) underpinning medication calculation, as well as an appreciation of the importance of checking that their result is realistic and makes sense in relation to each individual patient.