Assessment of the mathematical skills of nursing students in calculating mandatory doses

Introduction

Every year, nurses’ competencies become wider. This means not only greater responsibility but also the need to have comprehensive knowledge of mathematics. Evidence of the development of the nursing profession is the expansion of rights in nursing prescriptions and the supply of medicinal products without a doctor’s order. Under the Act on the Professions of Nurses and Midwives of July 15, 2011, nurses who hold a master’s degree in nursing or a bachelor’s degree and complete a specialist course may independently prescribe and issue prescriptions or continue prescribing medicines for specific active substances and foodstuffs intended for particular nutritional uses [1, 2]. The Regulation of the Minister of Health of January 18, 2018 includes a number of active substances prescribed by nurses, such as anti-emetics and anti-infectives used in diseases of the ear, throat, urinary tract, periodontium and skin. However, the list of medicinal products to be administered without a doctor’s order is specified in the Regulation of the Minister of Health of February 28, 2017. This act lists 33 substances for self-administration and 47 substances that can be administered by a system nurse in life-threatening situations [3].
The decision to self-administer medications requires an appropriate level of knowledge in pharmacology and appropriate mathematical competencies in the area of ​​calculating drug doses. For this reason, developing these skills in future nursing students is extremely important. In the first year of their studies, as part of the Fundamentals of Nursing subject, nursing students learn how to prepare drugs, store them, administer medicinal products in various ways, and calculate drug doses. In the next year of study, students acquire the necessary knowledge about pharmacotherapy and pharmacokinetics during pharmacology classes, where they also practice calculating drug doses. The competencies acquired during studies are practiced during practical classes in the hospital conducted under the supervision of experienced practitioners [4].
The education of nurses in Poland is established according to the European Union and the National Accreditation Council of Schools of Nurses and Midwives. The profession of a nurse can only be taught at universities that are available within the framework of the educational outcomes. According to the new standard of education, the student should obtain such educational outcomes as: calculating the dose of the drug, independent consequence of the patient’s treatment, following the professional regulations of the nurse or a written order of the doctor, and medicinal products from anti-shock kits. Additional information should be included in the topic regarding the analysis and its consequences. The new standard education of nurses emphasizes practical skills, social development and independence compared to the older, more advanced training. All of these are checked in exercises, introductory classes, professional practice and at the exam at the end of bachelor’s studies [5]. There are no additional exams. Each student who applies to a nursing program should pass secondary school final exam, where mathematical tasks, on a basic level, are obligatory.
Despite high educational standards, unfortunately, we still hear about medical errors. Some of the most common ones involve incorrect administration of medications, including incorrectly calculated doses. In Poland, after completing nursing studies, the level of mathematical skills is not verified as in other countries. There is also a lack of research on the mathematical skills of nursing students or professionally active nurses. This is undoubtedly a matter worth exploring. Knowledge in this area may contribute to reducing the occurrence of medical errors, improving patient safety and increasing the skill level of nursing staff.
The project aimed to assess nursing students’ competencies and mathematical skills in calculating drug doses at the bachelor’s level.

Material and methods

The study used three research methods. The first one was a review of Polish and foreign literature regarding the ability of nursing staff to calculate drug doses. When searching for materials, the following key words were used: drug dosage calculation, mathematical skills, nurses, and bachelor’s degree program.
The second tool used in the work was a diagnostic survey addressed to nursing students. The main inclusion criteria were student status in the nursing program for the bachelor’s degree in Poland. The main exclusion criterion was nurses who had their license and practiced in a clinical environment. An original interview questionnaire and surveys were prepared based on the Drug dosage calculation questionnaire. This Drug dosage calculation questionnaire is a competency examination in drug dose calculation for a Bachelor of Science in Nursing in the United States. Bachelor of Science in Nursing graduates should obtain a score of 90% to pass the exam and obtain a nurse’s license [6]. The main part of the survey questionnaire included 10 tasks. The answers of respondents were analyzed using the adopted key for previous calculations. The respondents received 1 point for each correct answer. The maximum number of points to obtain was 10. An assessment criterion by the Regulations of the Medical University of Gdansk was used to assess respondents’ skills related to calculating drug doses.
To pass the test at a satisfactory level, respondents should obtain 60% of the correct answers, which means 6 points. Further test evaluation criteria:
fairly good (3.5) = 70% and 80% of correct answers which means 7 points,
good (4) = 80% and 85% of correct answers which means 8 points,
better than good (4.5) = 85% and 90% of correct answers, which means 8.5 points,
very good (5) = 90% of correct answers, which means 9 points [7].
The third method used in the work was statistical analysis. Calculations were performed in IBM SPSS. Frequencies were calculated for qualitative variables, and bar charts were prepared. Means were calculated for quantitative variables, and histograms were made.
A c2 test was performed to assess the significance of differences between the frequency distribution of responses in the study group and the random distribution of responses. n = 0.05 was considered statistically significant.
The Kolmogorov-Smirnov test was performed to check compliance of the distribution of quantitative variables with the normal distribution; the significance level was set to n = 0.05.
To assess the significance of differences between groups (for variables whose value distribution was not consistent with normal), the Mann-Whitney U test was performed for two independent variables, and the KruskalWallis test for k independent samples; p < 0.05 was considered statistically significant.

Organization of research

Participation in the study was voluntary. Anonymity was maintained among the respondents.
The survey questionnaire was distributed online. The survey was distributed to groups such as Nursing of the 21st Century, Nurses to Nurses, Pomeranian Nurses and Midwives, and Nursing Students on the Facebook social media platform. A questionnaire developed using the Google platform was used to obtain respondents’ answers. Before starting the study, the respondent had the opportunity to read the instructions and the foreword. Then, after selecting the option, “I agree to participate in the study” – respondents were transferred to the interview sheet and the main part of the survey questionnaire. One hundred nursing students took part in the project. Various universities offer education in the bachelor’s nursing program. The study lasted from November 2021 to March 2022.

Results

100 respondents from various medical universities in Poland from 16 voivodeships involved in the education of first-cycle nursing programs participated in the study. When analyzing in detail the year of study, the vast majority of respondents were third-year students (n = 52, 52%), while the smallest groups were second-year students (n = 33, 33%) and first-year students (n = 15, 15%). A detailed summary of sociodemographic data is presented in Figures 1 and 2.
The next part of the questionnaire included task-solving questions regarding drug dose calculations. The first task in calculating drug doses concerned Coumadin, which is an anticoagulant drug. The respondent had to calculate how many tablets the nurse should administer if one tablet contained 5 mg of the drug and 15 mg was ordered. The respondents had four answers to choose from, and all of them (n = 100, 100%) gave the correct answer: 3 tablets. The second task included in the survey questionnaire concerned Diflucan, which is an antifungal drug. In this task, respondent had to calculate how much of the drug to administer to the patient if 1 ml contained 40 mg and 100 mg was ordered. All respondents (n = 100, 100.0%) gave the correct answer, which is 2.5 ml. The next task concerned potassium chloride, which is used to compensate for electrolyte disorders. In this task, it was necessary to calculate how many ml of the drug to draw into the syringe if 20 ml contains 40 mEq and the order is 20 mEq. All respondents (n = 100, 100%) correctly calculated this dose and answered 10 ml.
The next task in the survey questionnaire concerned the drug infusion time in ml/h. It was necessary to calculate the speed at which the infusion pump should be set to deliver 100 ml of the drug in 45 minutes. The correct answer should be a flow rate of 133 ml/h. Almost half of the respondents did not provide the correct answer (n = 42, 42.0%).
Another task that caused many problems for the students concerned the delivery of aminophylline, which is used in respiratory diseases. It was necessary to calculate how many mg/h of the drug the patient receives if 250 ml of fluid contains 2 g of aminophylline, which is absorbed at a rate of 20 ml/h. In this task, before performing the calculations, it was necessary to convert grams to milligrams and distinguish between ml/h and mg/h. Most respondents incorrectly calculated this task (n = 52, 52.0%). Only 48 respondents indicated that the drug flow rate should be 160 ml/h.
In the seventh question in the survey, one had to calculate how many ml of heparin to draw into the syringe if the order was 80U per kilogram of body weight. Heparin is an anticoagulant drug, 1 ml contains 10,000 U, and the patient weighs 85 kg. The mathematical operations included the same units of the drug but required knowledge of decimal fractions. The correct result of this task is 0.68 ml – this was the answer given by most respondents (n = 70, 70.0%).
The next task concerned the delivery of cefazolin, which is an antibiotic. It was necessary to calculate how many ml of the drug to draw into the syringe if 2 ml of the solution containing 250 mg and 125 mg of antibiotic was ordered. The mathematical operation required dividing in half and the vast majority of respondents (n = 97, 97.0%) gave the correct answer, which is 1 ml. Only 3% (n = 3) of people failed to give the correct answer. The ninth task concerned the delivery of Fragmin, which is also an anticoagulant drug. It was necessary to calculate how many ml to administer to the patient if 5000 U was ordered and 1 ml of the drug contained 10,000 U. This math task also required division. Most respondents (n = 97, 97.0%) gave the correct answer, which is 0.5 ml, while 3 people (3.0%) did not. A detailed summary of all respondents’ answers is presented in Table 1.
In the project, students were also asked whether they had taken part in classes expanding their mathematical skills in drug doses during their studies. Over 75% (n = 75) of respondents confirmed that they could participate in this type of classes.
After completing the drug dose calculation test, respondents were asked to determine its difficulty level. For the majority of nursing students, the test was not difficult (n = 62, 62.0%). 26% of respondents had no opinion on the level of difficulty of the test, and 12% of respondents stated that it was difficult for them.
The Kruskal Wallis statistical test showed no relationship between students’ knowledge and skills in calculating drug doses and the year of study (p = 0.428). The Mann-Whitney U test also did not confirm significant differences between the groups in the level of mathematical skills and participation in classes preparing for self-calculation of doses during studies (p = 0.19).

Discussion

The image of a nurse has changed significantly over the years [8]. Despite constantly growing expectations, the nursing profession enjoys unwavering public trust [9, 10]. Membership in the European Union requires states to standardize nurse education, i.e., to provide it at universities. After completing their studies, nurses have the opportunity to further develop their knowledge by participating in specialization, qualification, and continuing education courses, as regulated by the Act on the Professions of Nurses and Midwives [1]. Education is also provided at the academic level in other highly developed countries such as the United States and Great Britain. Despite guidelines and regulations, the education of nursing staff is not the same. Unifying the education system in all countries would avoid the need to complete additional courses in each EU member state to reduce program differences. For example, nurses in Great Britain acquire quite high competencies, meaning they take over activities that were performed only by doctors in the past. In Poland, this process is just beginning, which is proven by the possibility of nurses prescribing prescriptions, the independent delivery of certain medicinal products, and the treatment of wounds [11, 12]. To perform such responsible activities, nurses should also demonstrate high competencies in mathematical skills. The 2024 nursing education standards in Poland place strong emphasis on practical training, which accounts for more than 50% of the total European Credit Transfer and Accumulation System required for graduation. These practical sessions are designed to assess key competencies, including pharmacology, pharmacokinetics, and the administration of medications via various routes, as well as accurate dosage calculations. Students initially develop these skills in simulated environments, allowing them to safely practice and build confidence before applying their knowledge in clinical settings. The updated curriculum introduces additional learning outcomes, such as the preparation and administration of emergency medications from anti-shock kits, and the performance of nursing duties in emergency departments. At the conclusion of the undergraduate program, students are required to pass the objective structured clinical examination. This standardized exam, conducted under uniform simulated conditions for all candidates, is designed to verify the level of proficiency in practical skills through task-based performance [5].
The study was intended to present the issue of nursing students’ competencies in calculating drug doses. The analysis confirmed that most students have good knowledge and skills in calculating drug doses. Nursing students from various universities in Poland took part in the above study and their task was to complete a drug dose calculation test. To obtain a positive test result in accordance with the assessment criteria of the Medical University of Gdańsk, it was necessary to obtain at least 60% of correct answers, i.e. 6 out of 10 points. The statistical analysis shows that the prepared test was not passed by one of the respondents, while 60% of the respondents obtained a high score of 9 or 10 points. Similar research was conducted in one of the hospitals in Finland, and respondents were also given a test on calculating drug doses. The highest score that could be obtained was 29 points (100%), research showed that more than half of the surveyed nursing students obtained only 17.8 points (61.4%) [13].
A similar study was also conducted in 2015 at Uludag University in which 148 nursing students participated. Using a test on calculating drug doses, this time for a pediatric patient, it was confirmed that more than half of the respondents participating in the study (68.2%) answered 4 out of 5 questions correctly. In the same study, over 70% of students tested found the correct ratio and proportions, but only 65.5% of the final results were consistent with the answer key [14].
In Poland, at the end of nursing studies, mathematical skills are not verified by an exam, as in other countries. Perhaps in the future, it would be worth considering this type of solution, but as recent data show, more than half of nursing students do not pass exams in mathematical calculations, and errors related to the process of administering medications are still among the most common medical errors [1]. The dominant problems include cases of administering an inappropriate dose of a drug (27.9%), an incorrect drug (17.6%), and administering a medicinal product to the wrong patient (16.2%) [15]. Similar analyses, although carried out at the University of Malaga, showed that adverse events related to incorrect drug administration most often occur in intensive care units and pediatric wards [16, 17].
The study was the first project of this type in Poland. The topic undoubtedly requires in-depth study and further analysis. Reports from other authors confirm that the lack of mathematical skills may significantly induce people to resign from further work in their profession. Perhaps in the future, it is worth considering the introduction of unified examinations for medical staff in the field of mathematical skills in calculating drug doses, as is the case in other countries. Each such action will significantly improve the quality of care and patient safety.
This study has some limitations that should be acknowledged. As the first study of its kind, there were some methodological issues, including errors in the research design influenced by sociodemographic factors. Additionally, there are no available validated tools and tests in the Polish nursing literature, which led us to use an existing test developed in other countries.
Another limitation is the small sample size, which does not fully represent all nursing students. This means the findings should be interpreted with caution. Moreover, the study was preliminary, aimed mainly at identifying the extent of the problem rather than providing definitive answers. Based on the literature review, further detailed research is needed to explore this topic more thoroughly and to assess the quality and methods of teaching. We hope this discussion will be a starting point for future studies and improvements, especially in helping students develop skills in complex mathematical calculations.

Conclusions

Based on the research conducted and the verification of the hypotheses, the following conclusions were formulated:
1. The general level of students’ skills in calculating drug doses is good.
2. The ability to calculate drug doses does not depend on the year in which students study.
3. The most problematic issues for nursing students are complex mathematical calculations related to unit conversion, calculation of drug flow rates in infusion pumps (ml/h), or operations involving decimal fractions.
4. Mathematical tasks regarding drug doses involving multiplication and dividing in the same units do not cause problems for nursing students.
5. During their studies, most students had classes preparing them to independently calculate drug doses, but this fact does not affect the students’ skill level.

Disclosures

1. Institutional review board statement: Not applicable.
2. Assistance with the article: None.
3. Financial support and sponsorship: None.
4. Conflicts of interest: None.

References