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Assessing Pediatrics Residents' Mathematical Skills for Prescribing Medication: A Need for Improved Training

Glover, Mark L. PharmD; Sussmane, Jeffrey B. MD


Purpose. To evaluate residents' skills in performing basic mathematical calculations used for prescribing medications to pediatric patients.

Method. In 2001, a test of ten questions on basic calculations was given to first-, second-, and third-year residents at Miami Children's Hospital in Florida. Four additional questions were included to obtain the residents' levels of training, specific pediatrics intensive care unit (PICU) experience, and whether or not they routinely double-checked doses and adjusted them for each patient's weight. The test was anonymous and calculators were permitted. The overall score and the score for each resident class were calculated.

Results. Twenty-one residents participated. The overall average test score and the mean test score of each resident class was less than 70%. Second-year residents had the highest mean test scores, although there was no significant difference between the classes of residents (p = .745) or relationship between the residents' PICU experiences and their exam scores (p = .766). There was no significant difference between residents' levels of training and whether they double-checked their calculations (p = .633) or considered each patient's weight relative to the dose prescribed (p = .869). Seven residents committed tenfold dosing errors, and one resident committed a 1,000-fold dosing error.

Conclusion. Pediatrics residents need to receive additional education in performing the calculations needed to prescribe medications. In addition, residents should be required to demonstrate these necessary mathematical skills before they are allowed to prescribe medications.

Dr. Glover is associate professor at the College of Pharmacy, Nova Southeastern University, Ft. Lauderdale, Florida, and clinical pharmacist in the Division of Critical Care Medicine, Miami Children's Hospital, Miami, Florida. Dr. Sussmane is an intensivist and the ECLS director in the Division of Critical Care Medicine, Miami Children's Hospital.

Correspondence and requests for reprints should be addressed to Dr. Glover, Division of Critical Care Medicine, Miami Children's Hospital, 3100 SW 62nd Avenue, Miami, FL 33155-3009.

Medication errors are a significant source of morbidity and mortality among hospitalized patients.1 As reported by Bond et al.,2 a hospital medication error occurs every 22.7 hours, with 5% of inpatients receiving such errors. Additionally, among pediatric inpatients, Kaushal et al.3 reported 5.7 errors per 100 medication orders, which is equivalent to 55 medication errors per 100 admissions.

There are a number of types of medication errors; incorrect dosage calculations account for approximately 11% of these errors among hospitalized patients.4 Although calculations are used to prescribe medications to all patient populations, nowhere is this practice more prevalent than in pediatrics. Nearly all medications are prescribed to pediatric patients on the basis of weight or body surface area. Pediatricians, therefore, must be able to perform basic mathematical calculations to provide care to their patients. The purpose of our study was to evaluate the mathematical skills of pediatrics residents by providing them with a test consisting of basic mathematical calculations routinely used in prescribing medications to pediatric patients.

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Medical residents at Miami Children's Hospital are encouraged to attend a daily noon conference at which either a lecture is presented or announcements are delivered. In 2001, we worked with the chief resident to choose a mutually agreeable date to administer a mathematical calculations test to the residents during one of these noon conferences. We asked the residents to bring calculators to the meeting, but we did not inform them the test was planned.

The test consisted of ten questions on basic mathematical calculations (see the Appendix). Three of the questions were intentionally written to reflect errors in prescribed rates of drug administration. We included four additional questions to obtain the residents' levels of training (first-, second-, or third-year residents) and experience in the pediatrics intensive care unit (PICU), as well as to assess certain prescribing habits. Once they had received the test, we instructed the residents to read the directions carefully and not to collaborate with each other during the test. We told them the test was anonymous and that calculators were permitted. There was no time limit for completing the test.

We calculated the overall percentage score and the percentage scores of the individual resident classes and recorded each resident's year of training and the number of months he or she had had experience in the PICU. We also recorded and assessed whether the residents routinely double-checked their calculations for doses and titrated the doses according to the individual patients' weights.

A one-way ANOVA test was used to compare the associations of levels of training and previous PICU experience with the mean test scores. We used chisquare to compare the residents' levels of training with whether they double-checked calculations for doses and compared each patient's weight with the dose appropriate for that weight in prescribing. An independent t-test was used to compare differences between scores and whether the residents double-checked their calculations of doses or compared the prescribed doses with those appropriate for the patients' weights.

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Of the 21 residents who participated in our study, the majority were in their second year of training. The overall average test score was 65% and the mean test score of each individual class was less than 70% (see Table 1). Although the second-year residents had the highest mean test score, we observed no significant difference between the resident classes (p = .745).

Table 1

Table 1

First-year residents are not scheduled for PICU rotations, however, the second- and third-year residents had completed between one and three four-week rotations in the PICU. Nevertheless, we observed no significant association between the amount of PICU experience and test scores (p = .766). We also asked the residents whether they always doubled-checked their calculations and whether they always compared a prescribed dose with that appropriate for each patient's weight. We found no difference between residents' levels of training and whether they double-checked their calculations (p = .633) or whether they considered each patient's weight in determining the dose prescribed (p = .869). We also noted no difference between the residents' mean test scores and whether they double-checked their calculations (p = .768). Interestingly, we did find a significant difference between the mean test scores of residents who always considered a patient's weight in determining the prescribed dose and residents who did not do so, with the latter achieving the higher test scores (p < .05). No resident in our study identified any of the three infusion-related errors in the test. Of note, seven residents performed tenfold dosing errors and one resident performed a 1,000-fold dosing error.

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An Institute of Medicine report published in 1999 highlighted concerns about medical errors and their impact on the health care system.5 According to the report, as many as 98,000 patients die each year due to medical errors, the eighth leading cause of death in the United States. Errors involving medications have been implicated in approximately one fifth of injuries or deaths among hospitalized patients each year, making medication error one of the major medical errors.6

Nevertheless, as reported in 2000, only 19 of 114 U.S. medical schools required a college mathematics course prior to admission.7 Furthermore, once a student was admitted, often no further assessment of his or her mathematical skills was done, as a component of either didactic or clinical education. In our institution, pediatrics residents write the majority of the medication prescriptions, most of which require mathematical calculations. Similarly, other medical institutions have reported that their interns write approximately 50% or more of all patient medication prescriptions.8 Residents at our institution do not receive any formal training in the mathematical calculations needed to prescribe medications.

Our study demonstrated a lack of competent mathematical skills, and, therefore, a need for additional education and assessment of such skills in pediatrics residents. Each resident class failed to achieve an average of higher than 70% on the test. An even more alarming (but not statistically significant) discovery from our data was that the third-year residents had a lower average score than either the first- or second-year residents. This is an obvious concern because among the three groups, the third-year residents had the greatest amount of experience calculating and prescribing medication doses for patients.

Unbeknownst to us during the development and performance of our study, Rowe et al.9 published a similar study of pediatrics residents. In their study, Rowe et al. administered two mathematical calculation tests similar to our test to two groups of residents with a period of two years between the tests. They reported that 19 of 34 and nine of 30 residents committed more than one error in the first and second exams, respectively. As with our results, Rowe et al. reported no correlation between the length of training and the likelihood of committing an error.

Similarly, Potts et al.10 assessed the mathematical skills of first-year primary care interns. Overall, the mean score on their mathematics tests was 42%. Pediatrics interns scored significantly higher than family practice interns, with mean scores of 57.8% and 34.4%, respectively. Hence, the test scores of the pediatrics interns in the Potts et al. study were similar to the test scores of the residents in our study, who scored a mean of 64.3%.

We presumed that residents in our study who had completed more clinical rotations in the PICU would perform better on the test. We reasoned that most patients in the PICU receive drug therapy requiring more meticulous calculations than that for patients on the hospital wards. Such patients are often prescribed loading doses, bolus doses, and medications via continuous infusion, each requiring additional calculations. However, we found no significant difference in test scores relative to amount of clinical experience in the PICU. Oddly enough, the first-year residents, who had no PICU clinical experience, performed better on the test than did the third-year residents, who had the most PICU experience.

The residents' demanding schedules place them at increased risk of mental lapses or mental slips, which have been shown to contribute to medication errors.4 Given the physical and mental stresses under which residents must perform, they must pay particular attention to detail and make a conscious effort to focus on the task at hand. One means of reducing medication errors under these conditions is to double-check calculations. Therefore, we wished to determine how often the residents double-checked their calculations and whether they adjusted the dosages for individual patients' weights. Interestingly, 80% of the third-year residents stated they always double-checked dosage calculations, compared with 51% of first-year residents and 56% of second-year residents. Eighty percent of the third-year residents stated they always checked the dosages against those appropriate for the weights of the patients, compared with 71% of first-year residents and 67% of second-year residents. Therefore, the residents with the least medical experience appeared to be less meticulous about prescribing medications to their patients.

Tenfold dosing errors involving the misplacement of a decimal point are a common prescribing error.4,11 Depending on the medication in question, such an error can have devastating effects on the patient's health. The residents in our study committed seven tenfold calculation errors; one second-year resident committed two of these tenfold calculation errors. With one exception, the second- and third-year residents committed the tenfold errors, with the majority being second-year residents. Our findings contrast with those of Rowe et al.,9 which indicated that six of seven residents who committed ten-fold errors were in their first year of training.

In conclusion, our study illustrates the need for additional education for pediatrics residents in performing the basic mathematical calculations needed to prescribe medications. Perhaps as a component of the residents' orientation, the teaching institution could provide classes in the basic mathematical skills essential to the practice of medicine. Residents should be required to demonstrate these mathematical skills before they are allowed to prescribe medications.

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1. American Academy of Pediatrics Committee on Drugs and Committee on Hospital Care. Prevention of medication errors in the pediatric inpatient setting. Pediatrics. 1998;102:428–30.
2. Bond CA, Raehl CL, Franke T. Medication errors in United States hospitals. Pharmacotherapy. 2001;21:1023–36.
3. Kauchal R, Bates DW, Landrigan C, et al. Medication errors and adverse drug events in pediatric inpatients. JAMA. 2001;285:2114–20.
4. Lesar TS, Briceland L, Stein DS. Factors related to errors in medication prescribing. JAMA. 1997;277:312–7.
5. Institute of Medicine. To Err Is Human: Building a Safer Health System. Washington, DC: National Academy Press, 1999.
6. Leape LL, Brennan TA, Laird N, et al. The nature of adverse events in hospitalized patients. Results of the Harvard Medical Practice Study II. New Engl J Med. 1991;324:377–84.
7. Medical School Admissions Requirements—2001-2002—United States and Canada. 51st ed. Washington, DC: Association of American Medical Colleges, 2000:28.
8. Lesar TS, Briceland LL, Delcoure K, Parmalee JC, Masta-Gornic V, Pohl H. Medication prescribing errors in a teaching hospital. JAMA. 1990;263:2329–34.
9. Rowe C, Koren T, Koren G. Errors by paediatric residents in calculating drug doses. Arch Dis Child. 1998;79:56–8.
10. Potts MJ, Phelan KW. Deficiencies in calculation and applied mathematics skills in pediatrics among primary care interns. Arch Pediatr Adolesc Med. 1996;150:748–52.
11. Koren G, Haslam RH. Pediatric medication errors: predicting and preventing tenfold disasters. J Clin Pharmacol. 1994;34:1043–5.
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Mathematical Calculations Test Given to Pediatrics Residents, Miami Children's Hospital, Florida, 2001

Information and Instructions:

This is an anonymous questionnaire. Please provide your answers to the following questions in the blanks provided. You may use a calculator to assist you. Where appropriate, please show calculations. Please comment on any dosages or orders that are not appropriate.

  1. A male patient weighs 60 lbs. His equivalent weight in kilograms is ____ kg.
  2. A child is prescribed 4 mL of potassium phosphate (phosphorus 3 mMol/mL; potassium 4.4 mEq/mL) to be infused over 1 hour. How many mEq of potassium will he receive? ____ mEq.
  3. A child is receiving propofol (10% lipid base) via continuous intravenous infusion at a rate of 5 mL/hr. How many grams of lipid will he receive in 24 hours? ____ grams.
  4. A 20-kg child is receiving norepinephrine via continuous intravenous infusion at a rate of 0.8 mL/hr. The infusion pump contains a label that reads “N = 0.1.” What dose of norepinephrine is this child receiving? ____.
  5. A 15-kg child is prescribed a loading dose of fosphenytoin of 18 mg PE/kg to be infused over 3 minutes. The drug is supplied as a 50 mg/mL solution. How many mL should the patient receive for the prescribed dose? ____ mL.
  6. A 40-lb child is receiving fentanyl (50 mcg/mL) via continuous infusion at a rate of 0.4 mL/hr. What dose is he receiving in mcg/kg/hr? ____ mcg/kg/hr.
  7. A child is to receive 1.5 gm of intravenous magnesium sulfate over 5 minutes. Magnesium sulfate is supplied as a 500 mg/mL solution. How many mL of magnesium sulfate should the child receive? ____ mL.
  8. A dexamethasone dilution is to be prepared for a final concentration of 1 mg/mL. How many mL of the stock solution (4 mg/mL) must be used for a final dilution volume of 5 mL? ____ mL.
  9. A child is receiving sodium supplementation via TPN as NaCl 40 mEq/L and NaPO4 20 mEq/L. The TPN is infusing at a rate of 30 mL/hr. How many mEq of sodium will the child receive in a 24-hour period? ____ mEq.
  10. A 5-kg child is prescribed an intravenous bolus dose of aminophylline (80% theophylline) of 6 mg/kg. How many milligrams of theophylline will he receive? ____ mg.


  1. 27.3 kg
  2. 17.6 mEq
  3. 12 grams
  4. 0.08 mcg/kg/min
  5. 5.4 mL
  6. 1.1 mcg/kg/hr
  7. 3 mL
  8. 1.25 mL
  9. 43.2 mEq
  10. 24 mg]

Please provide your answers to the following questions.

  1. I am a ____.
    1. First-year resident.
    2. Second-year resident.
    3. Third-year resident.
  2. How many months (rotations) have you served as a resident in the PICU? ____ months.
  3. When calculating doses of medications, I ALWAYS double-check my calculations.
  4. Yes ____ No ____
  5. When reviewing my patient's medications, I ALWAYS check the dose of each medication based on the patient's weight.
  6. Yes ____ No ____
© 2002 Association of American Medical Colleges