Teaching Tip: Math in Medicine

Math and science education in the United States and the application of math and science skills in the workplace have come a long way since we used multi-volume printed encyclopedias, searched the card catalog for references, and used pencil and paper for the majority of our computations. This teaching tip deals with the reinforcement of the basic understanding of numbers and being able to perform calculations accurately. Many calculations in medicine can be done with an app or automated program, but using the formula itself, paper and pencil, or just doing calculations in your head can help with learning.

Do you tend to do these in your head, or do you reach for a calculator?

1. a) 25% of (11 x 12)
2. b) 600(1- (30+15)/135)
3. c) log10 (10-8)

I have noticed that many students would have to reach for a calculator for simple equations such as those above. The problem with this is that they are less likely to be able to recognize when the answers that appear on the calculator or smartphone screen are way off.  We, of course, have incredibly capable students–many of whom have dealt with very complex math and science. Most trainees will do just fine, but it is our job to make sure that no one slips through while lacking appropriate skills. Slight keystroke errors can result in large numerical errors, and since with patient care, there is already enough uncertainty without incorrect math, we must reinforce the importance of developing strategies to feel comfortable with numbers.

On rounds, it can help to have everyone on the team participate in most numeric calculations, by using whichever of these methods they prefer.  In many cases, using the actual formula as opposed to simply plugging a problem into an app gives the trainee a better understanding of the meaning of the formula itself. The app can be used after the formula is used and understood. Have everyone on the team show you their calculated results individually, and then investigate why someone ended up with an incorrect answer. After everyone tries the calculation, if the formula is straightforward, challenge everyone to try an even simpler calculation in their head or on paper (without a calculator).

On the nephrology service, an example would be teaching about the electrolyte free water clearance = V(1-(Urine Na + Urine K) / Plasma Na). V is the urine volume per unit time, and the electrolyte free water clearance is the volume of free water cleared by the kidneys per unit time. The electrolyte free water clearance for a 1 liter urine volume/24 hrs, a plasma Na of 140 mEq/Liter, a urine Na of 35 mEq/L, and a urine K of 35 mEq/L = 1 (1-(35+35)/140) =1(1-70/140)= 1(1-1/2) = ½ liter/24 hrs. The act of doing the calculation itself without an app helps drive home the concept that the 1 liter urine volume with 70 mEq/L of electrolytes can be thought of as ½ liter of a solution with 140 mEq/liter of electrolytes mixed with ½ liter of free water.

For numeric results, it is useful to drive home the range of clinical values that are possible for various situations. It is also important to discuss the meaning of negative results for calculations that usually yield positive values. For example, a negative electrolyte free water clearance means the patient has net free water retention. For other formulas, such as those regarding body surface area, negative values would always mean the calculation was performed incorrectly.

Mastery of basic math is a skill that is increasingly delegated to our handheld devices, but it is not yet obsolete.

*Brought to you by the Emory University Department of Medicine’s Education Community.