Calculus as a Tool

Abstract

I read the short article by Barry Cipra about calculus teaching reforms (News, [16 Feb., p. 901][1]) with interest. I studied calculus for an entire year in college, but without really understanding it. Proving all the theorems constituted a considerable portion of the course, but I memorized the proofs. I felt then and feel now that proofs are irrelevant to the great majority of us who use calculus as a tool. In using it in physical chemistry class, I suddenly experienced an epiphany. The entire topic of calculus became clear in the course of understanding partial derivatives of thermodynamic functions; and in that one second, I learned more than I had ever learned in an entire year of calculus. If calculus were taught as a useful tool rather than as a theoretical discipline, I believe more students would learn it, understand it, and enjoy it. I have taken this same approach to my own teaching, particularly of enzyme kinetics. I find that the traditional way of teaching theory first reaches maybe 10% of students, while teaching the methodology first and then teaching the theory reaches 80 to 90% of students. I encourage the reformers to continue, particularly in eliminating irrelevant proofs. [1]: /lookup/doi/10.1126/science.271.5251.901b