Transitioning students to calculus: Using history as a guide Nicolas Haverhals & Matt Roscoe

Most American high schools and universities offer a course entitled “Precalculus”. As the name implies, these courses are meant to prepare students for the subsequent study of differential and integral calculus. A typical catalog description obtained at a large, public university in the western United States summarizes the course content:

As the description makes clear, the study of precalculus is primarily concerned with the study of the various families of elementary mathematical functions. And while a firm notion of function is surely a prerequisite to the study of calculus, it is the assertion of these authors that the study “precalculus” has significantly migrated away from the historical account of the discovery of the subject. In this paper we advocate for a historical perspective towards precalculus as a means of bridging the calculus divide that is described below.