Promoting Productive Understandings of Rate of Change in Calculus Courses

Abstract

A productive understanding of rate of change concept is essential for constructing a robust understanding of derivatives. There is substantial evidence in the research that students enter and leave their Calculus courses with naive understandings of rate of change. Implementing a short unit on “what is rate of change” can address these issues and better support students in understanding the fundamental ideas of Calculus. This paper provides a short teaching intervention that instructors can utilize to help students build a productive understanding of rate of change that will aid them in understanding derivatives as instantaneous rates of change.