Student understanding of the limit definition of a derivative

Abstract

The study of Calculus requires an understanding of the limit-definition of the derivative. This study examined students’ concept images of functions, limits, and average rate of change, and how these relate to the limit-definition of the derivative. Four Calculus II students were given a task-based interview, and their responses were coded via a framework. The results suggest that students tend to rely on graphical representations, and that students require a symbolic understanding of average rate of change to be able to have a conceptual understanding of the limit-definition of the derivative.