Where does the calculus go? An investigation of how calculus ideas are used in later coursework

Abstract

Teachers of post-calculus courses frequently lament their students’ proficiency in calculus. While research outlines the topics mathematicians consider to be the core concepts and skills of calculus, there is no consensus on what calculus might be needed for students in different disciplines nor how we might want our students to understand these ideas. We argue that teachers may be lamenting the fact that students were not prepared to know calculus in a way that it is compatible with how it must be used post-calculus. Using differential equations as an exemplary post-calculus course, we explore the consequences of an analysis of foundational calculus topics in terms of how such topics are used. We present evidence and characterize elements of an epistemological mismatch between calculus and post-calculus.

Keywords:

• calculus
• differential equations
• curriculum study

Acknowledgements

This work was supported by the Marilyn Ruth Hathaway Fellowship.