Calculus is the study of change, but differential equations students need help quantifying it

Abstract

Students exit calculus with understandings of change that want for conceptual depth and are disconnected from real-world contexts. In this paper, we present a problem that will develop their skills in using change concepts for learning differential equations through modelling. The problem comes from a qualitative study of how STEM majors approach and think about differential equations as models for real-world scenarios. Our purpose is to inform faculty who are using open, authentic, scenario-driven instructional materials about the ways their students think about what are often taken-for-granted concepts in advanced mathematics and to support faculty in ensuring their students get the most from their innovative instructional materials.