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

Abstract

AbstractStudents 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.KEYWORDS: Modellingdifferential equationsundergraduate educationconceptions of change Disclosure statementNo potential conflict of interest was reported by the authors.Notes1 In this paper, we share the task, its rationale, some supports and some samples of student work. It is not intended to be a research report, but we do provide some additional details on the qualitative methods used to generate the results in a supplement.2 The full Cancerous Mass and Weight Loss Problems, along with suggested prompts, are included in supplemental material, to help students reflect on their understanding of the developing model, are in a supplement.Additional informationFundingThis work was supported by the National Science Foundation under [grant number 1750813].