Characterizing covariational reasoning in physics modeling

Abstract

Covariational reasoning—considering how changes in one quantity affect another, related quantity—is a foundation of quantitative modeling in physics. Understanding quantitative models is a learning objective of introductory physics instruction at the college level. Prior work suggests that covariational reasoning in physics contexts differs from the reasoning about functions and graphs in purely mathematical contexts that students develop in math courses; this reasoning is effortful in physics even for mathematically well-prepared students. In order to improve physics students’ covariational reasoning, we must first characterize covariational reasoning with physics quantities. To this end, we present a framework of covariational reasoning in physics contexts, to describe the ways that covariational reasoning is used in physics modeling. The framework can be used as a lens through which to analyze student reasoning, and can help inform instructional interventions. We describe an application of this framework in the development of a set of computer-based training assignments.