Framework for the Natures of Covariational Reasoning in Introductory Physics

Abstract

Covariational reasoning--how a change in one quantity is related to a change in another quantity (e.g., a 1/r potential, or the exponential decay with time of a charged capacitor)--is integral to how scientists model the physical world. It is also a skill we expect students to develop as a result of introductory physics instruction. Little research has been done to characterize physics experts' covariational reasoning. Our research suggests that physics experts use a number of strategies--distinct from those of mathematics experts--that optimize thinking about physical quantities and how they relate to each other. We present a framework that describes physics expert covariational reasoning in introductory-level physics contexts as an important first step toward an understanding of students' covariational reasoning, how students' covariational reasoning changes over the course of physics instruction, and how instruction can be designed to help develop this important type of reasoning.