Identifying Covariational Reasoning Behaviors in Expert Physicists in Graphing Tasks

TL;DR

This paper investigates how expert physicists engage in covariational reasoning during graphing tasks, revealing new behavioral modes that differ from previous mathematics-focused studies.

Contribution

It extends covariational reasoning research into physics, identifying novel behavioral modes in expert physicists not previously documented.

Findings

Identified two new covariational reasoning behaviors: compiled relationships and neighborhood analysis.

Observed differences in reasoning modes between physics and mathematics contexts.

Provided preliminary insights into expert physicists' reasoning strategies in complex physics questions.

Abstract

Covariational reasoning -- how one thinks about the way changes in one quantity affect another quantity -- is essential to calculus and physics instruction alike. As physics is often centered on understanding and predicting changes in quantities, it is an excellent discipline to develop covariational reasoning. However, while significant work has been done on covariational reasoning in mathematics education research, it is only beginning to be studied in physics contexts. This work presents preliminary results from an investigation into expert physicists' covariational reasoning in a replication study of Hobson and Moore's 2017 investigation of covariational reasoning modes in mathematics graduate students. Additionally, we expand on this work to include results from a study that uses slightly more complex physics-context questions. Two behavioral modes were identified across contexts that appear distinct from those articulated in the Hobson and Moore study: the use of compiled relationships and neighborhood analysis.