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Covariational reasoning--considering how changes in one quantity affectanother, related quantity--is a foundation of quantitative modeling in physics.Understanding quantitative models is a learning objective of introductoryphysics instruction at the college level. Prior work suggests thatcovariational reasoning in physics contexts differs in important ways fromreasoning about functions and graphs in purely mathematical contexts; thisreasoning is effortful in physics even for mathematically well-preparedstudents. In order to help students learn to reason covariationally in physicscontexts, we need to characterize what we mean by physics covariationalreasoning. To this end, we present a framework of covariational reasoning inphysics contexts, to describe the ways that covariational reasoning is used inphysics modeling. The framework can be used as a tool by which instructors canrecognize physics covariational reasoning patterns and researchers can analyzestudent reasoning. The framework can also help inform the development ofeffective instructional materials and methods.

A framework for characterizing covariational reasoning in physics