Exploring student facility with "goes like'' reasoning in introductory physics

TL;DR

This paper investigates how introductory physics students understand and use "goes like" covariational reasoning, revealing their current reasoning patterns and suggesting instructional strategies to develop expert-like understanding.

Contribution

It provides evidence on students' covariational reasoning in physics and proposes instructional approaches to enhance their "goes like" reasoning skills.

Findings

Many students use prior math tools for reasoning

Students' reasoning can be developed into expert-like thinking

Recommendations for instructional development are provided

Abstract

Covariational reasoning -- reasoning about how changes in one quantity relate to changes in another quantity -- has been examined extensively in mathematics education research. Little research has been done, however, on covariational reasoning in introductory physics contexts. We explore one aspect of covariational reasoning: ``goes like'' reasoning. ``Goes like'' reasoning refers to ways physicists relate two quantities through a simplified function. For example, physicists often say that ``the electric field goes like one over r squared.'' While this reasoning mode is used regularly by physicists and physics instructors, how students make sense of and use it remains unclear. We present evidence from reasoning inventory items which indicate that many students are sense making with tools from prior math instruction, that could be developed into expert ``goes like'' thinking with direct instruction. Recommendations for further work in characterizing student sense making as a foundation for future development of instruction are made.