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

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.

Toward understanding and characterizing expert physics covariational reasoning

“…Across tasks and expert populations, we observed physicists use the phrase "goes as" or "goes like" to refer to such a relationship (ex: "the height goes like a sine function"). We view the use of the phrase "goes as" or "goes like" to be a clue that someone is engaged in reasoning about a functional relationship between two quantities [64].…”