Exploring Students' Understanding of Linear and Quadratic Relationships in a Projectile Motion Context

TL;DR

This study investigates how covariational reasoning, supported by specific task features and technology, helps middle school students understand linear and quadratic relationships in projectile motion.

Contribution

It demonstrates that targeted prompts and task design can enhance students' covariational reasoning about mathematical relationships in physics contexts.

Findings

Prompts comparing linear and quadratic relationships foster better covariational reasoning.

Task features and technology affordances support understanding of covarying quantities.

Students' covariational reasoning evolved through the digital task exploration.

Abstract

Previous research has shown that students often struggle to develop an understanding of linear and quadratic relationships. Covariational reasoning has been identified as a way to support this development. This study aims to investigate how covariational reasoning supports students in developing understandings of linear and quadratic relationships within a projectile motion context. A teaching experiment was conducted with two middle school students who engaged in a digital task exploring the relationship between height and time. The analysis characterizes how the students' covariational reasoning evolved as they interpreted the changing quantities in the task. The findings suggest that prompts encouraging students to compare linear and quadratic relationships can foster more sophisticated forms of covariational reasoning. The discussion highlights how specific features of the task design, including the affordances of technology, the emphasis on conceiving graphs as representations of covarying quantities, and the use of non-canonical graphing tasks, can support covariational reasoning.