RUME 26
2024
Omaha, Nebraska
What is the Correct Amount of Change? A Case Study on Kala’s Covariational Reasoning
Page: 45
Students’ understanding of the mathematics of change has been a crucial topic in the teaching and learning of precalculus. Various studies have indicated that covariational reasoning – reasoning about two quantities changing together—is critical for constructing productive meanings for rate of change. The Bottle Problem is one way teachers have supported students’ covariational reasoning. We report on a case study of one student – Kala – an Applied Precalculus student. Through analysis of her work on the Precalculus Content Assessment (PCA), course assignments, and a cognitive interview, we report on her reasoning with amounts of change—a level of covariational reasoning. As a result, we highlight the importance of using appropriate amounts of change to analyze situations covariationally. This study contributes to literature on students’ development of productive amounts of change reasoning.