Abstract

This study investigated how six students developed a quantitative understanding of concavity founded in covariational reasoning through a series of task-based teaching interviews. A key finding was the importance of multivariational reasoning--the coordination of more than two variables--in helping students reason deeply about concavity in context. Common difficulties, including confusion about negative rates and overreliance on visual representations, served as productive opportunities for learning when addressed through carefully designed tasks and discussions. The findings extend existing frameworks of covariational reasoning and highlight instructional approaches that can support students in developing a robust, quantity-based understanding of concavity.

Degree

College and Department

Computational, Mathematical, and Physical Sciences; Mathematics Education

Rights

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