RUME 28
2026
Alexandria, Virginia
Coordinating Point and Rate: A Framework for Students’ Reasoning About Slope
Page: 10
This study examines how precalculus students reason about rate and point as multiplicative objects in the contexts of linear equations and approximation. To capture students’ developing conceptions, I introduce a framework distinguishing three levels of abstracted ratio: generalized ratio, unit rate, and interiorized ratio. Findings show that although students progressed toward interiorized reasoning, their understanding was fragile when working with non-integer or symbolic values. They also struggled to coordinate slope with a reference point, which limited their ability to interpret points as records of covariation. Geometric approaches to linear approximation highlighted these conceptual difficulties more clearly than symbolic tangent line equations, underscoring the need for instructional support that fosters covariational reasoning.