PROCEEDINGS OF THE 23RD ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2020
Boston, Massachusetts
Elementary school geometry to university level calculus: Building upon learning trajectories rooted in covariational reasoning with area contexts to support covariational reasoning related to implicit differentiation
Page: 1287
Building from Panorkou’s (2017) learning trajectory for dynamic measurement developed from elementary students’ reasoning with dynamic shapes, I use the results of a semester-long teaching experiment to demonstrate how covariational reasoning with a dynamic rectangular area context can extend beyond the elementary school classrooms to develop reasoning about rates of change as it relates to constructing formulas that are representative of the an equation resulting from implicit differentiation. Specifically, I relate a secondary mathematics pre-service teacher’s reasoning with dynamic area contexts to the learning trajectory proposed by Panorkou. I then identify her additional covariational reasoning used to construct formulas that re-presented relationships between the lengths and areas of the dynamic shapes. I conclude by providing suggestions for how her reasoning can be used to build towards meanings about implicit differentiation.