PROCEEDINGS OF THE 18TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2015
Pittsburgh, Pennsylvania
How might students come to see a differential equation as a function of two variables?
Page: 185
Using Tall and Vinner’s notion of Concept Image (1981) we analyzed the concepts students used while working with the differential equation 𝑃′=3𝑃 and the connections between these concepts. We identified five interconnected elements in the students image of 𝑃′ in the context of differential equations that played an integral role in the students’ reasoning while attempting to solve interview tasks. In this study we report our findings concerning a pair of students’ beginning to treat a differential equation as a function of two variables by reasoning with their notions of slope and rate. Specifically we address the students’ transition from seeing a differential equation as solely an algorithm for verifying a function is a solution to a differential equation, to treating the differential equation as a relationship between a function’s rate of change and evaluated value.