PROCEEDINGS OF THE 18TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2015
Pittsburgh, Pennsylvania
An extended theoretical framework for the concept of the derivative
Page: 919
This paper extends the theoretical framework for exploring student understanding of the concept of the derivative, which was developed by Zandieh (2000). We expand upon the concept of a physical representation for the derivative by extending Zandieh's map of the territory to provide higher resolution in regions that are of interest to those operating in a physical context. We also introduce the idea of "thick" derivatives, which are ratios of small but not infinitesimal changes, which are practically equivalent to the true derivative.