PROCEEDINGS OF THE 19TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2016
Pittsburgh, Pennsylvania
Students’ concept image of tangent line compared to their understanding of the definition of the derivative
Page: 1360
Our research explores first-semester calculus students' understanding of tangent lines and the derivative concept through a series of three interviews conducted over the course of one semester. Using a combination of Zandieh's (2000) derivative framework and Tall and Vinner's (1981) notions of concept image and concept definition, our analysis examines the role that students' concept image of tangent lines plays in their conceptual understanding of the derivative concept. Preliminary results seem to indicate that students are more successful when their concept image of tangent includes the limiting position of secant lines, as opposed to a tangent line as the line that touches the curve at one point.