PROCEEDINGS OF THE 17TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2014
Denver, Colorado
Calculus Students’ Early Concept Images of Tangent Lines
Page: 803
In this study, we use Newton’s method as a means to examine first-semester calculus students’ understanding of tangent lines. Within that context, we found that many students had difficulty sketching and describing tangent lines. We examined the language students use to describe tangent lines as well as their graphical illustrations of tangent lines. Task-based interviews were conducted with twelve first-semester calculus students who were asked to verbally describe a tangent line, sketch tangent lines for multiple curves, and use tangent lines within the context of Newton’s method. Six prominent categories describing students’ concept images of tangent lines emerged, and we found that individual students often possessed multiple concept images. Furthermore, data shows that these concept images were often conflicting, and students were usually willing to modify their concept images in different contexts.