In-Service Secondary Mathematics Teachers’ Conceptions of Tangent Lines in Calculus

Abstract

Previous investigations into first year calculus students’ understandings of tangent lines have revealed common misconceptions arising either from students’ prior experiences with the topic or from the treatment of the subject in the calculus classroom. This study seeks to examine in-service secondary mathematics teachers’ conceptions of tangent lines to see if similar misconceptions are held by this group. To this end, we conducted one-on-one interviews with 16 secondary-certified mathematics educators in which they were asked to complete an assessment which had them define, identify, and construct tangent lines. After analyzing the results, we found that the majority of the teachers that were interviewed did hold misconceptions that were similar to those misconceptions that are commonly held by first year calculus students.