Student perspectives on the relationship between a curve and its tangent in the transition from Euclidean Geometry to Analysis

Abstract

The tangent line is a central concept in many mathematics and science courses. In this paper we describe a model of students' thinking - concept images as well as ability in symbolic manipulation - about the tangent line of a curve as it has developed through students' experiences in Euclidean Geometry and Analysis courses. Data was collected through a questionnaire administered to 196 Year 12 students. Through Latent Class Analysis, the participants were classified in three hierarchical groups representing the transition from a Geometrical Global perspective on the tangent line to an Analytical Local perspective. In the light of this classification, and through qualitative explanations of the students' responses, we describe students' thinking about tangents in terms of seven factors. We confirm the model constituted by these seven factors through Confirmatory Factor Analysis. ABSTRACT FROM AUTHOR]; Copyright of Research in Mathematics Education is the property of Routledge and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)