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

Biza, Irene, Christou, Constantinos and Zachariades, Theodossios (2008) Student perspectives on the relationship between a curve and its tangent in the transition from Euclidean Geometry to Analysis. Research in Mathematics Education, 10 (1). pp. 53-70. ISSN 1479-4802

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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.

Item Type: Article
Uncontrolled Keywords: tangent line,concept image,analysis
Faculty \ School: Faculty of Social Sciences > School of Education and Lifelong Learning
Depositing User: Pure Connector
Date Deposited: 29 Nov 2013 14:44
Last Modified: 24 Jun 2020 23:48
URI: https://ueaeprints.uea.ac.uk/id/eprint/44743
DOI: 10.1080/14794800801916457

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