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

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journal contribution
posted on 28.09.2011 by Irene Biza, Constantinos Christou, Theodossios Zachariades
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.

History

School

  • Science

Department

  • Mathematics Education Centre

Citation

BIZA, I., CHRISTOU, C. and ZACHARIADES, T., 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

Publisher

Taylor and Francis © British Society for Research into Learning Mathematics

Version

AM (Accepted Manuscript)

Publication date

2008

Notes

This article was published in the journal, Research in Mathematics Education [Taylor and Francis © British Society for Research into Learning Mathematics]. The definitive version is available at: http://www.tandfonline.com/doi/abs/10.1080/14794800801916457

ISSN

1479-4802

Language

en

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