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

Irene Biza, Constantinos Christou, Theodossios Zachariades

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23 Citations (Scopus)
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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.
Original languageEnglish
Pages (from-to)53-70
Number of pages18
JournalResearch in Mathematics Education
Issue number1
Publication statusPublished - 1 Mar 2008


  • tangent line
  • concept image
  • Analysis

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