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

By Irene Biza, C. Christou, T. Zachariades. 2008

49 citations recorded by the source corpus.

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.

Subfields: Education, Theoretical Computer Science

View Paper: https://www.semanticscholar.org/paper/375698cf2cecd7f728ea32eb92661725592c192d

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In Education

1. Irene Biza
2. Elena Nardi
3. T. Zachariades
4. G. Lewis

Citations in the corpus

• ‘Warrant’ revisited: Integrating mathematics teachers’ pedagogical and epistemological considerations into Toulmin’s model for argumentation (2012, result): “Therefore, teacher knowledge is likely to be better explored in situation-specific contexts (Biza et al., 2007). In this sense, our study’s aims and rationale resonate with those of several other researchers: Herbst and colleagues’ (e.g. Herbst & Chazan, 2003; Miyakawa & Herbst, 2007) eliciting teac”