Abstract
This chapter provides theoretical and methodological tools, both to reconstruct argumentation structures in mathematical proving processes and to shed light on the rationales of those processes. Toulmin’s functional model of argumentation is used for reconstructing local arguments, and it is extended to provide a ‘global’ model of argumentation for reconstructing proving processes in the mathematics classroom. Several examples drawn from empirical research are included, illustrating each stage of the methods used. Comparison of argumentation structures reveals differences in the rationale of proving processes in different mathematics classrooms.
Keywords
This chapter is adapted from Knipping and Reid (2013b).
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In linguistics, a deictic term is an expression, for example a pronoun, that gets its meaning from its context. The meaning of “this” depends on what is being pointed to. The meaning of “I” depends on who is speaking. In philosophy the word “indexical” is used to express the same idea.
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Knipping, C., Reid, D. (2015). Reconstructing Argumentation Structures: A Perspective on Proving Processes in Secondary Mathematics Classroom Interactions. In: Bikner-Ahsbahs, A., Knipping, C., Presmeg, N. (eds) Approaches to Qualitative Research in Mathematics Education. Advances in Mathematics Education. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-9181-6_4
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