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The Argument of Mathematics pp 119–146Cite as

Revealing Structures of Argumentations in Classroom Proving Processes

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Part of the book series: Logic, Epistemology, and the Unity of Science ((LEUS,volume 30))

Abstract

Proving processes in classrooms follow their own peculiar rationale. Reconstructing structures of argumentations in these processes reveals elements of this rationale. This chapter provides theoretical and methodological tools, both to reconstruct argumentation structures in 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 classroom.

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Notes

  1. 1.

    For an overview of these studies see as well Harel and Sowder (1998) and Hanna (2000).

  2. 2.

    Äuerungen besitzen “a priori keine von allen Beteiligten geteilte gemeinsame Bedeutung, sondern erhalten diese erst in der Interaktion. In konkreten Situationen des Verhandelns bzw. Aushandelns wird nach einer solchen gemeinsamen semantischen Bedeutungsplattform gesucht”.

  3. 3.

    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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Authors and Affiliations

  1. FB3: Didaktik der Mathematik, Universität Bremen, Bibliotheksstraße 1, 28359, Bremen, Germany

    Christine Knipping & David Reid

  2. School of Education, Acadia University, Wolfville, NS, B4P 2R6, Canada

    David Reid

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  1. Christine Knipping
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  2. David Reid
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Correspondence to Christine Knipping .

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Editors and Affiliations

  1. , Dept. Humanities & Communication, Florida Institute of Technology, W. University Blvd. 150, Melbourne, 32901-6975, Florida, USA

    Andrew Aberdein

  2. , Department of Philosophy, University of Nevada, Maryland Parkway 4505, Las Vegas, 89154, Nevada, USA

    Ian J Dove

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Knipping, C., Reid, D. (2013). Revealing Structures of Argumentations in Classroom Proving Processes. In: Aberdein, A., Dove, I. (eds) The Argument of Mathematics. Logic, Epistemology, and the Unity of Science, vol 30. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-6534-4_8

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