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Proof, Proving, and Teacher-Student Interaction: Theories and Contexts

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Proof and Proving in Mathematics Education

Part of the book series: New ICMI Study Series ((NISS,volume 15))

Abstract

This chapter focuses on the teachers’ role in teaching proof and proving in the mathematics classroom. Within an over-arching theme of diversity (of countries, curricula, student age-levels, teachers’ knowledge), the chapter presents a review of three carefully selected theories: the theory of socio-mathematical norms, the theory of teaching with variation, and the theory of instructional exchanges. We argue that each theory starts by abstracting from observations of school mathematics classrooms. Each then uses those observations to probe into the teachers’ rationality in order to understand what sustains those classroom contexts and how these might be changed. Here, we relate each theory to relevant research on the role of the teacher in the teaching and learning of proof and proving. Our review offers evidence and support for mathematics educators meeting the challenge of theorising about proof and proving in mathematics classrooms across diverse contexts worldwide.

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Authors and Affiliations

  1. Mathematics and Science Education Research Centre, School of Education, University of Southampton, Highfield, Southampton, UK

    Keith Jones

  2. School of Education, University of Michigan, Ann Arbor, MI, USA

    Patricio Herbst

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  1. Keith Jones
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  2. Patricio Herbst
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Correspondence to Keith Jones .

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Editors and Affiliations

  1. Ontario Institute for Studies in Education (OISE), University of Toronto, Toronto, ON, Canada

    Gila Hanna

  2. Faculty of Education, University of KwaZulu-Natal, Edgewood Campus, Ashwood, South Africa

    Michael de Villiers

Additional information

*NB: References marked with * are in F. L. Lin, F. J. Hsieh, G. Hanna, & M. de Villiers (Eds.) (2009). ICMI Study 19: Proof and proving in mathematics education. Taipei, Taiwan: The Department of Mathematics, National Taiwan Normal University.

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Jones, K., Herbst, P. (2012). Proof, Proving, and Teacher-Student Interaction: Theories and Contexts. In: Hanna, G., de Villiers, M. (eds) Proof and Proving in Mathematics Education. New ICMI Study Series, vol 15. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-2129-6_11

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