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Proof and Proving in Mathematics Education pp 215–229Cite as

The Need for Proof and Proving: Mathematical and Pedagogical Perspectives

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

Abstract

This chapter first examines why mathematics educators need to teach proof, as reflected in the needs that propelled proof to develop historically. We analyse the interconnections between the functions of proof within the discipline of mathematics and the needs for proof. We then take a learner’s perspective and discuss learners’ difficulties in understanding and appreciating proof, as well as a number of intellectual needs that may drive learners to prove (for certitude, for causality, for quantification, for communication, and for structure and connection). We conclude by examining pedagogical issues involved in teachers’ attempts to foster necessity-based learning that motivates the need to prove, in particular the use of tasks and activities that elicit uncertainty, cognitive conflict and inquiry-based learning.

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Acknowledgements

We wish to thank Larry Sowder and the reviewers for their helpful comments on an earlier version of this paper.

Author information

Authors and Affiliations

  1. Department of Teaching and Learning, New York University, New York, NY, USA

    Orit Zaslavsky

  2. Department of Education in Technology and Science Technion – Israel Institute of Technology, Haifa, Israel

    Orit Zaslavsky

  3. Department of Mathematics and Statistics, San Diego State University, San Diego, CA, USA

    Susan D. Nickerson

  4. Faculty of Education, University of Cambridge, Cambridge, UK

    Andreas J. Stylianides

  5. Applied Mathematics Department, Jerusalem College of Technology (JCT), Jerusalem, Israel

    Ivy Kidron

  6. Department of Mathematics and Statistics, California State Polytechnic University, Pomona, CA, USA

    Greisy Winicki-Landman

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  1. Orit Zaslavsky
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  4. Ivy Kidron
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Correspondence to Orit Zaslavsky .

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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

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Zaslavsky, O., Nickerson, S.D., Stylianides, A.J., Kidron, I., Winicki-Landman, G. (2012). The Need for Proof and Proving: Mathematical and Pedagogical Perspectives. 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_9

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