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An illustration of the explanatory and discovery functions of proof

Michael de Villiers

Pythagoras; Vol 33, No 3 (2012), 8 pages. doi: 10.4102/pythagoras.v33i3.193

Submitted: 02 September 2012
Published:  30 November 2012

Abstract

This article provides an illustration of the explanatory and discovery functions of proof with an original geometric conjecture made by a Grade 11 student. After logically explaining (proving) the result geometrically and algebraically, the result is generalised to other polygons by further reflection on the proof(s). Different proofs are given, each giving different insights that lead to further generalisations. The underlying heuristic reasoning is carefully described in order to provide an exemplar for designing learning trajectories to engage students with these functions of proof.

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Author affiliations

Michael de Villiers, Mathematics Education, University of KwaZulu-Natal, Edgewood Campus, South Africa

Keywords

discovery; explanation; generalisation; proof; Viviani’s theorem

Metrics

Total abstract views: 5274
Total article views: 16093  

Cited-By

1. Rethinking the discovery function of proof within the context of proofs and refutations
Kotaro Komatsu, Yosuke Tsujiyama, Aruta Sakamaki
International Journal of Mathematical Education in Science and Technology  vol: 45  issue: 7  first page: 1053  year: 2014  
doi: 10.1080/0020739X.2014.902135

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ISSN: 1012-2346 (print) | ISSN: 2223-7895 (online)

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