Search this journal:     Advanced search
Original Research

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


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.

Full Text:  |  HTML  |  EPUB  |  XML  |  PDF (620KB)

Author affiliations

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


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


Total abstract views: 5274
Total article views: 16093  


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

Comments on this article

Before posting your comment, please read our policy.
Post a Comment (Login required)

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

Connect on: Facebook, Twitter, Google+, LinkedIn and YouTube

Subscribe to our newsletter

All articles published in this journal are licensed under the Creative Commons Attribution 4.0 International (CC BY 4.0) license, unless otherwise stated.

Website design & content: ©2017 AOSIS (Pty) Ltd. All Rights Reserved. No Unauthorised Duplication Allowed.

AOSIS Publishing | Empowering Africa through access to knowledge
Postnet Suite #110, Private Bag X19, Durbanville, South Africa, 7551
Tel: 086 1000 381
Tel: +27 21 975 2602
Fax: 086 5004 974

publishing(AT) replace (AT) with @

Please read the privacy statement.