An illustration of the explanatory and discovery functions of proof | Zendy

Michael De Villiers | Zendy

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An illustration of the explanatory and discovery functions of proof

Author(s) -

Michael De Villiers

Publication year - 2012

Publication title -

pythagoras

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.374

H-Index - 7

eISSN - 2223-7895

pISSN - 1012-2346

DOI - 10.4102/pythagoras.v33i3.193

Subject(s) - mathematical proof , conjecture , calculus (dental) , heuristic , computer science , proof of concept , proof complexity , combinatorial proof , mathematics , algebra over a field , artificial intelligence , pure mathematics , discrete mathematics , geometry , medicine , dentistry , operating system

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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