An illustration of the explanatory and discovery functions of proof

Pythagoras

Michael de Villiers¹ 

[1] Mathematics Education, University of KwaZulu-Natal, Edgewood Campus;

关键词: discovery;    explanation;    generalisation;    proof;    Viviani’s theorem;   

DOI  :  10.4102/pythagoras.v33i3.193

来源: DOAJ

【 摘 要 】

This article provides an illustration of the explanatory and discovery functions of proof withan 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.

【 授权许可】

Unknown