What for Proof vis-a-vis Education Reform Issues? Author: Wann-Sheng Horng(Department of Mathematics, National Taiwan Normal University)

Vol.&No.：Vol. 49, No.1
Date：April 2004
Pages：1-14
DOI：10.6300/JNTNU.2004.49(1).01

Abstract：

Mathematical capabilities like problem-solving, communication and connection have been primarily concerned by mathematics educators since 1980s. Underlying these capabilities there is a crucial denominator, namely, mathematical argumentation. In this article, the author will try to make a sketchy review on the related research publications. In the light of HPM, my theme will first be to remind designer of mathematics curriculum / editors of textbooks of the logical fallacy manifested with some conventional geometrical arguments. Take for example, logical order of geometrical propositions suggested by the Mathematics Framework for California Public Schools will apparently commit circular fallacy in the context of Euclid's Elements. Based on Freudenthal / Hanna & Jahnke's idea of "local organization", I will then go on to argue that a compromise between methodological visualization and logical rigor could be reached by teachers in the context of classroom practice. This may well explain how researches on HPM can benefit mathematics educators / teachers in a way that they can make proof more sense in their teaching as one can learn from Clairaut and Liu Hui. As a conclusion, I hope my argument in terms of the HPM has shown that proof should be presented not only to make convincing but more importantly, to explain mathematical knowledge.

Keywords：mathematical argumentation, proof, ancient texts, HPM

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