Abstract
This article briefly reviewed How Chinese Learn Mathematics and thereby synthesized author’s own studies concerning HPM. The aim was to abstract some relevant concepts upon which this study based to analyze mathematical reasoning of traditional Chinese mathematicians Liu Hui, Xu Guangqi, Mei Wending and Li Shanlan. As for the methodology, this study adopted the analysis of historical literature as well as comparative historiography. On the one hand, this study contrasted Liu Hui and Euclid, Liu Hui and Archimedes as well as Liu Hui and Heron in order to understand how Liu Hui makes reasoning on his own terms. On the other hand, this study investigated how Xu Guangqi, Mei Wending and Li Shanlan adapted the Western mathematics and integrated it with the Chinese mathematics under the influence from Western mathematics. The basic tool for comparative study was Mei Wending and Li Shanlan’s proof on Heron’s formula. As concluding remarks, the author comes to suggest three different connections, namely those between two forms of conceptual knowledge, between one form of conceptual and one procedural, as well as between two forms of procedural knowledge, can be used to characterize some aspects of traditional Chinese mathematical argumentation in which the four mathematicians had due role to play. Since these terms are due to mathematics education, the author hopes this article can serve as a demonstration for integration of researches in mathematics education and those in history of mathematics.
| Keywords: | conceptual knowledge; procedural knowledge; reasoning; synthesis of proposition and diagram; traditional Chinese mathematician |
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