Procedural Aspects of Mathematical Knowledge in the Suan Shu Shu

Author: Wann-Sheng Horng (Department of Mathematics, National Taiwan Normal University)

Vol.&No.：Vol. 50, No. 1
Date：April 2005
Pages：75-89
DOI：10.6210/JNTNULL.2005.50(1).05

Abstract：

In this article the author will explore the Suan Shu Shu in terms of the notion of procedural knowledge. In the past three decades, historians of Chinese mathematics have successfully adopted the term "algorithm" - a concept from computer science - to characterize some aspects of ancient Chinese mathematics. Thus we can now refer to research in mathematics education in order to enrich our historical understanding of ancient Chinese mathematics. In some sense, the study of mathematics and the study of the history of mathematics can benefit each other, and the same goes for studies of the history of mathematics and studies in mathematics education. Therefore, here I will first contrast procedural knowledge with conceptual knowledge and show the relevance of this contrast to studies in mathematical reasoning. By looking carefully into the mode of presenting and solving problems in the Suan Shu Shu, I will then investigate how these problems can be explained in terms of procedural knowledge and/or Gray & Tall's notion of the "procept". In conclusion, I will try to show the connection between and among some aspects of the ancient text's methodology in order to clarify the types of mathematical reasoning involved here.

Keywords：Procedural knowledge, Suan Shu Shu, History of mathematics, HPM, Procept

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