The tradition of "bequeathed problems" is a major factor in promoting the development of Wasan. Japanese mathematicians put forward some unsolved problems at the end of mathematics books. Other readers who solved these problems generally wrote books about their solutions, and at the end of these books, they asked more difficult questions and encouraged those willing to study and solve them. In this study, the researchers investigate “Mushikuizan” under the Japanese tradition of “bequeathed problems” from a perspective of didactic transposition to unfold how such historical problems and contexts could be transposed to mathematics teaching and learning today. This study is conducted from the perspectives proposed within the Anthropological Theory of the Didactic developed by Yves Chevallard and subsequent scholars. Specifically, the researchers analyze the "original" mathematical knowledge produced by Japanese mathematicians in the Edo period; develop two classes in the university course introducing the tradition of Japanese "bequeathed problems" and the problems of "Mushikuizan"; and investigate students’ reactions to these classes through the worksheets comprising students´ work and feedback. In the analysis, the notion of praxeology is used to better understand the mathematical knowledge required to solve “Mushikuizan” problems and the mathematical knowledge used by students. Through research, we found that the notion of praxeology can be used as a tool to analyze the historical texts of mathematics and describe the mathematical knowledge used by students to solve problems; the theme of "Mushikuizan" allows students to experience three aspects of mathematical thinking, cultural experience of mathematics, and understanding of mathematics.
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“Mushikuizan” Under the Japanese Tradition of “Bequeathed Problems”: Through the Analysis of Ancient Texts and University Students’ Work
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