日本「遺題繼承」傳統下的「蟲蛀算」：經由古文本以及大學生實作之分析

“Mushikuizan”Under the Japanese Tradition of“Bequeathed Problems”: Through the Analysis of Ancient Texts and University Students’Work

「遺題繼承」的傳統是促使日本傳統數學（和算）發展的一大因素，和算家在所著的和算書卷末，提出一些數學難題，讀者經過努力研究，解決難題之後，一般要著解答之書，並在卷末提出難度更高的問題，讓有心人士去研究解決。本研究從教學轉置觀點，探究日本「遺題繼承」傳統下的蟲蛀算問題，並展示如何將這些原典及其脈絡轉置於今日的數學教學和學習。本研究運用Yves Chevallard及後續學者所提出的教學人類學理論，分析江戶時代和算家所產生的「原始」數學知識，發展兩節課100分鐘的大學課程。研究者介紹日本「遺題繼承」的傳統，以及「蟲蛀算」問題；經由學習工作單分析學生實際解題所使用的數學知識，也運用學習意見表探討大學數學系學生對於「蟲蛀算」學習之回應。經由研究得知，行知模型可做為分析數學史文本及刻畫學生解題所用數學知識之工具；「蟲蛀算」主題，也可以讓學生經驗到數學思考、數學的文化體驗以及對數學的觀點三個面向的潛能。

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.