內外有別的知識價值：文化如何影響數學知識的教育與傳播？以十七至十九世紀的朝鮮與日本為例

Internal Values vs. External Values: How Cultures Influence the Education and Transmission of Mathematical Knowledge? Taking Korea and Japan in the 17^(th) to 19^(th) Centuries as Examples

英家銘(Jia-Ming Ying) ； 黃俊瑋(Jyun-Wei Huang)

《臺灣教育哲學》 5卷1期 (2021/03) Pp. 1-31

https://doi.org/10.7001/JTPE.202103_5(1).0001

摘要

本研究從文化的視角入手，探索古代東亞社會與數學的關聯。在介紹早期東亞國家的數學文化脈絡之後，本文比較十七至十九世紀朝鮮與日本的數學文化，即「東算」（Tongsan）與「和算」（Wasan），並說明文化如何影響數學知識的教育與傳播。整體而言，朝鮮「東算」發展時，資源的限制使得知識的傳遞無法擴及兩班貴族與中人技術官僚階級之外，事大慕華思想使東亞古代的算學經典受到重視，而科舉考試的制度讓知識的內涵變得穩定不易失傳，以上這些原因讓東算具有強烈的官學性格，在算學內容發展上偏向應用，反映出國家「治理」的需要以及對算學外在價值的追求。相對來說，日本「和算」的發展，如同東亞地區其他文化的數學發展一樣，起初來自真實世界的需要，例如工程、測量與曆法等等，但江戶時代的鎖國環境、經濟發展，加上日本自古以來各種技能的「藝道化」，使得日本和算的發展與教育模式十分獨特，發展出「遺題承繼」、「算額奉納」與「流派競爭」等特色，也就是在真實世界的應用之外，和算家為了崇敬神佛與超越競爭對手而研究數學，且算學內容也包含跨越階級與性別的「趣味」元素，某種程度展現出對算學內在價值的追求。由此可見，即使是算學這樣技術性的學問，也會受到文化的影響，而有不同的表現方式。

關鍵字

數學知識傳播 ； 數學教育 ； 東算 ； 和算

並列摘要

This study explores the relationship between pre-modern East-Asian societies and mathematics from the perspective of culture. After introducing the context of early mathematics cultures in East Asia, this paper compares the mathematics cultures of Chosŏn Korea (1392-1910) and Edo Japan (1603-1867) in the 17^(th) to 19^(th) centuries, which are known as Tongsan and Wasan respectively. This paper then explains how cultures influence the education and transmission of mathematical knowledge. Generally speaking, when Tongsan was developing, the limited resources prevented the transmission of knowledge beyond the noble yangban class and the chungin class of technocrat. The admiration of Chinese culture maintained the canonical statuses of medieval Chinese mathematical treatises, and the system of state examination stabilised the contents of mathematical knowledge without losses. All those features gave Tongsan a strong character of ＂official study＂, and directed its developments towards application, reflecting the need of ＂governance＂, and the pursuit for the external values of mathematics. In contrast, although Wasan started from real-world necessities such as engineering, measurement and calendar, the isolationist policy of Edo shogunate, the development of economy, and the trend of forming schools of thoughts for technical arts all contributed to making Wasan a unique culture with features of ＂bequeathed problems＂, ＂dedication of mathematical tablets＂, and ＂competition of schools＂. Hence, besides real-world applications, Wasan scholars practised mathematics to honour deities and surpass competitions. Culture was enriched by practitioners of different social statuses and genders, which demonstrated elements of ＂fun＂. All these reflect, to some extent, a pursuit for the internal values of mathematics. Therefore, even a technical study such as mathematics can be influenced by cultures and manifests itself in very different manners.

並列關鍵字

transmission of mathematical knowledge ； mathematics education ； Tongsan ； Wasan

參考文獻

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