從數學與文化的關係探討數學文化素養之內涵──理論與案例分析

Discourse on the Constituent of Literacy for Mathematical Culture in Terms of the Relationship between Mathematics and Culture - Theoretical and Case Analysis

數學是人類重要的智識遺產，可是卻鮮少人注意它和文化的關係。本文嘗試從數學與文化的關係出發，特別是數學與東西方文化的互動關係，探討數學文化的內涵，並主張數學文化包含「文化中的數學」和「數學中的文化」兩大構面。再者，數學素養一詞雖為大眾所耳熟能詳，然對其真正概念仍認識不清，而目前文獻對其內涵的論述仍然莫衷一是，難以釐清，甚至國際間的用詞也不盡相同。本文整理國際間數學素養相關文獻，分析相關詞彙定義的異同之處，以具體界定數學素養的概念。此外，本研究結合數學文化和數學素養，進一步提出數學文化素養的定義。希望透過培養學生的數學文化素養，能增進他們對數學本質的理解和學習認同。為釐清數學文化素養的概念，本文分別從「文化中的數學」和「數學中的文化」兩大構面中各介紹與分析一個具體案例，以做為數學文化素養之參考教材。我們希望經由定義數學文化素養、論述數學文化素養的內涵、和實際分析數學文化案例等程序，能夠建立一個概念框架，以做為數學文化相關的教學、評量、與實證研究的理論基礎。

Mathematics is a vital intellectual heritage of human beings, but few are aware of its relationship with culture. This study attempted to identify the constituents of mathematical culture in terms of the interrelationship between mathematics and culture, particularly the interaction of mathematics with Eastern and Western culture. We claim that mathematics in culture and culture in mathematics are the two main facets of mathematical culture. Furthermore, though the term “mathematical literacy” is well-known by the general public in Taiwan, its components and constituents are interpreted differently in the educational literature. In this study, we conducted an international comparison by reviewing and organizing relevant literature discussing mathematical literacy, and clarified the vagueness of similar concepts to find commonalities. This study then defined literacy for mathematical culture by integrating mathematical culture and mathematical literacy. Hopefully educating students in literacy for mathematical culture may increase students’ understanding of the nature of mathematics and their positive attitudes toward the learning of mathematics. In addition, we propose two exemplary cases, one for mathematics in culture and the other for culture in mathematics, to illustrate the prototype of the literature for mathematical culture. We hope that our works of defining the literacy for mathematical culture, discussing the constituents of literacy for mathematical culture, and analyzing the exemplary cases of mathematical culture may provide as a theoretical framework for the teaching, assessment, and empirical study of mathematical culture.