文化取徑的數學課程與學習──初始倡議

The Cultural Approach for Mathematics Curriculum Design and Learning Activities—An Initiative

本文是「數學自身是人類諸多文化中的一種次文化，數學文化對於該地區的數學教育有著舉足輕重的影響」此一主張的發展，倡議以數學文化作為數學課程與教學設計的啟發與參照。為表示此倡議合理，本文提出一些支持性的證據。以文化作為課程探究的進路，不僅引用歷史事實，也關注跨文化比較，但在應用各地文化中的數學發展史之餘，更留意器物制度與社會習慣對於數學教育的啟示；因此它座落在民族數學和「數學史與數學教學之關聯」的交集內。此倡議的動機源自於數學存在一個放諸於四海皆準的主流次文化，而個人的數學學習受其當地母文化孕育薰陶，有一定之初始知識、技能與習慣，因此數學的學習可以視為使學生適應一個新文化的過程。就母文化對於數學教育的影響而言，本文首先指出華語對於數學學習的支持：一字一音與內建十進制，接著探討華語數詞的分節結構對學習的影響；其次分析《九章算術》對數學學習與數學觀造成的影響，本文認為有些影響值得維繫，而且它恰好符合時代潮流，另外一些則值得細心察覺，並加以討論。文化取徑並不鎖定母文化，當母文化不足以提供典範時，外地文化必須成為觀摩對象。本文最後在「數與量」的學習內容中舉例，解釋文化取徑的課程探究方式。本文所提之倡議嘗試將「數學史與數學教學之關聯」放在課程層次，從社會文化與民族數學探究數學課程與教學設計的可能性；為表示此倡議有用，本文也嘗試據此理念提出有待實徵研究的問題。

This article suggests that ''mathematics itself is a subculture among many human cultures, and mathematical culture has a decisive influence on mathematics education in the region.'' It is advocated that mathematics culture be used as inspiration and reference for designing mathematics curriculum and teaching activities. This article presents some supporting evidence to show that this initiative is reasonable. The cultural approach for curriculum inquiries quotes historical facts and pays attention to cross-cultural comparisons. In addition to applying the history of mathematics development in various cultures, it also minds the enlightenment of artifact systems and social habits of mathematics education. Therefore, this approach lies within the intersection of ethnomathematics and HPM. The motivation for this initiative comes from the fact that there is a mainstream subculture of mathematics in the world, and an individual's mathematics learning is nurtured by his or her host culture. Therefore, the learning of mathematics can be regarded as the process of adapting students to a new culture. As far as the influence of host culture on mathematics education is concerned, this article first points out the support of the Chinese language for mathematics learning: monosyllabic and built-in decimal system. Then it discusses the impact of the group structure of Chinese numerals on learning. Secondly, it analyzes the impact of ''Nine Chapters on the Mathematical Art'' on mathematics learning and mathematical epistemology. This article believes that some influences are worth maintaining and are just in line with the trend of international views, while others are worthy of careful observation and discussion. However, the cultural approach does not focus on the host culture. When the host culture is not enough to provide a model, foreign cultures must become the object of observation. Finally, this article takes the teaching concept of ''Number and Quantity'' as examples to explain the cultural approach to curriculum inquiry. This initiative attempts to place HPM at the curriculum level and to explore the possibility of a mathematics curriculum from the perspective of sociocultural and ethnomathematics. To show that this initiative is useful for mathematics education researchers, this article also attempts to raise questions that need to be empirically researched based on this concept.