《乡土中国》视角下中国传统数学概念思维缺失及对数学教育的启示

Lack of Conceptual Thinking in Traditional Chinese Mathematics from the “From the Soil” Perspective and Its Implications for Mathematics Education

摘要: 中国古代数学的概念思维并不是太发达，这可以从费孝通《乡土中国》的视角进行追溯其形成的社会学根源并进行解释。中国传统社会是以血缘关系、地缘关系及农业文明为基础的熟人社会。熟人社会相对于西方陌生人的社会而言，对概念思维的形成乃至发展具有消极的影响。在熟人社会中，事物概念往往是约定的，文字有时候也是多余的。熟人社会不易产生法律，也使商品经济发展缓慢，而文字、法律与商品经济对概念思维的形成与发展都有积极的影响。另一方面，熟人社会的封闭性也导致了概念思维的不易形成。这从一个侧面说明了社会结构等情况也影响数学概念思维的形成。这对中国现当代的数学教育改革与发展也有着重要的启示。

Abstract: The conceptual thinking of ancient Chinese mathematics is not very developed, which can be traced back to the sociological root of its formation and explained from the perspective of Fei Xiaotong’s “From the Soil”. Chinese traditional society is an acquaintance society based on blood relationship, geographical relationship and agricultural civilization. Compared with the society of Western strangers, acquaintance society has a negative impact on the formation and development of conceptual thinking. In the acquaintance society, the concept of things is often agreed, and the words are sometimes redundant. Acquaintance society is not easy to produce law, but also makes the development of commodity economy slow. Words, law and commodity economy have a positive impact on the formation and development of conceptual thinking. On the other hand, the closeness of acquaintance society also leads to the difficult formation of conceptual thinking. This shows that the social structure also affects the formation of mathematical conceptual thinking. This also has important enlightenment for the reform and development of modern and Contemporary Mathematics Education in China.