微积分的辩证思想及其文化价值透视

Dialectical Thought of Calculus and Its Perspective of Cultural Value

微积分作为人类智慧的结晶,可以解读人类社会中许多思想认知,其中包括有重要教育意义的辩证思想。以数学方法论为指导,从历史及文化视角对微积分中的常量与变量、有限与无限、特殊与一般、整体与局部等对立统一关系进行了具体分析,由此揭示相关知识的内在联系,并给出方向性的教学建议。依据微积分中否定之否定、量变质变规律的具体体现,通过微积分辩证思想应用的实例分析,透视出其中的文化价值。

As the crystallization of human wisdom,calculus can interpret many thoughts and cognition in human society,including dialectical thoughts with important educational significance.Under the guidance of mathematical methodology,this paper analyzes the unity of opposites in calculus from historical and cultural perspectives,such as constants and variables,finite and infinite,special and general,whole and local and so on.Therefore,the inner relation of related knowledge is revealed,and the directional teaching suggestions are given.According to the concrete manifestation of the laws of the negation of negation and quantity and qualitative change in calculus,the cultural value of the dialectical thought of calculus through the instance analysis is affirmed.