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数学包括数学知识和蕴涵于知识中的数学思想方法两个部分。概念、定理、公式等知识是数学的外在的表现形式,而数学思想方法则是将数学知识转化为数学能力的内在动力,是发现概念、定理、公式的具体行为过程,促进着数学的发展。概念、定理、公式等可以通过资料而获得,但数学思想方法只能通过长时间的知识积累、探索数学家的思维发展过程、模仿数学家的思维发展过程去获得。换而言之,概念、定理、公式等只要看数学家的研究结论就可以获得,但数学思想方法就要“参与”数学家的研究过程才能获得。
Mathematics includes mathematical knowledge and mathematical thinking in the knowledge contained in two parts. Concepts, theorems, formulas and other knowledge are the external manifestations of mathematics. Mathematical thinking methods are the intrinsic motivation to translate mathematics knowledge into mathematical abilities. They are the specific behavior processes of discovering concepts, theorems and formulas, and promoting the development of mathematics . Concepts, theorems and formulas can be obtained through data. However, mathematical thinking and methods can only be obtained through prolonged accumulation of knowledge, exploring the process of thinking development of mathematicians and imitating the process of thinking development of mathematicians. In other words, concepts, theorems, formulas, etc. can be obtained only from mathematicians’ conclusions, but mathematic methods must be “involved” mathematically.