论数学知识的三种形态

On Three Forms of Mathematical Knowledge

一般认为数学知识有学术和教育两种形态,两者之间的关系对数学教育具有重要的意义。数学教材的编写者和教师就是要把数学的学术形态有效转化为教育形态。数学知识产生发展过程,数学学术形态的形成过程,是数学家与数学工作者劳动的结果。数学在成为教育形态时,不能回避数学史、数学的思考、发明创造过程,某一时期的数学结果,就是数学的历史形态,它的特征与数学的学术形态和教育形态之间有密切的关系。

It is generally believed that there are two forms of mathematical knowledge： academic form and education form. The relationship between them is of great significance to mathematics education. The compilers and teachers of mathematics textbook should transform the academic form of mathematics into education form. The development of mathematical knowledge as well as the formation of the academic form of mathematics is the result of the work of mathematicians and mathematics workers. When mathematics has become a form of education,the history of mathematics cannot be avoided. The thinking of mathematics and the process of the invention and creation,the mathematical result in a certain period of time all illustrates the history form of mathematics. The characteristics of history form are closely related to the academic and educational forms of mathematics.