On Three Forms of Mathematical Knowledge

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.