(A) the principle of "mathematical truth"

When using "realistic mathematics" in teaching, we must clearly understand the following points:

First, the content of mathematics teaching comes from the real world, and the most basic and core mathematical knowledge and skills that can best reflect the needs of modern production and modern social life are taken as the content of mathematics education.

Second, the content of mathematics education should not only be confined to the internal relations of mathematics, but also study the external relations and relations between mathematics and various fields in the real world. Only in this way can students acquire rich and complicated contents of "realistic mathematics" and master a relatively complete mathematical system. On the other hand, students can also apply their mathematics knowledge to the real world.

Third, mathematics education should serve all people and meet the needs of people of different levels in all fields of society for different levels of mathematics.

"Mathematics" principle

Friedenthal believes that mathematics teaching must be carried out through mathematization.

There are two forms of mathematization in realistic mathematics education: one is to transform practical problems into mathematization of mathematical problems, that is, to find the mathematical components in practical problems and symbolize them; The second is the mathematicization from symbol to concept, that is, the problem of symbolization is further abstracted in the mathematical category.

For the former, the basic process is:

1, to determine the mathematical components contained in a specific problem;

2. Establish the relationship between these mathematical components and students' known mathematical models;

3. Visualize, symbolize and formulate these mathematical components in different ways;

4. Find out the relationships and laws;

5. Consider the embodiment of the same mathematical composition in other fields of mathematical knowledge;

6. Make a formal statement.

"re-creation" principle

The core of Friedenthal's "re-creation" is the representation of mathematical process. The process of students "recreating" learning mathematics is actually a process of "doing mathematics", which is also an important viewpoint in current mathematics education.

What needs special attention is that Freudenthal's mathematics education theory is not a discussion of "pedagogy plus mathematics examples", but grasps the characteristics of mathematics education and closely follows the special process of mathematics education, so it has many unique concepts such as "mathematical reality", "mathematization", "mathematical reflection" and "speculative mathematics". Most of his works are based on his own experience in learning mathematics and observing children's experience in learning mathematics, and there are many speculative discussions.