Friedenthal was born in 1905, and received his doctorate from the University of Berlin in 195 1. He is an academician of 197 1- 1976. He is the director of the Netherlands Institute of Mathematics Education, and was a student of mathematician Brouwer in his early years. Friedenthal is very concerned about education. He has long regarded mathematics education as the object of his own thinking and research. Freudenthal is different from other scientists in this respect. Friedenthal published hundreds of books (departments) on mathematics education in his life, among which four representative works were published in many languages, which had a great influence in the world. They are: mathematics as an educational task, sowing and weeding, and the teaching phenomenon of mathematical structure.

Friedenthal's mathematics education thought mainly includes: emphasizing that mathematics education must face social reality, must be linked with daily life reality, and pay attention to cultivating and developing students' ability to discover mathematics problems from objective phenomena; Use the method of re-creation to teach, and oppose indoctrination and rote learning; Advocate discussion and guidance of teaching forms, and oppose the traditional lecture teaching forms.

His educational thought can be summarized in three words: mathematical truth, mathematization and re-creation.

Mathematical truth means that mathematics comes from reality, is also rooted in reality, and is applied to reality. This is the starting point of Freudenthal's mathematics education theory, and mathematics is a systematic summary of human experience in the real world. Judging from the development history of mathematics, both mathematical concepts and mathematical theorems and formulas are gradually formed based on the needs of the real world.

In his view, mathematicization means that people use mathematical methods to observe the real world, analyze and study various specific phenomena, and organize them. This process is mathematization. Simply put, the process of organizing the real world by mathematical methods is mathematization. Friedenthal believes that it is better to learn "mathematicization" than to learn mathematics; It is not so much a learning axiom system; It has not been said that learning is "axiomatic"; Rather than learning a formal system, it is better to say that learning is "formalized".

Specifically, the mathematization mentioned in realistic mathematics education is divided into two levels: horizontal mathematization and vertical mathematization. Horizontal mathematicization refers to the transformation from practical problems to mathematical problems, and from "life" to "symbol". Vertical mathematicization is the transformation from concrete problems to abstract concepts and from "symbols" to "concepts".

Re-creation is the core part of Freudenthal's mathematics education theory, which is based on the fact that mathematics is a human activity. He repeatedly stressed that the only correct way to learn mathematics is to implement re-creation, and the task of teachers is to guide and help students to do this re-creation work, rather than instilling ready-made knowledge into students. The process of mathematical development should be reproduced in individuals, not mechanically. Judging from the development of mathematics, this is in line with the law of human cognition.

But in reality, the arrangement of teaching materials is to reverse the thinking process and deduce other things from the results. Friedenthal called it "the inversion of teaching methods", which concealed the thinking process of mathematical creation. Without re-creation, it is difficult to really understand mathematics, let alone apply it.