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What are the basic viewpoints of Friedenthal's mathematics education theory?
H freudenthal (1905— 1990) is an internationally renowned Dutch mathematician and mathematics educator. Friedenthal directed, promoted and personally participated in the reform of mathematics education in the Netherlands, and made great contributions to the reform and development of international mathematics courses in the 20th century.

Freudenthal was born in 1905, and received his doctorate from the University of Berlin in 1930. From 195 1, from 197 1- 1976, he was an academician of the Royal Dutch Academy of Sciences and the director of the Dutch Institute of Mathematics Education. Friedenthal is a famous mathematician Brouwer.

As a famous mathematician, 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. Other high-level scientists often begin to pay attention to and invest in education after they are old, and Friedenthal was attracted by education from an early age. He himself has a very simple explanation: I have been a teacher all my life. The reason why I began to think about education from a very young age is to do a good job in teaching. As early as 1936, 3l-year-old Freudenthal organized the famous "Research Group on Mathematics Education" (WVO) in the Netherlands and became the leader of mathematics education research in the Netherlands. At that time, this group gathered in Freudenthal's home every weekend to discuss the development of mathematics education. During World War II, the activities of the research group could not be carried out due to the war, but Friedenthal still did not stop his research work. 1945, just after World War II, WVO held its first post-war seminar. Rajthar made a report entitled "Education of Thinking" at the meeting. This paper expounds his views on the problem of arithmetic education that has occupied his mind for a long time: children can't learn new mathematics knowledge by playing with Ze Law. In the long-term practice of mathematical education research, Friedenthal has gradually formed a mathematical education ideological system that adapts to children's psychological development, conforms to educational laws, can stand the test of practice and has its own unique style. His accumulated research results and practical experience not only changed the face of mathematics education in the Netherlands, but also exchanged ideas around the world. It has greatly promoted the development of international mathematics education research. As a mathematician with international prestige, he has been the chairman of the Dutch Mathematics Education Committee since 1954 and the International Mathematics Education Committee (ICMl) since 1967. He is also the founder of the most influential international mathematical education publication "Research on Mathematical Education".

Friedenthal published hundreds of books (departments) on mathematics education in his life, among which three 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. In these works, Freudenthal elaborated the reasons why traditional mathematics education must be reformed: systematically expounded the theoretical system of realistic mathematics education thought; This paper specifically discusses how to design mathematics courses and compile mathematics textbooks according to the viewpoint of realistic mathematics education. Many of his conclusions were drawn after long-term practice in primary and secondary schools. His work laid a theoretical and practical foundation for realistic mathematics education, and made clear the goal and direction of modern mathematics education reform.

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.

1987, Friedenthal, who was over eighty years old, visited China. He gave a speech in the Department of Mathematics of East China Normal University. The first thing he said when he stepped onto the platform was: "In Holland, the desks and chairs in middle school classrooms are arranged in circles, and teachers are active among students. If there is a school classroom with desks and chairs like today, with a podium in front and rows of desks and chairs below, then the principal of this middle school will probably be dismissed. At this time, a burst of laughter broke out in the classroom, which also caused people to think. His speech provided a new idea for China's mathematics education reform, and his thoughts had a positive and far-reaching impact on China's mathematics education research. Friedenthal devoted his life to mathematics and mathematics education. As the greatest and most influential mathematics educator in the 20th century, many of his viewpoints will affect the reform and development of mathematics education in the world.