(1) He thinks that the traditional mathematical education model is similar to training students into computers. Flandenthal's goal of opposing mathematics education is mainly to "devote himself to the development of intelligence (thinking ability)" He believes that if the value of intellectual education is the main purpose of mathematics education, there is no doubt that the content of mathematics education can only be those well-organized and well-organized mathematical structures, because only in this way can it be convenient to implant a complete set of mathematical structures and logical thinking methods into students' minds. That's the problem. The traditional mathematics education mode makes "most students don't know how to apply the mathematics knowledge learned in class to physics and chemistry learning, let alone how to apply the mathematics knowledge learned in class to daily life." The fundamental reason for this result is that traditional mathematics education adopts a mode of cultivating mathematicians, providing students with some formal mathematical systems and ready-made mathematical results. "Although these systems are perfect, they are also closed, so there is no entrance and exit, which can be processed by machines. Once the machine can intervene, the role of people is not important. " Therefore, such content teachers can only adopt "indoctrination" teaching methods, and learners' participation can only be passive. Flandenthal believes that this is an educational model similar to training students into computers, that is, students can only passively execute programs, leaving them no room for initiative and creativity. As a result, people are not only inferior to computers in calculation, but also seriously inhibit people's initiative and creative development in thinking.

(2) He believes that mathematics is essentially a human activity, and students may repeat the process of human mathematical discovery. The traditional mathematics education centered on teaching "ready-made results" and characterized by "indoctrination" must be changed. Flanden pointed out that this change should start with the process of how to make students take the initiative to learn mathematics and participate in mathematics education. Mathematics education needs development, and mathematics and mathematics learning as education should be understood from a new perspective. In the final analysis, mathematics is a human activity, so mathematics as education should also be treated as a human activity. "Mathematics in school is not a closed system, but mathematics as a human activity and a mathematical process starting from real life ..." Students have "potential discovery ability", and their own way of thinking and behavior already has some characteristics of teachers and even researchers, so it is possible to repeat the activities of human mathematics discovery on them. Mathematics education should develop this potential, so that the informal mathematical knowledge and mathematical thinking that already exist in students' minds can rise and develop into scientific conclusions and realize the "rediscovery" of mathematics. Mathematics education should guide students to repeat the process of human mathematics discovery and realize mathematics rediscovery and re-creation.

(3) He believes that mathematics education should start from the real life that students are familiar with, and take this as the starting point and the end point. According to Friedenthal's viewpoint, mathematics education can't proceed from the perfect mathematical system as the final result, and can't be carried out by embedding some abstract mathematical structures into students who are far away from real life. Mathematics education should start from students' familiar real life, follow the trajectory of human activities in the process of mathematical discovery, from problems in life to mathematical problems, from concrete problems to abstract concepts, from special relationships to general laws, and gradually learn mathematics and acquire knowledge through students' own discoveries. After acquiring abstract mathematical knowledge, we can apply them to new practical problems in time. In this way, mathematics education can better communicate the relationship between mathematics in life and mathematics in class, help students understand and love mathematics, and make mathematics a useful skill in life.