First, "good mathematics" is not only "mathematics", but also "human studies"
Our mathematics education is not only to let students master the necessary basic knowledge and skills, but more importantly, to let students feel more important basic ideas and basic life experiences. At the same time, students should learn to think by using mathematical thinking mode, understand the intrinsic value of mathematics, develop good study habits, have a preliminary sense of innovation and a scientific attitude of seeking truth from facts, and so on. In a word, our mathematics education is not only the training of knowledge, but also the accumulation of wisdom, and it is also the embodiment of life growth, life value and significance.
Humanism is an organic ideological system that takes human nature (human essence), meaning of life and code of conduct as the thinking object, takes the theory of human nature as the core, and includes the outlook on life (the theory of life value and code of conduct), the theory of rule by man (the theory of self-cultivation and the theory of governing politics by others) and the theory of human social ideal. It regards mathematics not only as "mathematics" but also as "admission", which is the dialectical unity of mathematical instrumentality and humanity. "Good Mathematics" is a mathematics with people as the core, and it is a real "human study".
Second, "good mathematics" not only teaches knowledge and methods, but also teaches ideas.
Teaching has three levels: teaching knowledge, teaching methods and teaching ideas.
The excellent quality of mathematical thinking method is that it supports the whole mathematical building, is everywhere, is everywhere, is widely used, and is easy to stay in people's long-term memory. Any subject should use mathematical thinking methods, but the ways and degrees of application are different.
Teachers' teaching and students' learning are a unity. "Good mathematics" should first ask four questions: First, what are the contents of teaching and learning (consider what should be taught and what can be taught respectively); Second, why should we teach and learn these contents? Third, what should teachers and students do; Fourth, why do you want to do this? On this basis, teachers should read the text thoroughly and carefully, investigate and analyze the logical starting point of students' learning, so as to understand what knowledge and skills students should master in a class, and what methods and ideas should be understood and improved. Mastering the mathematical thinking method, understanding the quantitative change law of the objective world, and using it to understand and transform the world are the true meaning of mathematical science.
Third, "good mathematics" not only focuses on yesterday and today, but also points to tomorrow.
Mathematics always coexists with challenges and crises. With the rapid development of science and technology, the total amount of human knowledge is increasing, and the speed of knowledge updating is also accelerating. The emerging new technologies and disciplines are closely related to mathematics, especially because of the development of computer technology, the application scope of mathematics is more extensive. We should keep pace with the times and have a forward-looking vision. Being good at math means being moved. She will not stay in the past, nor will she stay in today.
Yesterday, it means basic points and repetition; Today means the starting point and departure; Tomorrow is hope and direction. Yesterday's "old boat ticket" is difficult to board tomorrow's "new passenger ship", and it is really terrible to have no future math learning activities. "Good Mathematics" will not make students become mechanical porters who copy and paste, but let students raise their sails, stimulate their desire to think and explore, and move towards an uncertain and creative future.
Four. "Good mathematics" is not only memory and imitation, but also development and creation.
In a letter to Professor Zheng Yuxin, American scholar Sting sincerely pointed out: "An important difference between Chinese and American students is that China students are more adapted to the' algorithm' learning of specific solutions to specific problems, while American students are better at solving unconventional problems that are open, vague, have' realistic' significance and need more creativity."