What exactly is the fine tradition of Chinese math education

To summarize the characteristics of Chinese mathematics education in one sentence, it is: ? Seek students' mathematical development on a sound mathematical foundation.? Here? The mathematical foundations is the three major mathematical abilities: mathematical arithmetic ability, spatial imagination ability, logical thinking ability; here? Mathematical development means: to improve the ability to analyze and solve problems with mathematical thinking methods, and to promote the overall development of students in all aspects of moral, intellectual and physical development. The corresponding teaching method is to implement the spirit of dialectical materialism and carry out? Heuristic? teaching, focusing on the nature of mathematics in classroom teaching, advocating the teaching of mathematical thinking methods, using? Variation practice, and strengthen the study of problem solving rules.

Such characteristics can also be used to ? Mathematics double-base teaching? the customary expression of ? Double basic? means basic knowledge and basic skills. But? Double-basic teaching? is not the same as Double basic? itself. As a teaching idea, the As a teaching idea, "double-basic teaching" does not simply emphasize laying a foundation. does not simply emphasize laying a foundation, but also includes development on top of laying a good foundation. The idea of? Double-base teaching? Do not develop, that is a misunderstanding.

Mathematics classroom teaching in China has many features that are different from those of mainstream research in the world. There was a time when these features were either criticized and discarded, or considered trivial and unappreciated, while others remained at a simple level and lacked theoretical processing. In contrast to the much sought-after foreign concepts that have no practical effect, the concepts of the study have been criticized and rejected. Concept? and theories, we are a bit? Self-importance?

1. focus on? Introduction The link.

Tu Rongbao pointed out that the Chinese math teaching long by? old knowledge? The new knowledge? new knowledge?

Foreign introduction, emphasizing the connection of students' daily life? The situation set up? The first is the introduction of a new concept, which is a new way of doing things. The first is a kind of "introduction", which is a kind of "introduction" to the math classroom. In fact, as far as the math classroom is concerned, it is possible to set up a situation that is related to students' daily lives. The situation is only a few. are only a few. Most math classes, especially those with a lot of? numbers and equations? s procedural math content, most of them do not have realistic contexts to speak of. For example, factorization, combining like terms, power and exponent operations, etc., are difficult to set up realistic contexts. But they can be introduced in appropriate ways. For example, using ? prime factorization of integers? to derive? factorization? and the factorization of integers with? and the simple idea of "combining similarities and combinations". to introduce the simple idea of? Combining like terms? and using the simple idea of? Multiply by adding? to derive the idea of? Multiplication to powers? etc. are all feasible. The Chinese math classroom presents many unique ways of introduction, in addition to the reality? situation presentations? and? hypothetical simulation? The Chinese classroom presents many unique ways of introduction, which, in addition to realistic situation presentation, also include? Suspense setting? The following are some of the most common scenarios that can be used in the presentation of a story. storytelling What is the most important thing you can do for your students? Review of old lessons? _____ _____ _____ _____ _____ _____ _____ _____. Questioning? _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____. Exercise review? What is the most important thing you can do for your child? Build bridges? Comparative analysis? Comparative analysis? etc. These introductory methods, which are? Heuristic? An integral part of teaching. In recent times, we advocate? Situational teaching? is correct, but people can not have direct experience of everything, a large number of indirect experience. Mathematics teaching from students' daily life situations can only be heuristic? guide? It is a kind of strengthening and supplementing, not canceling or replacing? Introduction Teaching link set up.

2. The first is to try to teach.

In the 1980s, Gu Lingyuan summarized the excellent cases of mathematics education at that time through the masses, and put forward the idea of? The teaching strategy of "trying to teach and teaching back" became popular in the Yangtze River Delta. The teaching strategy of "try to instruct, teach back" became popular in the north and south of the Yangtze River. In elementary math education, Qiu Xuehua advocated the "try teaching method". Qiu Xuehua advocated the "Try Teaching Method", which had a national impact. which has had a national impact. All of them have the "try" method in their experience. Try The word "try" is found in all of their experiences. This is a valuable creation?

The corresponding Western philosophy is ? Explore, Discover, Create? However, for primary and secondary school students, in classroom learning, in just nine years of compulsory education, the most basic knowledge that human beings have thought over and over again for thousands of years and have been tested by practice? Explore, discover and create? , that is difficult to do.

In the teaching of mathematics, let students make ? try? that is more in line with the reality of basic education. Try means to come up with your own ideas, which can be right or wrong; can succeed or fail; can be done to the end, or can be stopped in the middle. To try, you don't have to ? yourself? to discover the results, but to envision, to dare to ask questions, and to experiment. Allow students to listen to the teacher's lecture based on their own either right or wrong? attempts? for comparison, and through the teacher-student interaction, and finally grasp the true meaning of knowledge, which is effective can be operated in the way of independent learning.

3. Problem-solving variant exercises.

Variation of teaching for the teaching of various subjects in China, but to the teaching of mathematics is more common. Especially in the mathematical problem solving process using variant exercises, become an important feature of Chinese mathematics education. Variation teaching in mathematics is a form of teaching that changes the meaning of certain mathematical objects and the presentation of mathematical problems from different angles, sides and backgrounds, so that the non-essential features of mathematical content are hidden from time to time, while the essential features remain unchanged. Variation enables students to do exercises with a suitable gradient of the thinking process, gradually increasing the creative element; sometimes a problem can be appropriately derived and varied to provide students with attempts to develop the ladder; the combination of exercises should be conducive to the students to generalize a variety of skills in solving problems, or from different perspectives to replace the skills and methods of solving problems.

Variation practice in the teaching of mathematical problem solving requires teachers to prepare a sequential arrangement of training questions to provide students with a ladder for the development of thinking. The practice problems are repetitive but not dull, and are conducive to students' construction of complete and rational new knowledge. Each variation, with a certain creative implication, but with a solid foundation, realizes ? Developing on a solid foundation? The concept of teaching.

A basic law of education is ? Progress in a sequential manner? In the face of students with lower and middle grades, there used to be ? small gradient, small turns, small steps? The? Three small? Teaching method; exam tutorials in a large number of preparation of various levels of variations of practice questions, these are closely related to the mathematical variations of practice.

Variable practice in math problem-solving teaching, teachers are required to prepare a sequential arrangement of training questions for the development of students' thinking to provide a ladder. The practice problems are repetitive but not dull, and are conducive to students' construction of complete and rational new knowledge. Each variation, with a certain creative implication, but with a solid foundation, realizes ? Developing on a solid foundation? The concept of teaching.

A basic law of education is ? Progress in a sequential manner? In the face of students with lower and middle grades, there used to be ? small gradient, small turns, small steps? The? Three small? Teaching method; exam tutorials in a large number of preparation of various levels of variations of practice questions, these are closely related to the mathematical variations of practice.

Variable practice in math problem-solving teaching, teachers are required to prepare a sequential arrangement of training questions for the development of students' thinking to provide a ladder. The practice problems are repetitive but not dull, and are conducive to students' construction of complete and rational new knowledge. Each variation, with a certain creative implication, but with a solid foundation, realizes ? Developing on a solid foundation? The concept of teaching.

A basic law of education is ? Progress in a sequential manner? In the face of students with lower and middle grades, there used to be ? small gradient, small turns, small steps? The? Three small? Teaching method; test tutorials in the preparation of a large number of variations of various levels of practice questions, these are closely related to the mathematical variations of practice.

4. Refinement of mathematical thinking

The refinement of mathematical thinking in mathematics teaching is an important feature of Chinese mathematics education. For a long time, China's mathematics teaching attaches importance to the understanding of concepts, the process of proof, the idea of solving problems, and advocates the teaching of the process of the occurrence of mathematical knowledge. These are teaching concepts that emphasize mathematical methods of thought.

In the 1980s, Mr. Xu Lizhi formally proposed ? Mathematical thinking method? s theory, which was used to guide the teaching of mathematics in primary and secondary schools. This idea quickly gained a warm response in the Chinese mathematics education community and was directly used in classroom teaching. In addition to? Analyze and synthesize The concept of analyzing and synthesizing induction and deduction and association and analogy? In addition to the general mathematical methods of thought, they also use? Combining numbers and shapes? The method of the method of reduction, the function idea, the equation idea, the principle of relation, mapping and inversion, and the principle of? , functional thinking, equation thinking, the principle of relation-mapping-inversion, and? Geometric transformations The geometric transformations. Equivalence transformation? and the "stepwise approximation" method. stepwise approximation? ,? Anatomy of a special case? and other problem solving strategies. As for? variable substitution? The method of coefficients to be determined? the method of coefficients to be determined? and? cross-multiplication? and other specific methods of problem solving have always been available, but now they have been enriched even more. The most valuable thing is that these mathematical methods of thought, rather than remaining in the theoretical discussion, but put into practice, and become the **** knowledge of every Chinese math teacher.

Mathematics teachers generally have a sense of teaching mathematical methods of thought, grasp the connotation of mathematical methods of thought, use mathematical methods of thought in solving problems, and are able to summarize and reflect with mathematical methods of thought. This is a great spiritual wealth. When students are engaged in mathematical learning, they not only solve problems, but also get the training and inculcation of mathematical methods of thought and develop their own mathematical thinking ability. What a bright educational landscape!

Until now, the western mathematics education community has not put forward can be directly related to the ? Mathematical thinking method? corresponding to the field of mathematics education research. As for the ? process? Teaching objectives are more generalized. (Zhang Dianzhou)