How to teach mathematics concepts Mathematics is the science of thinking, and concepts are the cells of thinking. Teaching concepts well is the inherent requirement of teaching mathematics well. If the concept teaching is not good, the realization of the goal of mathematics curriculum will lose its foundation. Academician Li Banghe pointed out: "Mathematics is basically playing with concepts, not playing with skills. Not enough skills! " Therefore, we must attach importance to the teaching of mathematical concepts. However, it is a common phenomenon to ignore concept teaching at present. The abstract explanation of "one definition, three attentions" requires students to comprehensively use concepts without a basic understanding of them. Many teachers even think that the teaching concept is not as good as talking about more topics "benefits". What is more worrying is that some teachers don't know how to teach concepts. This problem must arouse our full attention. From the perspective of education and developmental psychology, the core of concept teaching is "generalization": opening the mathematicians' thinking activities condensed in mathematical concepts, taking some typical concrete examples as carriers, guiding students to analyze the attributes of each case, abstractly summarizing the same essential attributes, inducing mathematical concepts and obtaining concepts. Mathematics teaching should emphasize the background, and concept teaching should emphasize that students experience the process of concept generalization. Because "mathematical ability is the ability based on mathematical generalization", it is of great significance to attach importance to the process of mathematical concept generalization for developing students' mathematical ability. Generally speaking, concept teaching should go through the following seven basic links: (1) background introduction; (2) Guide students to carry out analysis, comparison and comprehensive activities through typical and rich concrete examples (if necessary, let students give their own examples); (3) Summarize the essential characteristics of * *, and get the essential attributes of the concept; (4) Definition (expressed in precise mathematical language, which can be completed by reading textbooks); (5) Concept discrimination, that is, taking examples (positive examples and counter-examples) as the carrier, guiding students to analyze the meaning of keywords, including the investigation of concept special cases; (6) Specific examples of conceptual judgment, here we should use representative simple examples, and its purpose is to form specific steps of conceptual judgment; (7) The concept of "refinement" is mainly to establish the connection with related concepts and form a well-functioning mathematical cognitive structure. Concept teaching should be summarized as much as possible to provide students with the opportunity to summarize. For example, the first volume of the eighth grade textbook published by Suke arranged the teaching of the concept of "axial symmetry". According to the requirements of mathematics curriculum standards, the main task is to understand the axial symmetry through concrete examples. Because there is no concept of "corresponding point", the axis of symmetry can't be defined by "the middle vertical line connecting the corresponding point with the line segment", and students can only find the axis of symmetry through observation and operation, so the "mathematical taste" of this lesson is weak. How can we make this content have a "mathematical taste"? The key is to give students a general opportunity on the basis of their existing cognitive level, so that students can experience the same characteristics from specific examples and explain the rationality of their own operation conceptually. The main process is as follows: step 1, enumerate symmetrical examples in life, abstract an axisymmetric figure, and show that the parts on both sides of a straight line can overlap each other by "folding in half along the straight line", so we should pay attention to the typicality and richness of examples here; The second step, with the topic "Can you give a life example with the same substructure as the teacher's example", guide the students to use an axisymmetric image as an example; The third step is to summarize the * * * identity characteristics of the example-there is a straight line L, which is folded in half along L, and the figures on both sides can overlap; The fourth step is to define; The fifth step is to discriminate the key words of the concept, that is, to promote the understanding of the concept with variants based on positive examples and counterexamples. For example, ask students to give examples of common axisymmetric figures and point out the symmetry axes, and discuss how many symmetry axes there may be; Step 6, let the students make an axisymmetric figure, and ask them to tell the purpose and basis of each step, especially ask the students "why do you want to fold first" to let them know that the crease is the axis of symmetry. In this way, around the axis of symmetry, the core of the concept of axial symmetry, students are given more opportunities to observe, operate and reason with the concept, so that students can form an intuitive feeling of "axial symmetry figure" and "axis of symmetry" and explore the essence of axial symmetry figure for the follow-up.