There are two lines in mathematics teaching, one is the open-line mathematics knowledge teaching, and the other is the hidden-line mathematics thinking method teaching. Mathematical thinking method is the essence of mathematics, the link for students to form a good cognitive structure, the bridge for transforming knowledge into ability, and the carrier for cultivating students' good mathematical concepts and innovative thinking. We must attach importance to the infiltration teaching of mathematical thinking methods in teaching.

First, the definition of mathematical thinking method

Mathematical thought is the essential understanding of mathematical knowledge, methods and laws; Mathematical method is the strategy and procedure to solve mathematical problems, and it is the concrete embodiment of mathematical thought. Mathematical knowledge is the carrier of mathematical thinking method, and mathematical thinking is at a higher level than basic mathematical knowledge and common mathematical methods. It comes from basic mathematical knowledge and common mathematical methods, and has a guiding position in using basic mathematical knowledge and methods to deal with mathematical problems. For learners, the process of using mathematical methods to solve problems is the process of accumulating perceptual knowledge. When this accumulation reaches a certain level, it will make a leap and rise to mathematical thinking. Once mathematical thinking is formed, it will play a guiding role in mathematical methods. Therefore, people usually regard mathematical thoughts and methods as a whole concept-mathematical thoughts and methods.

Second, the main mathematical thinking methods that should be infiltrated in junior high school.

In junior high school mathematics teaching, at least the following main mathematical thinking methods should be infiltrated into students:

1. Thinking method of classified discussion

Classification is a way of thinking by comparing the similarities and differences of the essential attributes of mathematical objects, and then dividing mathematical objects into different categories according to certain attributes. Classified discussion is not only an important mathematical thought, but also an important mathematical method, which can overcome the one-sidedness of thinking and prevent missing solutions.

2. Analogical thinking method

Analogy is a form of reasoning based on two or two objects having some common properties, which is called the most creative way of thinking.

3. The thinking method of combining numbers and shapes

The thinking method of combining number and shape refers to a thinking strategy that combines number (quantity) and shape to analyze, study and solve problems.

4. Change thinking methods

The so-called "transformation" is to simplify the problem to be solved into another easy problem or solved problem.

5. Thinking methods of equations and functions

Using the thinking method of equation is to transform the problem into solving the equation (group) problem by using the symbolic language of mathematics according to the quantitative relationship between the known quantity in the problem and the unknown quantity in the teaching method.

The so-called functional thinking method is to analyze and study the quantitative relationship in specific problems from the viewpoint of movement and change, and to characterize and study this quantitative relationship in the form of functions, so as to solve problems.

6. Holistic thinking method

The whole thinking method is that when considering a mathematical problem, we should focus on the overall structure of the problem instead of its local characteristics. Through comprehensive and profound observation, we can understand the essence of the problem from a macro perspective and treat some independent but closely related quantities as a whole.

Thirdly, the way to infiltrate mathematical thinking methods in teaching.

1. In the process of knowledge generation, timely infiltrate mathematical thinking methods.

The content of mathematics teaching can be roughly divided into two levels: one is called superficial knowledge, which contains basic contents such as concepts, properties, laws, formulas, axioms and theorems; The other is called deep knowledge, which mainly refers to mathematical thoughts and methods. Surface knowledge is the foundation of deep knowledge and has strong maneuverability. Only by studying textbooks and mastering and understanding certain superficial knowledge can students further learn and understand relevant deep knowledge. Mathematical thinking method is based on mathematical knowledge and contained in surface knowledge. It is the essence of mathematics, which supports and guides superficial knowledge. Therefore, in the teaching process of concepts, properties and formulas, teachers should constantly infiltrate relevant mathematical thinking methods, so that students can grasp the surface knowledge and understand the deep knowledge at the same time, thus making students' thinking leap qualitatively. Only talking about concepts, theorems and formulas without paying attention to the teaching of infiltrating mathematical thinking methods will not be conducive to students' real understanding and mastery of what they have learned, so that students' knowledge level will always remain in the primary stage and it is difficult to improve. In the teaching process, we should guide students to actively participate in the process of exploration, discovery and deduction of conclusions, find out the causal relationship among them, understand its relationship with other knowledge, and let students experience the mathematical ideas and methods they have experienced and applied in creative thinking activities.