This paper describes the basic knowledge of junior high school mathematics as follows: "The basic knowledge of junior high school mathematics includes concepts, laws, disciplines, formulas, axioms, theorems and so on. Algebra and geometry in junior high school, as well as the mathematical ideas and methods reflected in its inherent substantive significance. " The definitions, laws, rhythms, formulas, axioms and theorems of mathematics must be memorized and catchy. We often say that we should remember on the basis of understanding. But there is no reason to talk about some basic knowledge, such as definitions. For example, the definition of one-dimensional linear equation: an equation containing only one unknown, whose infinite cycle is 1 and whose coefficient cannot be zero is called one-dimensional linear equation. In this definition, why there is only one unknown number instead of two or three, why the infinite cycle of the unknown number is 1 instead of 2 or 3, why the coefficient of the unknown number cannot be 0, and so on. These questions are worthless, or the definition is just the defined or inherent meaning of a substance or symbol. And some basic knowledge, such as laws, formulas, theorems, etc. Know not only why, but also why. For example, the temperament of parallel lines: two straight lines are parallel, the same angle is equal, the internal angle is equal, and the internal angles on the same side are complementary. Not only should you remember, but you should also be able to explain why two parallel lines have such temperament with what you have learned. This is what we call memory based on understanding. In the process of learning, it is inevitable that some basic knowledge will be ignored at any time. In this environment, remember even by rote. After remembering it, you will gradually understand it in the later learning process. In addition, some important mathematical methods and ideas also need to be remembered. Only in this way can you be confident in solving mathematical problems, thus experiencing the aesthetic value of mathematics and cultivating the decisive belief in learning mathematics well. Third, talk about "method" and contact "thought", and use "thought" to guide "method", which complement each other. Mathematical thought is a qualitative understanding of mathematical knowledge and methods, a rational understanding of mathematical disciplines, a tool belonging to mathematical concepts, and relatively abstract. The mathematical method is the basic procedure for solving mathematical problems, the concrete embodiment of mathematical thought and the hand-eye for implementing mathematical thought. Mathematical thought is the soul of mathematics, and mathematical method is the behavior of mathematics. The process of using mathematical methods to solve problems is the process of accumulation of perceptual knowledge. When the accumulation of these quantities reaches a certain procedure, it produces a qualitative leap and thus rises to mathematical thought. If mathematical knowledge is regarded as a magnificent building built with a clever blueprint, then mathematical method is equivalent to the hand-eye of building construction, and this blueprint is equivalent to mathematical thought. In the study of junior high school mathematics, we need to understand the mathematical ideas: equation function, combination of numbers and shapes, transformation, classified consultation, implicit condition, whole substitution, analogy and so on. The methods of "understanding" are: classification, analogy and reduction to absurdity; The methods that require "understanding" or "being able to use" include: undetermined coefficient method, elimination method, reduction method, collocation method, method of substitution method, image method and special value method. In fact, thoughts and methods cannot be completely separated. All kinds of methods used in junior high school mathematics reflect positive thoughts, and mathematical thoughts are rational understanding of methods. Therefore, it is an effective way to understand mathematical thoughts through the understanding and application of mathematical methods. In the process of mathematics learning, we must fully infiltrate mathematical thinking methods, learn a knowledge point or do a problem, and seriously think about what mathematical thinking methods are used. Although mathematical ideas and methods are different, they are limited after all. Correct use of mathematical ideas and methods to learn mathematics or solve problems is helpful to the comparison and classification of knowledge. Only in this way can you learn what you have learned systematically and flexibly, and truly incorporate what you have learned into your knowledge layout and become your own wealth. In addition, due to the abstraction of mathematical thinking, although the mathematical method is more detailed, the method itself is a science and more important knowledge, which is still difficult to determine. Therefore, when you first come into contact, it is inevitable that you can't sort out the clue. This is a normal sign, you don't have to be afraid. In particular, mathematical thought is a gradual infiltration process, which should be understood in combination with detailed mathematical knowledge or topics in the gradual learning process. For example, when learning rational numbers, triangular forms, quadrangular forms, the confirmation of 360-degree angle and tangent theorem of a circle, and the derivation of the root formula of a quadratic equation with one variable, the idea of classification consultation will be involved. The principle of classified consulting thought is: the same standard, neither weight nor leakage. Its advantage is obvious logic and uniqueness, which can train a person's thinking order and generality. The idea of equation makes it come true, which is a substantial leap in mathematical thought. The idea of equation is to deal with the relationship between unknown quantity and known quantity in mathematical problems by constructing equations. We will find that many problems are often solved by equations. The idea of combining numbers and shapes is helpful to visualize abstract knowledge. In junior high school mathematics learning, "number" and "shape" are inseparable. For example, the concept and operation of rational numbers can be well understood with the help of the number axis. Many problems in solving the application problems of series equations can be easily found out by drawing the meaning of the questions, and the function problems can not be separated from the graphs. Often with the help of images, the problem can be clearly explained, and it is easy to find the key position of the problem, so as to deal with the problem. The idea of transformation is embodied in the transformation from the unknown to the known, and from the general to the special. These mathematical ideas and methods will also run through the teaching process of teachers. In the lecture hall, we should pay attention to listening attentively, learning from the teacher and the lecture hall. Bruner pointed out that mastering mathematical thinking methods can make mathematics easier to understand and remember. It fully illustrates the importance of mathematical ideas and methods.