Mathematical cognitive structure is transformed from the knowledge structure of teaching materials. On the one hand, it retains the abstract and logical characteristics of mathematical knowledge structure, on the other hand, it integrates the psychological characteristics of students' perception, understanding, memory, thinking and imagination. It is the result of the interaction and coordinated development of scientific mathematical cognitive structure and students' psychological structure. How to guide children in junior high school to establish, develop and improve mathematical cognitive structure?

First, learn the basics well and establish a mathematical cognitive structure.

When learning a new mathematics course or a new subject that has little to do with previous knowledge, you will first encounter a series of new concepts, axioms, thinking methods, and some simple and basic theorems and formulas. These contents can not be assimilated by the original cognitive structure, but can only be abstracted from examples, models or existing experiences to form new concepts, axioms and methods, thus establishing a new mathematical cognitive structure. Students process and transform the new knowledge or adjust their own mathematical cognitive structure on the basis of the original knowledge, and then internalize the new knowledge they want to learn into their minds in a certain way, so that the old and new knowledge can be integrated into one, forming the corresponding mathematical cognitive structure, and storing the learned mathematical knowledge in this form.

The newly established cognitive structure is the basis of follow-up learning, which has a high level of abstraction and generalization. Therefore, although these contents are simple, but the learning requirements are high, we should pay special attention to them.

Second, step by step to promote the development of cognitive structure

Mathematics is a highly systematic subject, and its contents are closely linked. When learning, if you don't learn a certain link firmly and have a vague understanding, it will directly affect the good development of cognitive structure. If it is not solved in time, then continuing learning can only be mechanical learning. At this time, there are isolated "points" in the cognitive structure, which are not only easy to forget, but also lose their application value, leading to learning failure. For the learning of a specific mathematical knowledge, at the initial stage of learning, students can only form the embryonic form of the corresponding mathematical cognitive structure in their minds through the interaction between the original cognitive structure and new knowledge with the help of teachers. Its structure is extremely unstable, and it needs effective practice and further application in the subsequent content learning, so that the formed mathematical cognitive structure can be gradually consolidated and stabilized.

When learning every theorem and formula, we should clearly know how to draw a conclusion step by step, what concepts, axioms, theorems or formulas are used, what methods are used, and so on. If you want to know why, you should know why, not just remember its conditions and conclusions. The process of proposition learning is a positive thinking activity, from the situation of perception theorem to thinking, that is, to establish contact, interaction and assimilation with appropriate knowledge in the original cognitive structure, and then to incorporate it into the original cognitive structure, so that the original cognitive structure can be developed. In this thinking activity, we should not only understand the proof process, but also learn the thinking methods and key ways of mathematics from it. This is of great significance to the development of cognitive structure.

Third, refine knowledge and improve the mathematical cognitive structure.

Mathematical cognitive structure also has a process of formation, development and perfection, which is constantly changing. Moreover, the size of cognitive structure is relative, which can refer to the cognitive structure of mathematics in the whole middle school stage, the small one can refer to the cognitive structure of a chapter, and it can also refer to the cognitive structure of a certain part of the content. Therefore, at every stage, we should refine, improve the original cognition and improve the level of abstract generalization, so as to contribute to future study and application. Usually stage review and term review should play this role. With the gradual deepening of the learning process and the continuous accumulation of mathematical knowledge, students' mathematical cognitive structure will continue to expand and improve.

Mathematics learning is to transform the mathematical knowledge structure into the mathematical cognitive structure in the mind through active thinking activities.