Although what students learn is known by predecessors, this kind of knowledge is still new and unknown to students. The learning process of students is the process of students' understanding of mathematical knowledge, methods and skills, and our teaching process is the process of improving students' cognitive structure. How to make the process of imparting knowledge in class conform to students' cognitive laws is a problem that we should pay full attention to. The process of students' cognition is always from special to general, from concrete to abstract, from local to system. Therefore, the classroom teaching process we designed should conform to students' cognitive rules. Only in this way can students study smoothly, which is also the key to ensure the success of our teaching. However, our textbooks focus on general conclusions and abstract deductive processes, which often make it difficult for students to learn in classroom teaching. Therefore, our teachers often need to design some problems as transitional links, so that students can realize the background of the problems, the specific process of summarizing abstract concepts and theories from specific problems, and understand the practical significance of these concepts and theories, so that students can successfully complete the cognitive process from special to general and from concrete to abstract. For example, the introduction of polar coordinates in elective series 4 makes students feel that the abstraction is not easy to understand, so they can design a problem of artillery shooting. In order to hit the target, they always have to rotate the angle of the barrel to determine the distance between the gun position and the target. Through this concrete example, let students have a leap in understanding and complete the process of understanding from concrete to abstract. Mathematics teaching is a special cognitive activity, which is dominated by people's general cognitive laws and has its own characteristics. Understanding and mastering students' cognitive process and laws can make the process of teachers imparting knowledge coincide with students' cognitive process, so that students can have a deeper understanding and learn more smoothly.

Second, the principle of combining knowledge imparting with thinking training.

Thinking ability is the core of various mathematical abilities. Paying attention to the cultivation of thinking ability is one of the fundamental differences between modern mathematics teaching and traditional mathematics teaching. Objectively speaking, we all realize that just imparting knowledge is not enough. While paying attention to basic knowledge, we should pay attention to cultivating students' thinking ability. Psychology points out that thinking is a process of discovering and discovering new things in essence. At present, our teachers have a clear understanding of the necessity and importance of cultivating students' thinking ability, but how to cultivate students' thinking ability while paying attention to basic knowledge in classroom teaching is a problem worthy of our discussion. Mathematics always appears in the form of strict and systematic combination and deduction, which is the result of intuition, induction and analogy. Therefore, the expression of mathematics is only the result of thinking, but also the thinking process hidden behind the result. The composition of thinking ability is complex and cannot be simply understood as deduction. It should be pointed out that in deductive and various non-deductive thinking, the space for deductive innovation is the smallest. If thinking is limited to deduction, it is tantamount to binding the hands and feet of thinking. In fact, non-deductive thinking such as intuition, induction and analogy has greater creative possibilities. In teaching, we should pay attention to the "outside" and "inside" of mathematics, reveal and transform related thinking processes according to the needs of teaching, and bring them into the classroom, thus cultivating students' thinking ability. Teaching practice shows that only by reasonably designing problem situations in combination with teaching materials and guiding students to think actively can students have a deeper understanding of the problem. Cultivating thinking ability needs to reveal the thinking process, which coincides with the thinking process that students need to learn knowledge. It is an effective way for us to cultivate students' thinking ability to combine them organically and integrate them into the classroom, which can not only impart knowledge, but also implement thinking training.

In classroom teaching, teachers should not only reveal their own thinking process, but also attach importance to students' specific thinking process. It is an organic combination of these two thinking processes and a concrete process to improve students' thinking ability to design problem situations appropriately and reasonably and guide students to think and communicate gradually and deeply.

The principle of combining teacher guidance with students' autonomous activities.

Teaching is a bilateral activity, and both teachers and students have the task of understanding the objective world, but the purpose of teaching determines that students' cognitive activities are more important, and students are the main body of such cognitive activities. The leading role of teachers is to effectively guide students to deepen their understanding step by step, and in this process of understanding, students must be given a certain length of time and space for autonomous activities, so that they can deepen their understanding with their brains, hands and mouths. Students can't passively accept the teacher's cognitive process and passively understand the teacher's thinking results. For example, in the teaching of "binomial theorem", teachers do not need to give the conclusion of binomial theorem directly, but can design the process of students' independent activities, trying to discover and boldly guessing.