Most teachers think that they have finished their teaching activities, and seldom take the initiative to reflect on the process of summing up the activities. It can be said that the weakest link in mathematics teaching at present is after-class summary. Mathematical generalization is a process of continuous innovation in mathematical thinking activities. Without teaching summary, students' knowledge will not easily form a system, their thinking ability will not be innovative, and their cognitive level will not rise to a higher level. Because of the abstraction of mathematical objects, the exploration of mathematical activities, the rigor of mathematical reasoning and the particularity of mathematical language, students in the stage of thinking development often cannot master the essence of mathematical knowledge at one time. Only through continuous summarization, repeated thinking and in-depth study of self-regulation, can their knowledge be close to that of mathematics itself. Therefore, "Mathematics Curriculum Standards" points out in the preface: Mathematics teaching should not only consider the characteristics of mathematics itself, but also follow the psychological laws of students learning mathematics, and emphasize that students should gain an understanding of mathematics from their existing life experience and knowledge, and at the same time make progress and development in their thinking ability, emotional attitude and values. Therefore, when designing the classroom, we should design different classroom endings according to different teaching contents, so that our mathematics classroom teaching is not only reasonable in layout and perfect in structure, but also colorful and fascinating, and should also have an unforgettable ending, thus achieving the realm of "exhausted classroom and unfinished thinking".

First, the general form of mathematics classroom teaching summary

1. summarize the class summary. In order to make students have a comprehensive and systematic understanding of the knowledge and methods they have learned, teachers often use concise and accurate mathematical language, words, tables or graphics to summarize the main content and knowledge structure of a lesson or several knowledge points. This summary can accurately grasp the integrity of the external appearance and internal essence of each knowledge point, thus helping students to grasp the key and difficult points of knowledge and grasp the systematicness of the knowledge they have learned.

2. Summary of knowledge consolidation exercises. After the end of the new class, teachers should grasp the key points, break through the difficulties, grasp the key points of the problem, carefully design some exercises, and organize students to end the class through exercises. This can not only consolidate the basic knowledge learned by students and apply it to practice, but also make the effect of classroom teaching get timely feedback, which is convenient for teachers to guide students' information activities in time and accurately.

3. Knowledge comparison-comparison summary. Psychological research tells us that comparison is not only an important way to know things, but also an effective way for students to remember things, which can help us grasp the memory object from the relationship between things.

4. Comparison-comparison summary. Generally, it is to compare the contents with similar or different meanings in teaching, seek common ground while reserving differences, and cultivate students' comparative discrimination ability.

5. Pre-arranged summary of suspension. A good lesson summary can make students eager to know the content behind, or know why, just like novels and TV plays, when the plot comes to an abrupt end at a critical moment, it can arouse readers' strong desire to pursue the topic.

6. Summary of inquiry class. Question inquiry is the highest stage of students' thinking development level and the highest embodiment of cultivating innovative talents in classroom teaching. For example, in the teaching of "midline", you can make a summary of this knowledge: can you draw a knife on a trapezoidal piece of paper casually, so that you can spell out a parallelogram and divide it into two parts? What is the relationship between the trapezoid midline and the triangle midline? Let the students learn the triangle midline, and guide them to explore the nature of the trapezoid midline through the above questions. Through the study of the nature of trapezoidal midline, students will continue to explore the problem of transforming the nature of trapezoidal midline into triangular midline.

7. Summary of communication evaluation class. Mathematics classroom teaching should give students enough time and space to think and do activities. At the same time, students should have the opportunity to talk about their experiences, feelings and gains in mathematics, express their confusion and joy, and put forward suggestions and opinions. Therefore, we should also pay attention to students' learning feelings and experiences in class summary. Moreover, this kind of summary is open, which not only pays attention to the results of students' learning, but also pays attention to students' experience and feelings in learning mathematics, and pays attention to students' mathematical emotions, attitudes and values.

Second, the role of mathematics classroom summary

Classroom summary is the last stage for teachers to complete the teaching task in mathematics classroom, and it is a teaching behavior for teachers to guide students to re-understand, re-summarize, re-practice and re-sublimate knowledge and skills, processes and methods, emotional attitudes and values. Mathematics classroom summary is an integral part of mathematics classroom teaching. Summary is not only the summary and extension of this lesson, but also the basis and preparation for continuing to learn mathematics knowledge in the future.

According to different types of mathematics classroom teaching, different teaching contents and requirements, well-designed classroom summary can make our classroom teaching get twice the result with half the effort. The main function is to let students learn how to summarize and organize knowledge. At the conclusion of a class, teachers consciously try to sort out and summarize the teaching content and several knowledge points of this class, so as to help students grasp the key points and difficulties of the teaching content, systematize the knowledge they have learned, and firmly inject new knowledge and methods into students' cognitive structure, thus leaving a deep impression on students' cognitive structure and gaining the ability to solve practical problems flexibly. Feedback teaching information in time. Students' understanding of knowledge is often superficial, that is, they can only see, think and not do. The so-called situation is that they can see it at first sight, understand it when they say it, and make mistakes when they do it. If teachers carefully design a few small questions with specific knowledge when summing up in class, and let students answer them from different angles, they can fully understand the students' mastery of new knowledge, so that teachers can adjust their teaching in time and provide research materials for the establishment of teaching objectives and the improvement of teaching in the next class. At the same time, the process of teachers commenting on students' answers helps students to further master new knowledge, thus successfully completing teaching tasks, promoting the transfer of students' knowledge and activating students' innovative ability.

The inherent logical order of knowledge and students' cognitive laws determine that teaching must be a step-by-step and interlocking orderly process. At the end of classroom teaching, it is very valuable to ask questions related to this section or the following content and let students leave the classroom with questions, which will activate students' thinking, broaden their horizons and develop their intelligence. Contact inside and outside the classroom, improve the situation, put forward the problems that can't be solved in the classroom, and let students fully explore and analyze until they finally solve the problems and get a surprise of success. It is also helpful for students to transfer good learning methods to new knowledge and realize the goal of classroom teaching: teaching for migration and learning for migration.

In a word, teaching is a science and an art, and there is no fixed pattern to follow in this art, so is the summary of math class. Therefore, mathematics classroom summary should not be the reappearance of simple knowledge and methods, but should guide students' thinking activities of learning mathematics to new goals and encourage students to try to summarize, summarize and explore. That is, boldly let students summarize their own thinking process; The process of understanding the meaning of the problem; Knowledge, methods and mathematical ideas involved in completing learning activities; Issues related to activities; Problem-solving thinking, reasoning, operation and mathematical language expression. As long as we are diligent in exploration, brave in practice and good at summing up, we can create more and more beautiful forms of classroom summary, increase the charm of mathematics classroom teaching and improve the teaching effect.