First, look at the classroom teaching design: 1, look at the beginning, transition and summary of the class: a good beginning is half the battle. After the beginning, we should seize the opportunity to set out the topic and not give too many examples, thus losing the best opportunity to cut to the chase. It is best not to lead a class for more than five minutes, and don't take too much time away from the key research content. There are many ways to lead out a lesson. You can talk about practical examples of production and life closely related to the teaching content to be carried out. This method is generally used at the beginning of a chapter or a big section, and it is often used in the teaching of new courses. You can also review the knowledge and methods that students have learned and are closely related to the research content of this lesson. The main purpose is to pave the way for new research content. This method is generally used in the teaching of new courses. You can also lead out the content of this lesson by solving a problem, which generally has a lot of variant space and can be linked with many knowledge and thinking methods. This method is generally used in the teaching of exercises. 3. There should be appropriate interlanguage between the teaching of each part, so as to skillfully transfer the study of one problem to the study of another. People naturally integrate the contents of the whole class, making students and teachers feel that the class is rich in content, but there is no redundant research content. It is natural for people to transition from one problem to another. The last part of a class is also very important. A good ending can make students grasp the key content of this class, make the key points of this class vivid in their minds, make students feel unfinished, and make students look forward to the research of the next class. Second, look at the design of classroom teaching content: 1. See whether the teaching design of a class is from special to general, and whether it conforms to the cognitive law of students from concrete to abstract. 2. See if a course is realistic. In classroom teaching, teachers should be good at properly creating applied mathematics situations closely related to students' real life and social practice, so that students can find problems around them. 3. See if there is problem consciousness in the teaching design of a class. It is best to form a series of questions in a class. The questions put to students in class should be open, and open questions with open conditions, open methods and open conclusions should be created to guide students to dig out multiple solutions to one problem and multiple solutions to one problem, reflecting the mathematical thinking methods contained in the questions. 4. See if the teaching design of a class can guide students to change the perspective of observing problems, think about problems in multiple directions, cultivate students' divergent thinking, and cultivate students' ability to find and ask questions. For example, guide students to ask a few questions, why, why this conclusion exists, what is the relationship between conditions and conclusions, and how to get this conclusion. 5. See if the teaching design of a class conflicts. 6. See whether the content of ideological education can be found out in a class and whether ideological education can be integrated into mathematics teaching activities. Third, look at the connection between the content of a lesson and the question: 1. In the teaching process of a class, there should be a close relationship and a natural transition from the beginning to the main research content of this class and then to the end. Even the main research content of this course should be closely related to the problem. It can be that the condition changes from concrete to abstract, and another problem is obtained, or that the conclusion changes into condition, and the condition changes into conclusion, and a new problem is obtained, or that the condition and conclusion are linked with other unit knowledge and methods, and a deeper problem is deduced. 2. In the classroom teaching activities, the exercises in the classroom should consolidate the mathematical thinking methods in the examples, and it is best to change the examples from different angles instead of simply copying them. Fourth, look at the classroom teaching methods and teacher-student relationship: 1. See whether the teaching method is appropriate, whether the leading role of teachers and the main role of students are fully exerted, whether the teachers ask questions properly, whether the students ask questions actively, and whether the students propose reasonable solutions to problems. 2. Math teachers' classes can be summarized into three ways, reflecting three different teacher-student relationships. In the first category, teachers explain and show the process of mathematical thinking to students, but students are not allowed to interrupt, express their opinions and communicate with teachers after class. The advantage of this class is that the teaching process may be faster. At present, many teachers, especially young teachers, often adopt this teaching method considering the teaching progress. The serious deficiency of this teaching method is that it overemphasizes the leading role of teachers, suppresses the subject and dampens the students' thinking enthusiasm. The actual teaching efficiency is not high, and students' mastery of knowledge and methods is not profound. The knowledge and methods mastered by students are just copies of teachers, so the students processed in this way have no sense of innovation. The second category: teachers design teaching plans and distribute teaching handouts to students in advance, so that students can learn first and do first. In the classroom, combined with students' actual and teaching events at any time, the preset teaching scheme is flexibly used. In this class, under the guidance of teachers, students study mathematical problems, sum up thinking methods, and then use the obtained methods to solve various problems, including related variant problems. In this process, students can express their views on the problem at any time, and teachers and students are equal before the truth. In this class, teachers encourage students to actively participate in teaching activities, which not only gives full play to the leading role of teachers, but also gives full play to the main role of students, so that students can have their own stage to show themselves and deeply understand and remember knowledge. In this class, teachers no longer replace others, but guide students to think about mathematical problems and fully experience the process of mathematical research. Teachers care about students' experience and students' harvest in the process of classroom teaching, so this kind of teaching is practical and effective, and it is both disciplined, democratic and free. The third category: the teacher divides the students into several groups, and the seats in each group are together. The students sit around the table instead of facing the blackboard. Let the students ask questions actively in class, and we will study and solve the problems together. Teachers should talk as little as possible. This kind of class is probably the most advocated and appreciated by many experts. On the surface, this kind of class is very lively and conforms to the present form. However, there are also many shortcomings: First, the leading role of teachers is not well played, and even the methods and basic viewpoints of attending classes after a class are not very clear. Secondly, introverted students and students who are a little slower may get nothing in class, but it is always those students who gain a lot. Without the participation of teachers, the key points in the class can't be completed well. In this way, the so-called face and people-oriented are empty talk. In other words, such courses are too formal and lack realistic work style. 5. Look at the teacher's teaching language in class: 1. See if the teacher's language in class is accurate, simple and appropriate. Especially the description of mathematical problems should be accurate, so that people can't see loopholes and ambiguities. 2. See if the teacher's language in the classroom is cadence, lively and interesting, humorous and humorous, and see if students can finish their math study in a relaxed and happy atmosphere. 3. See if teachers can connect with the actual production and life, the related contents of other disciplines, organically infiltrate the ideological education content, and describe the beauty of mathematics with mathematical expressions and geometric figures. To do this, teachers should have more experience in production and life, know some common sense of other subjects and have a wider range of knowledge. Sixth, look at the effect of classroom teaching: look at students' psychology from their expressions, see if they are happy, and see their general knowledge and methods in this section. A valuable math class will benefit students a lot. From classroom exercises and students' answering questions and taking the initiative to speak, we can see the students' mastery of the knowledge and methods in this section. Students take the initiative to speak, students answer questions accurately, and most students practice smoothly in class, which shows that the classroom effect is very good.