Construction, Communication, Elaboration and Comprehension —— Talking about how to do a good job in senior high school mathematics review class: review class is a very important class type in middle school mathematics teaching and an indispensable link in our middle school mathematics teaching process. It can systematically deepen the study of old knowledge and fill the previous knowledge loopholes. The main function of review class is to develop students' ability on the basis of consolidating basic knowledge. High school mathematics knowledge is systematic, relatively independent and closely related. Therefore, in review, the traditional practice is often a lecture-style classroom teaching mode in which teachers list knowledge points, explain examples, consolidate variants and summarize review contents according to their own understanding and experience of curriculum standards and syllabus. The reason why this model has been adopted by teachers for a long time is mainly because it has a strong knowledge system, can highlight the key points of review and is simple to operate. Effective ways to achieve teaching objectives in a short time. In this teaching mode, although it is also inspired and guided by teachers, it basically adopts the teaching methods of one-way acceptance, passive acceptance and indoctrination by teachers and students. Students' independent review, active exploration and active development are not enough, and the immediate feedback of this teaching mode is often not strong, and classroom teaching is often divorced from students' reality. This review can neither strengthen students' knowledge, nor improve students' problem-solving ability, and it is not conducive to the cultivation of students' learning ability. As a result, the actual advantage is that you learn quickly and forget quickly. Why? One of the important reasons is that students don't really move, don't actively and systematically construct knowledge, refine mathematical thinking methods and lack mathematical experience. So it can't be digested, let alone sublimated. I think the review method of "construction, communication, intensive reading and understanding" can better solve this problem and achieve better review effect. Its main characteristics are: self-study, comprehensive improvement, students actively build and improve the network diagram of various knowledge systems and methods, so as to master knowledge, students independently choose topics, and actively recommend their own views and doubts. Teachers should be timely, precise, grasp at different levels, summarize, extend and spread in time, and urge students to effectively acquire new knowledge and ability on the basis of existing knowledge. Operation process: the construction of communication and understanding. Let's review the trigonometric function of sum and difference from two angles to illustrate the operation process of this model. 1. Give students homework before the last class: each student weaves the knowledge network of this chapter, summarizes the main mathematical ideas and methods involved in this chapter, sorts out and analyzes them, forms a scientific knowledge network, and then forms a * * * knowledge in groups, forming a written material to show their knowledge network. 2. Exchange On the basis of students' homework, organize students to exchange and show the knowledge of this chapter. Teachers and students * * * carefully study the charts displayed by classmates, find out the advantages and disadvantages, put forward suggestions for revision, actively explore and deepen their understanding of this chapter. Students actively review before the review class, fully understand the knowledge network, and achieve the goal of beginners mastering basic knowledge. Due to the need of communication, students actively prepare before class and deeply grasp the internal connection of knowledge. Intense and interesting exhibitions and discussions in the classroom will stimulate students' enthusiasm for learning, solve the purpose of reviewing basic knowledge, promote students' independent and cooperative learning and cultivate their learning ability. In this process, teachers should provide opportunities for students to cooperate with each other, guide students to help and learn from each other, and cultivate students' cooperative learning ability. Social communication between students (dialogue, consultation, cooperation, etc.). ) helps them to make up for the lack of thinking, and group discussion helps them to look at knowledge from multiple angles and form a more advanced understanding of knowledge. 3. Detailed example: given that SIN+COS = 5 1 and ∈ [0,], the value of tan is _ _ _ _ _. There are many ways to solve it. The whole class will do it by itself, the teacher will patrol and guide in time, and the student groups will exchange solutions and complement each other. Finally, the group representatives will speak, and the teachers and students will be on the same stage. Ask the students to explain why they do this. What is the basis? Of course, at this time, the requirements for teachers are very high. First, we must estimate the possible solutions. For example, (1) to find the values of sin and cos, you only need to jointly solve sin 2+cos 2 =1,and you can get the solution. (2) The square of both sides, and use Vieta theorem to solve the problem. (3) It is estimated that students will not think of the square before finding the value of sin -cos (or ignore its symbolic discussion of sin -cos). (4) According to the definition, the definitions of 5(x+y)=r, simultaneous R2 = x 2+y 2 and cotangent are obtained. (5) The Pythagorean numbers 3, 4 and 5 are used to obtain. At the same time, students' possible mistakes must be fully estimated and corrected in time. When speaking in groups, different solutions should be displayed separately. At the same time, teachers should summarize and explain, and teachers and students should sum up the law of solving problems together to improve the level of understanding. If there is a solution that the teacher didn't think of in advance, it should be written on the blackboard to fully encourage students. After the explanation, organize the students to think: 1 Put the condition [0]. 2], what's the result? 2. Replace 5 1 with m, what is the result? 3. change the conclusion to tan+ 1 tan, how to solve it? 4. What mathematical thinking methods are set for this problem? Compared with this chapter, it is a flexible application of sin 2 +cos 2 = 1, which allows students to think, discuss in groups and speak, and teachers and students * * * supplement and modify. Its purpose is to guide students to think about problems from multiple angles and levels, and to prevent students from just memorizing some independent problem-solving methods and forming a mindset. Of course, mathematics needs a set pattern, but it can't be formed by rote memorization alone, so students should understand the core of this problem and the "reason" when solving problems. The intention of this design is based on the age characteristics of students, curious, keen, lively and innovative thinking characteristics. Using multiple solutions to one question here can strengthen the vertical and horizontal connection between students and knowledge and optimize students' thinking quality. The variability of a problem can expose the essential characteristics of the problem, have a comprehensive and in-depth understanding of the problem-solving methods, find the fun of learning, eliminate the mystery of mathematics, and help cultivate students' creative thinking ability. 2. How to examine questions when solving problems? What problems should we pay attention to? Only in this way can we form a complete overall understanding of knowledge and ability. When the feedback is: 1. Given that sinx-cosx= 2 1, sin3x-cos3x = _ _ _ 2. The image of the function y=sin2x+acos2x is symmetric about the straight line X =-8, then a = _ _ _ _ _ _ _ This kind of feedback can easily find students' shortcomings and the direction of future efforts. Of course, teachers should create conditions for students to expose their shortcomings. Because of the characteristics of age, students are often reluctant to expose their shortcomings, which actually hinders their learning and development to a great extent, especially in the review class. If there are loopholes in students' basic knowledge and mathematical thinking methods are not mastered and solved, this is contrary to our review teaching goal. In short, in the review, teachers should handle the relationship between students' dominant position and teachers' leading role, so that there is guidance in the reading process, guidance in the reading process and proper guidance. From the aspects of teaching concept, teaching content, teaching process and teaching space, the exploration and practice of open teaching are carried out in an all-round way. We should trust students in thought, let them do it in action, arouse their enthusiasm and initiative, and let them study happily and efficiently in order to receive better review results. The key is that it is beneficial to Xinjiang, and mud and sand are everywhere. I went to listen to the spy collapse, and the ceremony was harmonious. 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