"Knowledge is not passively absorbed, but actively constructed by cognitive subjects." The meaning of this view is that knowledge is not taught unilaterally by teachers, but is actively constructed by students under certain circumstances, using existing learning experience and through the guidance of teachers and the cooperation of other students. This teaching mode emphasizes student-centered, and teachers only help and promote students' knowledge construction. In other words, mathematics teaching is a bilateral activity between teachers and students, and teaching activities should pay attention to students' subjectivity. To embody students' subjectivity, students must think, experience and acquire knowledge in interactive communication. In high school math class, some students are active in thinking and dare to answer questions actively, while some students are indifferent to the questions raised by teachers, as if they have nothing to do with the class. Therefore, as teachers standing in the front line of education, we should pay attention to the learning situation of the disadvantaged groups among students and truly face all students in the classroom. If we can do this well, students will be interested in learning and become active, and the teaching effect will be obvious. Therefore, mathematics teaching should be based on students' mathematics reality, so that all students can actively participate in learning. If this principle is followed in mathematics classroom teaching, students' learning will be an interesting and efficient activity. Let me talk about my views on this point:

First, be tolerant and kind to every student and create a harmonious classroom atmosphere.

In a harmonious classroom atmosphere, students will not regard teachers as dictators, but friends who can communicate with themselves on an equal footing. Especially for students with poor academic performance, they are very concerned about the teacher's attitude, even if it is a look from the teacher or a casual encouragement. Therefore, it is necessary to carry out interactive and cooperative learning activities between teachers and students on the basis of equality between teachers and students in the classroom. In class, teachers participate in students' group learning activities, and find and solve problems with students; Teachers put forward mathematical problems encountered in life and work and discuss and solve them with students; In collective communication, teachers and students ask me and answer, and cooperate to exchange and calculate the answers; Teachers' mistakes can be immediately pointed out by students, and teachers can immediately correct and apologize ... Only under such a democratic and equal teacher-student relationship can each student learn more actively.

Second, correctly understand the role of teachers in teaching.

Teaching is originally a two-way activity for teachers and students to exchange ideas and explore each other, and it is a process of learning from each other. Therefore, in teaching, teachers should be the leaders of students' learning activities, and their duty is to educate all students, and they should firmly believe that every student has learning potential. We should not only guide students to learn knowledge and solve problems, but also teach them how to think. In teaching practice, try to show the whole process of mathematical problem thinking, and encourage students to dare to question and have their own thinking and innovation. As the organizer of students' learning, teachers should attach importance to each individual student, guide students to express their opinions and put forward their own opinions, and provide students with the most important learning resources, such as space and time for cooperation and exchange. In teaching, we should not only be satisfied with imparting knowledge, but also pay attention to organizing teaching with a series of questions. In mathematics class, teachers are faced with a living teaching subject. Teachers can't use traditional knowledge teaching instead of subjective activities, but let students truly reflect their subjectivity in the space of free activities. Teachers should also abandon the concept of disciplinarians, establish an equal relationship with students with a cooperative attitude, form a good atmosphere of teacher-student interaction, democracy and harmony, and guide students to subtly increase their knowledge and accumulate experience in their thinking.

Third, cultivate students' self-study ability.

Classroom is the main position of teaching activities and the main channel for students to acquire knowledge and ability. Therefore, when determining the teaching goal, we should pay attention to that we can neither lower the goal at will nor raise the goal subjectively, and it is difficult to achieve the teaching goal divorced from the students' reality. Students should also be encouraged to actively participate in teaching activities, including active participation in thinking and action. As a math teacher, it is very important to change the previous "cramming" and "cramming" teaching methods. In classroom teaching, if we grasp students' psychological characteristics and create problem situations that every student is interested in, we can not only stimulate students' interest in learning and improve teaching efficiency, but also mobilize all students' cognitive system, expand their thinking and become the masters of learning. If creating situations can be combined with students' daily life, involving specific activity situations that students are familiar with and interested in, students can be guided to communicate from concrete perceptual practice to abstract generalization through association and analogy, which can not only enable students to acquire mathematical knowledge and solve practical problems with mathematical knowledge, but more importantly, make students realize that mathematics originally came from our lives. In teaching, we should pay attention to the methods of setting questions, controlling questions and answering questions, form a lively student-centered learning situation, stimulate students' creative passion, and thus cultivate students' problem-solving ability. While respecting students' subjectivity, we should explore each student's learning potential and try our best to achieve flexible management. In teaching, I often use the method of hierarchical guidance so that every student can make steady progress. In order to arouse their enthusiasm for learning, I didn't rush to tell the students the answers to the questions, so that they could master knowledge in communication and improve their ability in discussion. In the teaching process, the environment and conditions of exploration activities are created, so that students can explore the general through observation and induction, the general from the special, and the new knowledge from the old knowledge through analogy and association, which has achieved good results. In classroom teaching, we should also flexibly use a variety of evaluation methods, make full use of developmental evaluation, constantly hint that students "I can do it" in various ways, and rationally use diversified evaluation methods, which can also well mobilize students' initiative to participate in cooperative learning. We should be good at praise and encouragement, be more sure and less critical, find the bright spots of students in time, constantly ponder the students' ideas and methods and possible problems in learning, and take the form of a series of questions as well.

Fourth, pay attention to the process of students' mathematics learning and creation.

Classroom teaching needs not only teachers' instruction and guidance, but also students' independent exploration and cooperation, so as to cultivate students' good habit of active learning. Teachers should encourage students to discover mathematical laws and methods to solve problems, so that students can experience the process of knowledge formation and become the real masters of learning. At the same time, teachers should give full play to the leading role of "coach in different places". In addition, to improve the efficiency of mathematics classroom in an all-round way, we should not only pay attention to the cultivation of explicit knowledge and skill goals, but also pay attention to the cultivation of students' learning and creative process. Because mathematics doesn't need many experiments to prove the correctness of the content like physics and chemistry, its conclusions can be drawn independently by different people. Therefore, teachers should highlight students' dominant position, provide students with opportunities to learn and create, keep them in a proactive state, and stimulate students' creative desire. For example, in the teaching of related concepts of series, I first show students a series of specific series, and then let students compare, analyze, study and discuss themselves to find out the essence of series, and encourage students to form study groups to explore the characteristics of series. Through such a process, it has played a very good role in students' learning ability, practical research ability and mathematics learning interest.

In a word, the teaching process is not only a rational process of students' cognition, but also an emotional and socialized irrational process. It is a process in which teachers and students exchange experiences, exchange emotions, enlighten each other's hearts and create together. It is a unified development process in which students participate in the interaction between intellectual factors and non-intellectual factors. In this process, teachers provide students with phenomena and problems according to the internal structure of knowledge and students' mathematical reality, so that students can devote themselves to the classroom. In high school mathematics classroom teaching, in order to optimize teaching, we must grasp this process, update our learning concept, pay attention to the all-round development of students, and constantly improve our learning ability and teaching methods under the guidance of the spirit of new curriculum reform. The cultivation of students' mathematical ability runs through the whole process of mathematics classroom teaching. Students should seize the opportunity to analogize, popularize, explore and question, develop their general ability and lay a solid foundation for lifelong learning.