First, "not in the minority"-the class teaching system for all students is characterized by unified collective teaching, emphasizing the consistency of teaching requirements, teaching content, teaching progress and teaching test. It is based on the assumption that the knowledge base and learning ability of the whole class are the same, so it is easy to "cut across the board" in teaching. A good class should first really face all students, so that each student can get the greatest possible development on the original basis. Facing all students means acknowledging differences and teaching students in accordance with their aptitude. Students' cultural environment, family background and their own way of thinking restrict the learning results, and the resulting differences will lead different students to show different learning tendencies in mathematics. Admitting students' differences doesn't mean "filling the gap", but at the same time, we should devote ourselves to the development of most middle-level students, and at the same time let those outstanding students who have spare capacity in mathematics stand out, so that those students who have difficulties in learning can gain something and meet the basic requirements. To truly face all students, it is necessary to change the single classroom communication mode between teachers and students or between teachers and students according to the characteristics of teaching content and the reality of class students, and form a three-dimensional structure of multi-directional communication and multilateral interaction between teachers and students; We should effectively adopt active and exploratory learning methods, and play the role of "learning with the same body" through cooperation, discussion and exchange; On the practical level, "the top is not capped, and the bottom is guaranteed"; Special policies should be given to some special students (excellent students or students with learning difficulties); We should make the classroom a stage for every student to give full play to his ability. Second, "learning mathematics in activities"-paying attention to the learning process "Mathematics is a process in which people gradually abstract, generalize, form methods and theories and apply them on the basis of qualitative grasp and quantitative description of the objective world, which is full of exploration and creation" (quoted from the draft of National Mathematics Curriculum Standards for comments). Students' mathematics learning process can not only accept ready-made mathematics knowledge, but also actively construct it on the basis of students' existing knowledge and experience. Many things are difficult for teachers to teach, and it is up to students to understand them in activities. Only when students actively participate in learning activities can they learn effectively. In a good math class, teachers should pay close attention to students' learning process, show them the process of knowledge occurrence and development, guide them to participate in the formation of concepts and laws, and expose their thinking process of learning knowledge. Specifically, in teaching, we should grasp the connection point between old and new knowledge, and help students obtain the necessary experience and preparatory knowledge for learning new knowledge from their life experience and existing knowledge background (Ausubel called it "the first organizer"), so as to provide a cognitive fixed point for learning new knowledge and improve the availability of appropriate concepts in learners' cognitive structure; To inspire students to find the growth point of new knowledge from the original cognitive structure is not only the foundation needed to learn new knowledge, but also to know how much they already know about the new knowledge to learn, so as to determine the starting point of learning new knowledge (Vygotsky called it "the nearest development zone"); It is necessary to highlight the differences between old and new knowledge, find contradictions in comparison, trigger cognitive conflicts, make students reach an "angry" state, create scenarios for learning new knowledge, stimulate learning interest, maintain learning motivation, and help students construct the meaning of what they have learned at present. Pay attention to students' learning process, provide them with sufficient opportunities to engage in mathematical activities and exchanges, and help them truly understand and master basic mathematical knowledge and skills, mathematical ideas and methods in the process of independent exploration. In this process, let students experience what they can learn and never teach; Let the students do what they can, and never do it for him. Let the students speak for themselves and never speak for them. Create more thinking time, more activity space, more opportunities for expression and more pleasure of success for students, and truly "students are the masters of mathematics learning, and teachers are the organizers, guides and collaborators of mathematics learning." Third, "the life of mathematics lies in application"-paying attention to the combination of learning and application Mathematics is a highly applied subject, and its application has penetrated into all aspects of society. Many experts pointed out that mathematics teaching should not "pinch the head and burn the tail", but should pay attention to the establishment of mathematical model and the application of mathematics in real life. A good class should not only let students construct the meaning of knowledge, but also let them know the source and practical application of knowledge, "so that students can initially learn to use the mathematical knowledge and methods they have learned to solve some simple practical problems" (quoted from the revised edition of the Primary School Mathematics Teaching Outline). On the one hand, the teaching of a lot of knowledge in mathematics textbooks is conducive to cultivating students' application consciousness, especially the study of preliminary geometry knowledge, statistical knowledge and some application problems, which are all based on reality and sorted into mathematical problems through analysis; On the other hand, due to the limited capacity of textbooks, many students' familiar and favorite life stories failed to enter textbooks. Therefore, teachers should deal with the relationship between mathematics learning and application, pay attention to the combination of learning and application, and further understand and appreciate the application value of mathematics. Pay attention to the combination of learning and application, fully tap the mathematical application factors contained in the teaching materials in class, and insist on starting from students' life experience and knowledge accumulation; It is necessary to use the scenes and data in students' life as much as possible to write mathematical problems, reflecting the companionship between mathematics and life; In the presentation of teaching content, it is necessary to change the closed one-way structure into an open multi-directional structure; We should create as many opportunities as possible for students to use what they have learned to explore and solve some simple practical problems. In practice and application, students can understand the close relationship between mathematics and nature and human society, know the value of mathematics, enhance their confidence in understanding and applying mathematics, learn to observe and analyze the real society by using mathematical thinking mode, solve problems in daily life and other disciplines, and form a scientific spirit of being brave in exploration and innovation. Fourth, "Let the classroom be full of vitality"-paying attention to all-round development Professor Ye Lan said: "Classroom teaching should be regarded as an important life experience in the lives of teachers and students and a meaningful part of their lives." (Quoted from Ye Lan's "Let the Classroom Rejuvenate") In the mathematics classroom, students not only learn mathematics knowledge and develop intelligence, but also devote themselves to the classroom with their own emotions, motivations and needs; Besides teachers, students also interact with their peers; In addition to cognitive and emotional development, students also include group cooperation ability, behavior habits, communication awareness and ability and many other aspects.