In traditional mathematics teaching, teachers often speak very seriously, students listen very attentively, students' active learning consciousness is weak, and they are very dependent on teachers. The traditional learning style overemphasizes acceptance and mastery, ignoring the process of students' discovery and inquiry, which leads to extreme treatment of students' cognitive process. Students only accept book knowledge, and their learning becomes a purely passive memory process. This way of learning will stifle people's thinking and intelligence and destroy people's enthusiasm and interest in learning. The newly promulgated mathematics curriculum standard clearly points out that "effective mathematics learning activities cannot rely solely on imitation and memory, and hands-on practice, independent exploration and cooperative communication are important ways for students to learn mathematics." Teachers are only "organizers, guides and collaborators of mathematics learning", and their duties are to "stimulate students' enthusiasm for learning, provide students with opportunities to fully engage in mathematics activities, and help them truly understand and master the basic knowledge and skills of mathematics, mathematics ideas and methods in independent exploration and cooperative practice, so as to gain rich experience in mathematics activities. It can be seen that the real implementation of the new curriculum standards urgently needs the transformation of teaching activities and students' learning methods. 1. Strengthen induction and realize the transformation from traditional explanation to guiding students to explore independently. Teachers are often accustomed to the so-called "authoritative" explanation according to textbooks and implement "standard answer teaching", which is extremely unfavorable to the development of students' thinking. Too much "norms and authority" will greatly imprison students' innovative thinking and make them form rigid thinking patterns. Modern educational theory holds that teaching is an inherent activity of human beings and a process in which the subject makes a series of changes to the object in order to achieve a certain goal. Mathematics is not taught. The process of students' learning mathematics should not only be that students passively absorb the ready-made conclusions in textbooks, but that students personally participate in a practical activity full of rich and vivid thinking and experience a process of active practice and innovation. Specifically, starting from "mathematical reality", with the help of teachers, students use their own hands and brains to participate in drills and calculations; Learn to use observation, imitation, experimental conjecture and other means to collect mathematical materials, gain learning experience, and conduct analogy analysis, induction and summary, and gradually form their own mathematical knowledge, that is, students can explore and study independently. Therefore, autonomous cooperative inquiry learning is particularly important in mathematics teaching. In order to change students' passive learning state and promote their active learning, we can try to implement "clever guidance and concise" in teaching. That is, by setting the situation, students are encouraged to think and explore independently. For many math problems, teachers don't give answers prematurely, but "kick the ball to the students", so that students can discuss it themselves, learn to express their views and find the correct answers in debates and discussions. In addition, counterexamples can be used to demonstrate, so that students can enjoy the fun of exploration in analysis and comparison. For example, "equilateral and equilateral" is the property theorem of isosceles triangle. In order to finish the teaching task on time without spending too much time, teachers usually draw graphs according to propositions, and then instruct students to construct congruent triangles to prove it. The new curriculum standard emphasizes students' practical ability. For this reason, we can let students make their own models of isosceles triangle and equilateral triangle, measure and compare them with protractor or folding method, so that students can obtain first-hand perceptual materials, and then construct congruent triangles as an auxiliary line through comparison and guess. This will take longer, but the students will gain a lot. Practice has proved that through the process of knowledge discovery and multi-party induction, students are diligent in thinking, do it themselves, dare to explore and practice, and learn more actively and interestingly. At the same time, it is more helpful to cultivate students' exploration ability. 2. Enlighten thinking and advocate the diversification of students' mathematics learning methods. Every student has his own life background and family environment. This specific life and social and cultural atmosphere can lead different students to have different ways of thinking and problem-solving strategies. Therefore, teachers should respect each student's personality, allow students to understand problems from different angles and express their views in different ways, so that students at different levels can develop to different degrees. Therefore, teachers should actively encourage students to diversify their problem-solving strategies and algorithms and allow the existence of non-unique answers, which is both "labor-saving and effective". However, the traditional mathematics teaching method is used to imposing the thinking mode of adults on students, only letting students learn to solve a problem with a solution, which artificially stifles students' independent thinking ability. However, it is very natural for students to learn strategies and algorithms to solve mathematical problems in the practice of independent exploration. In this regard, "Mathematics Curriculum Standards" emphasizes that "because of the different cultural environment, family background and their own way of thinking, students' mathematics learning activities should be a lively, proactive and personalized process. "Mathematics curriculum standards, especially as specific teaching method suggestions, highlight the diversification of problem-solving strategies from this perspective. Therefore, according to the characteristics of teaching materials, students can be provided with necessary perceptual materials first, so that they can actively explore through observation, discussion and analysis, hands-on operation, and then inspire them to think and seek multiple solutions to a problem from different angles with different thinking methods, thus stimulating students' innovative consciousness and cultivating innovative ability. 3. Emphasize cooperation and realize the transformation from authoritative teaching form to cooperative communication form. Mathematics teaching is a bilateral activity of mathematics teaching and a process of interactive development between teachers and students. Therefore, teachers should attach importance to the cultivation of students' sense of cooperation, strive to form an atmosphere of "researching problems" in the classroom, give full play to students' subjectivity, and advocate students' active practice, independent exploration and cooperative exchange. " Mathematics Curriculum Standard divides students' cooperation and communication into two important goals: problem solving and emotional attitude. For example, in the goal of solving problems, it is pointed out that "in solving problems, you have the experience of solving problems with your peers, initially learned to cooperate with others, and understood the importance of cooperation with others"; In the goal of Emotion and Attitude, it is put forward that "it is necessary to realize that many practical problems can be solved by mathematical methods and expressed and communicated in mathematical language. Mathematics is an important tool for solving practical problems and communicating, and can benefit from communication." For example, in the practice of "the midpoint of a line segment", the whole class is divided into several groups. In order to ensure the balance between groups, each group chooses a leader, and each student in the group has to ask his own questions during the discussion, and everyone can express his personal views. Small problems are solved in the group, and big problems are put forward by the group leader on behalf of the group. In class, students or teachers from other groups guide the solution. In this way, the discussion atmosphere in the class is warm, the students become the protagonists, the students in the group unite and cooperate, and the groups compete with each other. Some students follow the methods introduced in the textbook: ① measure first and then calculate to find the midpoint of the line segment; (2) using the ruler-rail method; (3) Some students who don't study well at ordinary times use the game method instead. They cut a piece of paper as long as their own lines, then fold the paper in half to find the midpoint, and then draw the midpoint on the map; (4) Some students draw line segments with white paper, then fold them in half, and then use symmetry to find the midpoint. Finally, what is the scientific basis for some students to put forward the second painting method? At this time, under the premise of affirming students' active inquiry, teachers should also seize the opportunity to give guidance. This kind of interactive and equal dialogue between teachers and students in mathematics teaching is advocated by the new curriculum. Teachers should abandon the viewpoint of "I am teaching students", form an atmosphere of "I am teaching with students", change their roles and become promoters of students' all-round harmonious development, independent development and personality development. As long as students' desire for expression is awakened and they are given the space to express freely, a beautiful, novel and spiritual world will appear in the mathematics classroom. 4. Pay attention to the reflection of the inquiry process and get the solution to the problem. The implementation of the new curriculum standards will definitely change teachers' teaching methods, and teachers need to explore, try, practice and summarize the laws constantly, so teaching reflection is very necessary. Mainly manifested in: reflection on classroom design, reflection on specific implementation, reflection on teaching gains and losses. The implementation of new curriculum standards will also change students' learning style. Teachers should guide students to reflect in teaching, and change the situation that teachers only summarize important and difficult knowledge and ignore students' own reflection and experience in traditional teaching. Teachers can ask some questions, such as "What did the inquiry process give you? How did you learn this lesson and how did you come to this rule? What do you think of the study in this class? " Wait for questions. There is no standard answer to these open-ended questions, but students' answers can reflect their personality and way of thinking, and students are the main body, so that students can get solutions to problems from reflection, not just results. The new mathematics curriculum standard puts forward newer and higher requirements for teachers' teaching and students' learning. Teachers' teaching role and students' learning methods should be greatly changed. Teachers' simple "solving puzzles" can no longer meet the learning requirements of students. Students' passive lectures and isolated homework can no longer adapt to the development of the times. As mathematics teachers who implement the reform of curriculum standards, they should actively provide students with all kinds of opportunities to fully engage in mathematics activities. Let students know mathematics in the atmosphere of independent exploration, personal practice, cooperation and exchange, master the core content of mathematics, promote students' learning of other disciplines through mathematics learning, and guide students to directly use mathematics knowledge to actively participate in various mathematical practice activities.