The new curriculum standard of mathematics puts forward that teaching is to teach students the ability to acquire new knowledge with the help of existing knowledge, so that learning becomes a thinking activity. The fundamental way out for the reform of mathematics teaching in primary schools lies in creating a broad space for cultivating children's own learning ability, creativity and self-development ability, filling the gaps through teachers' necessary inspiration and guidance, guiding students to master knowledge in thinking and developing their thinking ability in mastering knowledge. Effective independent inquiry has two preconditions: First, students will explore. In other words, the selected mathematical problems should be suitable for students to solve through exploration, and the strategies and methods for solving problems are what students can think of. Second, students will explore. In other words, the concept of exploration is not imposed on students by teachers, but the students themselves work out strategies and methods to solve problems through individual or group efforts. Of course, effective exploration does not exclude the interaction between students and teachers and students. It is inseparable from the guidance of teachers and the mutual inspiration between students. It is an exploration and exploration based on the cooperation between students and teachers under the guidance of teachers. Teaching is to let students actively participate in the process of exploring knowledge, so that students' ability can be developed. Then, how to guide students to better explore mathematical knowledge and cultivate scientific independent inquiry ability? First, create a life situation and build an autonomous learning platform. Mathematics curriculum standard clearly points out: "we should pay attention to learning and understanding mathematics from students' life practice and existing knowledge." "This requirement points out that primary school mathematics teaching should enable students to learn to look at mathematics from the perspective of life and think about life with mathematical ideas, so as to feel the interest and usefulness of mathematics in rich mathematics learning activities. In teaching, teachers should create life-oriented problem situations according to students' psychological characteristics, build a life platform for students, and provide students with opportunities for operation and practice. You can choose pictures of toys, stationery, food or animals as learning materials for counting and statistical activities; At the same time, it is students' nature to be naive and imaginative. Beautiful fairy tales, interesting games and riddles are also what they are willing to accept and think about! By selecting vivid and interesting materials closely related to students' life, we can stimulate students' desire to actively explore, experience the close relationship between mathematics and life, build a platform for students' autonomous learning, broaden their research horizons, develop mathematical thinking and improve their ability to solve practical problems! In the past, when teaching interesting graphics, it was enough to tell students what a rectangle is and what a square is, and how to distinguish it. Now, teachers need to guide students to experience the process of "doing mathematics", and communicate with students on an equal footing in this process, paying attention to what information students have obtained and what questions they can ask, so that students can solve their own problems and further feel the close connection between mathematics and real life. Second, encourage exchanges and cooperation to promote the development of autonomous learning. Under the guidance of the new curriculum concept, mathematics classroom teaching should also provide students with sufficient time and space, and turn the classroom into a collective lecture hall for students' independent exchange and cooperation from multiple angles and in all directions, so that every student can experience the happiness of learning in prosperity, the success of exploration in adversity and the rich emotional experience of active participation. Students sing "leading role" in class, while teachers are only "supporting roles", leaving time and space for students to think, explore and communicate, and paying attention to students' emotions, attitudes and thinking in the learning process. Maybe some students can't remember at the moment, but after all, he is participating. Teachers strongly encourage students to express themselves, discuss different answers on the basis of deepening understanding, and prompt those fresh and meaningful communication examples that appear among students. We should be good at grasping students' ideas, inspiring them to pay attention to important aspects of the problem, guiding them to share their ideas and achievements, and re-examining their own ideas. In this course, I try to establish an open relationship between teachers and students. The relaxed and democratic teaching atmosphere allows students to speak freely and truly reflect their vitality. For example, in the teaching process, some students suggested that "if the four corners of a circular piece of paper are cut into arcs, it may become a square". Then another student said, "You can cut a circle in a rectangle or a triangle. "Students have different ways of thinking. In teaching, we should recognize and respect students' differences and let them expose different thinking, so as to ensure that students' learning is full of personality. Third, open your mind and leave enough space for independent inquiry. Students are the masters of learning. Cultivating students' ability and developing their intelligence is the ultimate goal for students to play their main role. Students need to constantly master various methods of autonomous learning in exploration and practice, and develop their own abilities in the process of flexible use of methods and active participation in learning. Therefore, in teaching, students are encouraged to learn actively in their favorite way, and through observation and operation experiments, students can mobilize their eyes, mouth, hands, brain, ears and other senses to participate in cognitive activities, explore the laws of knowledge, and create conditions for the internalization of knowledge. For example, in the lesson "The Basic Nature of Fractions", we once designed the same learning style for students, asking them to learn according to the process designed by the teacher. This kind of classroom teaching seems to be effective. In order to create personalized learning space for students and encourage them to learn in familiar ways, I guide students to verify their guesses in this way (score = score = score): "There are some materials in the envelope on the desk. You can choose materials according to your own needs to verify your guess. If you don't think you need these materials, of course. " This design not only provides students with the opportunity to choose freely in the exploration activities, but also makes the activities interesting and challenging. In fact, students' verification methods are colorful, even unexpected and creative. Some use physical objects to verify the equation relationship according to the meaning of the score; Some don't use physical objects to calculate the score value according to the relationship between score and division to verify the equality relationship; Some rewrite the fraction into division and then verify the equality relationship according to the quotient invariance of division; More importantly, we don't have to rely on nature or write, we just rely on imagination. According to 48 students in the class, some are 36, which proves that the three scores are equal ... even if you choose physical verification, the situation is different. Some of them use the length of the rope to verify; Some people also use the equal size of the shadow parts in the circle to verify; Others use the number of sticks to verify. It can be seen that leaving enough space for students to study and explore can provide a broad learning space for students' personalized learning and make the activities truly independent and open. At the same time, let students experience the application process of knowledge and feel the joy of success. In class, teachers should teach students to discuss and cooperate, so that students can become the masters of learning. In teaching, let go boldly, give students enough time to discuss and cooperate in learning, and let students become the protagonists of learning and the active explorers of knowledge. I often say to students, "The classroom is yours, and the math class is yours, triangle." These learning tools, such as protractor and compass, are yours, and so are the learning tasks of this class. Teachers and classmates are all your assistants. If you want to learn better knowledge, you must rely on yourself. At the same time, we can also cooperate, discuss and compete with each other. "In the learning atmosphere of discussion and competition, students are always in the state of thinking of constantly discovering and solving problems. After a class, they not only learned what they were interested in, but also gave full play to their autonomy. Teachers should not only stimulate and maintain students' enthusiasm for participating in the classroom independently, but also effectively extend generate's enthusiasm for participating in the classroom after class, so as to urge them to actively explore the mysteries of mathematics knowledge after class, so as to experience the charm of mathematics knowledge, further stimulate their strong interest in learning mathematics, and keep students in an atmosphere of active and conscious participation from one class to another. For example, teachers design more questions after class, "You will test everyone in the next class and compare who is the' best little teacher'." I think such a creative proposal will immediately arouse the enthusiasm of students and stimulate a lot of enthusiasm for after-school participation. In short, as long as teachers attach importance to teaching and persist in training, students' autonomous learning ability will be developed and their enthusiasm for inquiry will be improved over time.