We encourage students to do mathematics, so that students can improve their abilities through continuous exploration, instead of watching and listening to mathematics. In classroom teaching, students should first participate in colorful activities as cognitive subjects, reorganize their internal cognitive structure and construct their own understanding of content and meaning in the interaction with situations. Only when students thoroughly study the problem before the teacher explains it can they have the "capital" to have an equal dialogue and exchange with the teacher and truly become the main body of learning. As long as you practice before you speak, even if the teacher's speech is the main form, it is also a kind of communication. In the process of the teacher's speech, students must compare and evaluate their own ideas with those in the teacher's mind. We also have various forms of "talk" such as group discussion, group defense, and mutual questions between teachers and students, which can make teachers and students communicate better! Another important function of "practice before speaking" is to let students fully feel the endless pleasure of seeking knowledge in the subject. We should impress students with the inherent charm of this subject. The most exciting time for students to learn mathematics is when they finally find a solution to the problem through hard thinking! After the implementation of "practice before speaking", several students are reluctant to leave the classroom and often wake up after ringing the bell, because students are still immersed in the fun of mathematical inquiry.

First, create situational strategies.

Homlinski said: "In people's hearts, there is a deep-rooted need to be a discoverer, researcher and explorer, and this need is particularly strong in students' spiritual world." In teaching activities, by combining different teaching contents to create problem situations, students' thinking can be mobilized, students' internal drive can be stimulated, and students can really enter the learning state, thus achieving the purpose of mastering knowledge, training thinking and improving practical inquiry ability. Mathematics has a high degree of abstraction, strict logic and wide application. Practice tells us that creating mathematical problem situations can better stimulate and satisfy students' desire for mathematical inquiry, and has a positive effect on improving students' original cognitive structure, learning new knowledge and cultivating mathematical thinking and ability.

Second, the strategy of independent inquiry

Learning to survive ―― Today and Tomorrow in Education: "Education should not spend so much effort on transmitting and storing knowledge, but should work harder to find ways to acquire knowledge (learn how to learn)." The Decision on Deepening Education Reform and Promoting Quality Education issued by the Central Committee and the State Council further clarified that the implementation of quality education should focus on cultivating students' innovative spirit and practical ability, and innovative education with cultivating innovative spirit and practical ability as the core has become the theme of education development. The new curriculum reform of mathematics is based on this theme, focusing on students, cultivating students to learn to learn, paying attention to students' active development, and laying the foundation for their lifelong study, life and work. The focus of mathematics curriculum reform is how to promote the change of students' learning style, encourage students to study independently and cooperatively under the guidance of teachers, change the long-term single and absolute learning style, and advocate the diversification of learning styles.

Third, questioning strategies

Using modern educational technology with multimedia technology and network technology as the core, we can create situations in the mathematics laboratory as truly as possible, so that learning can be carried out in situations that are basically consistent with or close to the actual situation. Create a variety of teaching situations to stimulate students' enthusiasm for learning. In the teaching process, teachers and students can fully communicate, and students can participate in the teaching process in a democratic, harmonious and rational way. This is the best form of interaction between teachers and students, and it is also a reliable guarantee to give full play to the overall benefits of teaching. The ability to solve problems is the core of thinking ability, and one of the important goals of imparting knowledge to students is to improve their ability to solve problems by using knowledge. In the process of students' independent exploration, the teacher's task is to inspire and guide students to experience the process of mathematics discovery and creation through various forms of independent learning and exploration activities, improve students' problem-solving ability and develop students' innovative consciousness.

Fourth, cooperation and communication strategies.

In the network environment, students have many study partners to choose from. Students choose what they have learned through the internet and look for learners who are learning the same content. By mutual consent, they choose one of them as their learning partner. When one of them encounters a problem, the two sides will discuss it with each other, exchange views on the same problem from different angles, and help and remind each other until the problem is solved. Two or more learners compete for the same learning content or learning situation to see who can achieve the educational goal first. First, ask a question and provide relevant information to solve the problem, or students can freely choose competitors or teachers can specify competitors, and then let students start to solve the problem independently, and at the same time, let them monitor their opponents' problem-solving situation at any time.

Through communication and interaction, students will see different understandings and ideas. Students should learn to clarify and express their own views, learn to listen and understand other people's ideas, learn to accept, appreciate, argue and help each other, and constantly reflect and judge their own and other people's views. Through this kind of cooperation and exchange, students can see different aspects of the problem and solutions, so as to have a new understanding of knowledge.

The reflection of inquiry activity is the learners' reverse thinking about the process of their own mathematical inquiry activity and the learning characteristics of related things involved in the activity process. The basic feature of reflective mathematics learning is inquiry. At present, the weakest link in mathematics teaching is the reflection of mathematics activities, but it is the most important link in mathematics inquiry teaching. The abstraction of mathematical objects, the exploration of mathematical activities, the rigor of mathematical reasoning and the particularity of mathematical language determine that it is impossible for middle school students at the stage of thinking development to directly grasp the essence of mathematical activities at one time. Only after repeated thinking, in-depth research and self-adjustment can they gain insight into the essential characteristics of mathematical activities.