The so-called "autonomous learning" means that students take the initiative to learn under the guidance of teachers, requiring students to have a conscious awareness and response to questions such as why to learn, whether to learn, what to learn and how to learn. It is a comprehensive ability, and it is the ability that students show in the whole learning activity. As long as students have this ability, they will have a strong thirst for knowledge and use scientific learning methods to arrange their own learning activities reasonably. Can think positively, dare to question, and show enterprising spirit and exploration spirit in the learning process. Autonomous learning requires students to complete the prescribed learning tasks independently in the learning process. The autonomous learning of junior high school mathematics can be carried out according to the following steps:

1, create questions, and students have doubts about self-study. The ancients said, "Learning begins with thinking, and thinking originates from doubt." It can be seen that the key to teaching lies in "doubt", which is the driving force of teaching thinking, the direction of thinking, the starting point of exploring knowledge and the fulcrum of inspiring students. This step is the first step of the whole autonomous learning and training. In order to provide motivation and direction for mathematical thinking activities and make them develop continuously, teachers should constantly ask new questions to students in mathematics classroom teaching. Using the existing environmental conditions, aiming at the key points, difficulties and keys of the teaching content, we skillfully ask students questions from different new angles. (1) Questioning with clear purpose or consciousness can guide students' thinking towards the established three-dimensional teaching goal. (2) It is more difficult to ask the "doubt" of the question, which makes students fall into a temporary state of confusion from the beginning. (3) The questions should be enlightening and can stimulate students' interest and motivation in learning.

2. Dare to question and explore solutions. In the process of learning, through self-study, many problems that cannot be solved within one's own ability surface, which is called questioning. In the teaching activities full of exploration and challenges such as observation, conjecture, operation, simulation, experiment, communication and reflection, teachers should change the previous teaching methods of explaining and imitating examples, let students "move", let students think independently, boldly express their different opinions, and let students actively explore and communicate in learning activities. On the one hand, teachers should guide students to be brave in questioning and exploring solutions on the basis of learning new knowledge. On the other hand, in teaching, if students can't ask questions or ask valuable questions, we should encourage them to dispel the fear of asking questions and stimulate their enthusiasm for asking questions. Reflect students' dominant position, give full play to students' autonomous learning, and each student can participate in learning independently.

3. Analyze the questions and answer them. Questioning is the means, and solving doubts is the purpose. Zhu, a philosopher in the Southern Song Dynasty, said: "Those who learn without doubt will be taught to have doubts, while those who have doubts will have no doubt. Only here can they make progress. " Once you have a "problem" in your mind, you will try your best to solve it. First of all, when setting doubts, teachers should set the knowledge points in textbooks as doubts, so that students have the desire to solve these problems, thus stimulating their interest in exploring problems and being able to take the initiative to explore. Secondly, the teaching process should be designed scientifically to stimulate students' autonomy in exploring problems, and the process of learning knowledge points becomes their active exploration process. At the same time, add some interesting and challenging contents in the teaching process, so that students can actively observe, explore, cooperate, communicate and answer questions in their study. Change the previous teaching mode that teachers speak and students listen, and become a learning mode for students to learn and explore independently.

Second, cultivate students' cooperation and communication.

Suhomlinski once said: "There is a deep-rooted need in people's hearts, that is, to be discoverers, researchers and explorers." Cooperative learning is a teaching theory that advocates students to help each other in group activities, accomplish learning tasks together, and reward them with the overall performance of the group. Group cooperation is the way we often adopt. There are nearly 50 students in each class. In general, 7-8 students in each class are arranged as study groups to discuss and exchange self-study information. In the group, in order to complete the same task of each class, the students have a clear division of labor and number them according to the quality of the foundation. The leader of each group is 1, the difference is 2, and so on. In group activities, each member has his own task and can actively participate in group learning, leaving no dead ends. Being able to give full play to each member's advantages, cooperative learning, discussion, exchange or demonstration of their respective learning methods, and complete the self-study content well, the advantages are obvious.

Advantages 1: In the process of interactive learning, give full play to the advantages of each member, give full play to the advantages of each member's thinking, and solve learning difficulties, which will not only enable members with good foundation to fully develop in cooperation and exchange, but also enable members with poor foundation to share the success and happiness of learning, establish self-confidence in learning, and gradually form good habits of thinking positively and being good at expressing, and form good habits of learning from others.

Advantage 2: In cooperation and exchange, every member has the opportunity to speak and express his opinions without psychological pressure. In this learning atmosphere of chasing after each other, students' thinking is extremely active, their imagination is rich and bold, they speak enthusiastically, and they often argue over a small opinion. At this time, you can give full play to the guiding role of teachers and firmly remember the knowledge points. In this way of learning, teachers should not pay attention to whether students' answers are comprehensive, but should pay attention to creating this kind of free and harmonious discussion and warm learning atmosphere, so that each member can freely show his own thinking process, be inspired by communication, expand his thinking imagination, fully train his logical thinking ability and let students dare to express themselves.

Third, cultivate students' inquiry learning.

The so-called inquiry learning is "the learning method and process in which students acquire knowledge, skills and emotions through inquiry activities such as finding problems, investigating and researching, hands-on operation, guessing and asking questions, and communicating with each other". Inquiry learning mainly lies in students' learning. Carry out exploratory and research-based learning activities in an independent or group cooperative way, emphasizing students' active exploration, emotional experience and innovative thinking. After years of teaching, I think the inquiry learning of junior high school mathematics should start from the following three aspects:

① Inquiry learning through problem solving. Problem solving refers to the comprehensive use of various mathematical knowledge to creatively solve problems that are not just exercises, including real-life problems and problems derived from mathematics. If the topic with complete conditions and conclusions can be transformed into the form of giving conditions, first explore the conclusion and then prove it; You can also transform a problem that needs to be sorted out and screened to be solved or proved after giving multiple conditions; It can also be transformed into a topic that requires multiple solutions or conclusions, strengthening divergent thinking training and improving students' ability to explore problems. Starting from the real life situation, or from the basic knowledge of mathematics, we should consciously and skillfully include the problems to be solved in the basic knowledge that conforms to the students' reality, introduce students into the situation related to the problems, and stimulate their interest and curiosity in inquiry.

② Inquiry learning through mathematical modeling. In mathematical modeling activities, students should proceed from the reality of the problem, read the important information of the topic, use reasonable assumptions, simplify the topic, establish the corresponding mathematical model, connect the required professional materials with mathematical theory through thinking, integrate and run through the whole knowledge network, establish the appropriate mathematical model, then make the necessary mathematical reasoning, process the data, calculate the results, and finally check whether the results obtained by the model are in line with reality. This process is an active and efficient exploration and learning process for students.

③ Inquiry learning through open questions. When solving standard questions, imitating examples is the main solution; To solve the open question, we should think from different angles and consider different backgrounds, and we can give different answers. There is no absolute right or wrong answer. Open topic is the most effective carrier of inquiry learning. Open topics should not only reflect the thinking method of mathematical research, but also explore the solution process of the whole topic, which can not only reflect the formation process of mathematical problems, but also reflect the thinking state of students in the actual solution process. Open-ended mathematics topics are conducive to stimulating students' desire to explore at different levels, teaching students in accordance with their aptitude, and cultivating students' flexibility and divergence of thinking, so that students can enjoy the joy of exploration in the process of solving problems. The core of this topic is to cultivate students' innovative consciousness and ability. By observing, recording, analyzing, summarizing, exploring and communicating practical problems, students' independent thinking and innovative ability are stimulated, which provides students with multi-channel access to knowledge and comprehensively applies the acquired knowledge to the open learning environment, thus cultivating innovative spirit and practical ability and improving students' ability to conduct mathematical inquiry learning.

The ultimate goal of our teaching is not to teach students all the knowledge, but to let students learn to study independently and explore new knowledge actively. In the process of independent inquiry and cooperative inquiry, they can form the study habit of independence, cooperation and inquiry, learn to explore and innovate at a higher level, adapt to the development of society as soon as possible, and finally make them acquire new knowledge continuously.