"Mathematics Curriculum Standards" clearly points out that effective learning activities can't just rely on imitation and memory, and hands-on practice, independent inquiry and cooperative communication are important ways for students to learn mathematics. However, traditional teaching methods still occupy most classrooms, with teaching as the center, teaching plans as the basis and teaching materials as the focus. I talk about you, I ask questions and you answer them, and the classroom atmosphere is dull. Seriously stifled the child's naive and lively nature. After many teaching and research discussions in our mathematics group, the original single and passive learning mode has been fundamentally changed, and a learning mode aimed at fully mobilizing and giving play to students' subjectivity has been established and formed, which promotes students to learn actively and individually under the guidance of teachers. With the implementation of the new curriculum, the new period has put forward new requirements for junior high school mathematics teaching, that is, stressing practical results, improving efficiency, reducing students' excessive academic burden and improving teaching quality in a large area, which has put forward new goals for teachers. How to improve efficiency and quality in 45 minutes? Teachers play a leading role in classroom teaching, so they should grasp the teaching materials, have a clear consciousness, grasp the basic links, attach importance to practice and improve teaching efficiency. First, the preparation before class should be sufficient: the new curriculum standard holds that textbooks are an important medium in the process of mathematics teaching. Teachers should use teaching materials flexibly and creatively in the process of mathematics teaching according to curriculum standards, make full use of diversified curriculum resources including teaching materials and school-based resources, and expand students' development space. The new curriculum has changed the previous teaching method of full-time irrigation and advocated students' initiative and subjectivity. Adequate preparation before math class can directly improve the efficiency of classroom teaching. In preparing lessons, we should not only prepare teaching materials, but also prepare students, that is, we should grasp the teaching materials, define the purpose, connect with the students' reality, understand the key points and difficulties in class, grasp the main line of teaching design, prepare teaching AIDS adequately and design the blackboard clearly. As the educator Mr. Tao Xingzhi said: "The responsibility of teachers is not to teach, but to teach students to learn. The method of teaching must be based on the method of learning. " For example, when teaching "Three Views", students can make multiple cube learning tools, which can be used to spell and do in class, so that students can experience the joy of success. Students are living individuals with different experiences, knowledge structures and concepts. If students' subjectivity is truly reflected, the generation in the classroom will be rich and colorful. Just like life can't live without water, sunshine and air. Without time and space, students cannot study. Leave enough time and space for thinking, so that students can develop freely, and their imagination can spread its wings and roam in the learning airspace. Classroom teaching should not be dominated by teachers, but should take students as the main body and students as the center, and create a kind of "the best way to learn any knowledge is to discover it by yourself". For knowledge, the process of students' independent thinking, mutual discussion, communication and clarification is the process of self-discovery. Give students time and space to study and explore, and let students enjoy the fun and achievements of learning. Students, teachers and students become equal partners in exchange and learning, making the classroom a world where students can independently obtain information, accumulate knowledge, solve problems and cultivate their abilities. Only in this way can we truly realize the diversification of students' learning methods. Second, new knowledge dares to break through: under the traditional teaching mode: the same mathematics, the same classroom and the same closed sky, a boring "soap opera" has been staged around books and teachers every day for several years. Students are teachers' marionettes. They are firmly controlled by teachers and must not cheat. Now, it is particularly urgent to reform classroom teaching, change this way of learning and regard the world as a classroom for students to carry out inquiry learning. Because inquiry learning has achieved five changes compared with traditional learning methods: from emphasizing teachers to emphasizing students' independent inquiry; From classroom to extracurricular activities; From focusing on results to focusing on processes; From attaching importance to book knowledge to social practice; From information-oriented one-way communication to multi-directional communication. It can be understood that the concept system of mathematics is famous for its rigorous logic, and the solution of mathematical exercises often follows the sufficient reason rule in formal logic, which can only be obtained after many inferences or calculations. Those students who have a solid foundation and strong reasoning ability will often have a certain degree of correct self-confidence after completing a problem. Even if you encounter a problem that can't be solved at the moment, you can certainly analyze it. You only need to solve a certain step of reasoning or complete some data calculation through problem setting, and the problem can be solved. The reasoning of a certain step or the calculation of a certain data is just a doubt. Being able to analyze the "crux" and know where the card is, requires a certain degree of mathematical literacy, which requires a gradual process for some students. It has become a "legal act" for students not to do the problems they can't do, and no one will do stupid things like plagiarism again. In this relaxed atmosphere, most students can calm down and analyze the crux of the problem with a research mentality, even in the process of analysis, let the problem be solved and get unexpected gains. Among them, the spirit of seeking truth is cultivated, the analytical ability is improved, and the bad style of study of self-deception is abandoned. "Interest is the best teacher." According to students' age characteristics, cognitive rules and life experience, we should seize the excitement of students' activities and provide students with rich background materials. Starting with the facts, objects and facts that students like to see and hear, vivid and interesting scenes are created in the form of stories, games, competitions and surveys to stimulate students' interest and their desire to explore, find problems and learn independently. Pay attention to the cultivation of students' thinking ability and cultivate innovative thinking. Mathematics is the gymnastics of thinking. Therefore, it is very beneficial to students' thinking training if they can skillfully arrange mathematics textbooks, skillfully guide questions and create good thinking situations. In teaching, it is necessary to break the conventional teaching of "teachers talk and students listen", change "teaching" into "inquiry", fully expose the process of knowledge formation, and urge students to enter the state of innovative thinking from the beginning, find problems and summarize laws as explorers. Generally speaking, students often master knowledge through practice to achieve their goals. In the new teaching, teachers should grasp the key points and break through the difficulties. When designing exercises, we should focus on the word "breakthrough". Generally speaking, there can be: 1. Basic exercise: this kind of exercise before the new prize is clear in purpose and strong in pertinence, paving the way for the new prize. For example, when learning the subtraction of rational numbers, we can review the addition of rational numbers first, while when learning the division of rational numbers, we can recall the multiplication operation and each operation method first, so that students can have a psychological transition and better devote themselves to the study of new knowledge. 3. Operation practice: Through drawing, cutting and spelling, the education is put into practice, which not only cultivates the practical ability, but also develops the thinking in images. For example, when teaching "the sum of the internal angles of a triangle", students can use self-made square paper to fold into two triangles, or the three internal angles of a small triangle can make a right angle, or tear off the three internal angles of a triangle to make a right angle on the table. Third, we should strengthen the consolidation of knowledge: mathematics can not only train people's thinking ability in images, but also train people's thinking ability in logic. Subjective thinking is good at developing vertically and horizontally at different levels of things, developing to the depth and breadth of problems, and achieving a comprehensive understanding of things. Therefore, teachers should pay attention to reveal the essence of mathematical problems in the process of mathematics teaching and help students improve their concise thinking ability. In the process of solving problems, we should first analyze the problem as a whole, build a mathematical thinking model, and then reveal the essence of the problem from the outside to the inside. When the problem tends to be solved, we should systematically study the related problems from one to another, so that we can solve a class of problems by solving one problem, that is, analogy. Taking the training of practical problems as an example, teachers should be good at evolving, expanding and deepening from horizontal, vertical, reverse and systematic levels, so as to improve the density and capacity of mathematics classroom teaching. Only in this way can we improve the teaching quality without increasing the burden on students. In every math class, teachers should set aside ten minutes to do exercises for students, think about teachers' questions or answer students' questions, and further strengthen the teaching content of this class. In mathematics problem-solving teaching, we should guide students to observe, think and associate from many angles, cultivate students' keen observation and positive inspiration, let students reflect and extend after solving problems, encourage students to actively seek differences and creative imagination, and cultivate students' innovative thinking. In the stage of knowledge consolidation, students have established a preliminary representation of what they have learned. How to deepen this representation, in order to understand, master and apply knowledge, from perceptual knowledge to rational knowledge, generally includes: 1, consolidation exercise: deepen the understanding of knowledge and turn it into skills. For example, in elementary arithmetic of rational numbers, we can focus on basic knowledge and strengthen the operation order; Special training for key steps to turn them into skills; The operation is simple and complete, and the application of operation rules is strengthened. 2. Contrast exercise: seek common ground while reserving differences and deepen understanding. For example, in the part of merging similar items, teachers can let students discover themselves. They can find their similarities, analyze their differences, deepen their understanding and consolidate their knowledge through comparison. 3. Variant exercise: get rid of students' mechanical imitation, overcome the fixed thinking, solve more than one question and change one question. For example, when solving basic formal engineering problems, students can list different equations from different quantities, so that students can deepen their understanding of the topic, and then they can strengthen variant exercises, which can lead to the problem of "1" in the whole process, and can change their working methods, resulting in "joint homework … half done …", "single homework … the rest of the joint homework …" and "joint" When teaching Pythagorean Theorem, we can not only master the four methods in books, but also inspire students to find a variety of solutions, fully mobilize students' learning emotions, and organically combine new knowledge and old knowledge with the solutions found by students. Fourth, summary homework has its own characteristics: in classroom teaching, teachers will get feedback of teaching information at any time. Teachers should take timely measures to adjust, evaluate, feedback or correct mistakes, and teachers should know fairly well. In the summary, we should guide students to summarize the content of this lesson or let them summarize it themselves, so that students can better grasp the content of this lesson and better organize the teaching of the next lesson. The new curriculum standard requires that teaching should organize students to fully discuss according to the teaching objectives, and evaluate, feedback and encourage each other with a positive attitude. Only in this way can we give full play to collective wisdom and carry out cooperative learning, thus achieving good teaching results. We should choose homework topics carefully. As far as "quantity" is concerned, doing more math problems seriously can really improve math scores. However, it is too heavy to win by "challenging the sea". Mathematics learning is a step-by-step process, and students can't master knowledge overnight. This determines from two aspects that math homework should not be overused, let alone become proficient with practice, but must be carefully selected, which is an important means to reduce the burden. Of course, being able to choose homework from the vast number of math problems is indeed the embodiment of the basic skills of math teachers. This is not only to choose suitable imitation training questions to consolidate memory and skillfully use, but also to look at the direction of education, especially mathematics education reform from a higher angle. As far as specific concept teaching is concerned, we should strive to firmly grasp the exercises corresponding to the "ring" associated with the ring in the concept system, and assign these exercises to each assignment in a planned and step-by-step manner. In addition, it is best to present a certain gradient for each homework question. Teachers can choose some exercises that embody profound concepts and flexible problem-solving methods according to the composition of homework questions, and even make up some open questions that discriminate wrong solutions, question paradoxes and have no definite solutions, leaving room for students who have spare time to study. For exercises that do not meet the above requirements, we should boldly give up or postpone them. Only in this way can each assignment reflect the word "choice", just like a dish with good color, smell and taste that the teacher dedicated to the students after cooking. Under the new curriculum standard, the process of mathematics teaching can be expressed as follows: the process of mathematics teaching is an activity process in which both teachers and students organize and guide students to master mathematics knowledge, develop mathematics ability and form good personality and psychological quality under the guidance of mathematics teaching objectives and with mathematics textbooks as the intermediary. The mathematics teaching process under the new curriculum is an organic combination of various elements. There is no fixed method in teaching, what is important is proper method. Anything that can conform to the teaching rules and follow children's cognitive rules in teaching can improve classroom efficiency. In order to optimize mathematics classroom teaching and develop students' thinking ability, we must achieve clear teaching objectives, prominent teaching focuses and reasonable teaching methods, so as to ensure the teaching effect and reduce students' excessive burden.