The main ability of middle school students to learn mathematics is logical thinking. Logical thinking is a conditional, gradual, well-founded and gradual way of thinking. It is a thinking activity with the help of concepts, judgments, reasoning and other thinking forms. Therefore, it is particularly important and urgent to cultivate and improve students' logical thinking ability, especially in the study of senior high school entrance examination and Olympic Games. We should do the following: 1. To cultivate and improve students' mathematical logical thinking ability, students must be organized into the thinking process of analyzing, synthesizing, comparing, abstracting, judging and reasoning what they have learned. Attention should be paid to the organization of thinking process in teaching. First of all, provide sensory materials and organize abstract generalization from sensory to rational. From concrete sensory materials to abstract rational thinking is a remarkable feature of middle school students' logical thinking. With the increase of students' perception of specific materials, logical thinking is gradually strengthened. Therefore, in teaching, teachers must provide students with enough sensory materials, organize their activities from perception to abstraction, and help them establish new concepts. For example, when teaching scientific notation, students can observe the relationship between the number of digits moved by the decimal point and n in the n power of 10. Students will find that the number of digits moved by the decimal point is exactly the absolute value of n, and the forward movement should be positive and the backward movement should be negative. The development of this abstract generalization process depends entirely on the precise organization of the "observation-thinking" process. Second, guide active divergence and expansion, and promote the process of transforming old knowledge into new knowledge. The process of mathematics teaching is actually a process in which students systematically learn the indirect experience of predecessors under the guidance of teachers. It is a shortcut for students to inherit the experience of predecessors by guiding students to actively spread knowledge and promoting the transformation of old knowledge into new knowledge. There are * * * the same factors among all parts of middle school mathematics textbooks, which make them organically linked. We should explore these factors, communicate their relations, guide students to transfer the known to the unknown, assimilate the new knowledge into the old knowledge, let students reason with the obtained judgment, and then obtain new judgments, thus expanding their cognitive structure. Therefore, on the one hand, when teaching new content, we should pay attention to arouse the old content that has been learned. Third, strengthen practice guidance and promote the application from general to individual. In order to understand the concepts, principles and methods, students should not only go through the development process from the individual to the general, but also go through the regression from the general to the individual, that is, apply the general law to solve individual problems, which is a process of knowledge concretization accompanied by the thinking process. Therefore, first, we should strengthen basic exercises; Second, we should strengthen the practice of variant exercises and the exercises of questions appearing in the senior high school entrance examination and the Olympic Games. Third, we should pay attention to the comparison and expansion of contact in practice; Fourth, we should strengthen practical exercise. Fourth, guide the sorting and promote the systematization of thinking. Instruct students to sort, classify and integrate their knowledge according to certain standards or characteristics, form a certain structure and form a whole, thus promoting the systematization of thinking. For example, when we talk about the binary linear equation, we can sort out all the knowledge systems of the equation, and there is a process of "from shallow to deep, from point to surface" in students' minds. Second, seek training in the correct thinking direction. First, logical thinking is multi-directional and guides students to know the direction of thinking. Positive thinking is a thinking method that directly uses the existing conditions and draws correct conclusions through generalization and reasoning. Reverse thinking is a kind of thinking method that starts from the problem and looks for the conditions related to the problem, and changes the one-way association that only works from one aspect into the two-way association that works from two aspects. Lateral thinking is to explore the given knowledge from the local or side, turn the problem into another situation, arouse students' memory of the existing knowledge, communicate the internal connection of knowledge, and thus broaden their thinking. Divergent thinking is the opposite of concentrated thinking. It thinks from different angles, directions and sides, thus producing all kinds of novel ideas and answers. In teaching, we should pay attention to cultivating students' good habits of thinking in many ways, so that students can face all kinds of problems calmly. We should "teach people to fish, it is better to teach them to fish"! Students should be taught how to think, not just a problem. Second, guide students to seek the correct way of thinking. To cultivate logical thinking ability, we should not only let students know the direction of thinking, but also guide students to seek scientific methods in the correct direction of thinking. In order to make students be good at seeking the correct thinking direction, we should pay attention to the following points in teaching: 1. Carefully design thinking and sensory materials. To cultivate students' thinking ability, teachers need not only to provide students with rich sensory materials, but also to carefully design and skillfully arrange a large number of perceptual materials, so that students can smoothly realize the transformation from perception to abstraction. 2. Conduct thinking activities according to basic knowledge. The basic knowledge of middle school mathematics includes concepts, formulas, definitions, rules, theorems, axioms and inferences. Students can think about problems according to the above knowledge and find the correct thinking direction. For example, some students don't know how to do the center line of a triangle, and how to seek the correct thinking direction. It is very simple, that is, it is not difficult to calculate the center line of the triangle first. 3. Contact the old knowledge, make association and analogy. Old knowledge is the foundation of thinking, and thinking is the bridge to new knowledge. Associating analogy from old knowledge is also an effective way to seek the correct thinking direction. Association and analogy compare two similar or similar knowledge or problems, find the connection and difference between them, and then find the correct answer to the question. 4. Repeated training to cultivate multi-directional thinking. The cultivation of students' thinking ability can not be achieved by one or two exercises and training, but needs repeated training and practice. Because students' thinking direction is often single, there is a certain mindset, so we need not only repeated training, but also pay attention to guiding students to think from different directions and cultivate multi-directional thinking. Third, we should pay enough attention to the cultivation of good thinking quality. To cultivate students' logical thinking ability, we must pay attention to the cultivation of good thinking quality, because the quality of thinking will directly affect the strength of thinking ability. 1. Cultivate the agility and flexibility of thinking. In teaching, we should pay full attention to the examples in textbooks and other solutions in exercises, compare which one is the best, how to analyze it and whether there are any shortcomings, guide students to broaden their thinking, choose the best thinking through association and analogy, and cultivate students' agility and flexibility in thinking. 2. Cultivate the breadth and depth of thinking. Paying attention to the communication of knowledge in teaching can cultivate the breadth and depth of thinking. 3. Cultivate the independence and creativity of thinking. In teaching, we should creatively use teaching materials, participate in thinking in images and cultivate students' independence and creativity in thinking. In textbook examples, the first part is mostly to pave the way for learning new knowledge, and the second part is to consolidate and deepen what has been learned. Therefore, the teaching focus of the first few examples is to let students clearly understand the principle, while the teaching focus of the last few examples is practice. The following exercises should be further deepened, expanded and divergent. Good thinking quality and logical thinking ability are the necessary conditions for students to get high scores and full marks in the senior high school entrance examination and the Olympic Games. Students should exercise themselves hard in their studies, and strive to become the masters of learning, the masters of exams and the strong ones of life! Come on, class!