On the Cultivation of Mathematics Thinking Ability in Senior High School Mathematics plays an irreplaceable and unique role in cultivating and improving people's thinking ability, which is well reflected in the concept of ability adhered to by mathematics in college entrance examination. In the whole high school mathematics, with the students' existing mathematical knowledge, there are countless concepts and theorems involved. If you use it flexibly on the basis of understanding, students will only learn some "dead" knowledge. Some students just remember some topics and think about what the teacher said before. None of these can learn math well. As long as we pay attention to the cultivation of mathematical thinking ability, we can establish a good learning attitude and cultivate a strong interest in mathematics. This is an effective way to learn math well. So, what does mathematical thinking ability include? Several abilities that can be directly cultivated in mathematics learning are: abstract generalization ability, logical reasoning ability, selective judgment ability and mathematical exploration ability. Now many college entrance examination questions, on the one hand, are considered by teachers to be well written, well written, easy to use, and the amount of calculation is correspondingly reduced. On the other hand, students taught by teachers find it difficult and strange to write, and they don't know how to get to the point and can't do it effectively. For example, in the multiple-choice questionNo. 12 of the college entrance examination (Fujian Volume) in 2005, f(x) is an even function with a period of 3 defined on R, and f(2)=0, then the minimum solution number of the equation f(x)=0 in the interval (0,6) is () A.5B.4C.3D.2 Therefore, in mathematics teaching, we must strive to cultivate thinking ability, so that students can get mathematical inspiration in the process of learning mathematics. (1) abstract generalization ability Mathematical abstract generalization ability is the ability of mathematical thinking and the core of mathematical ability. It is embodied in the unique enthusiasm for generalization, the ability to find differences in common phenomena, the ability to establish relationships between various phenomena, the ability to separate the core and essence of problems, the ability to get rid of non-essential details, the ability to distinguish between essential and non-essential things, and the ability to abstract specific problems into mathematical models. Students with different mathematical abilities have different abilities in mathematical abstraction and generalization. When collecting the information provided by mathematical materials, students with mathematical ability obviously show that they can formalize mathematical materials and quickly complete the task of abstract generalization. At the same time, they have a general desire and are willing to sum up actively. Abstract generalization ability is the basis of learning mathematics. We must grasp the essence of concepts, so that we can apply concepts to solve problems. For example, to find the intersection of two sets, students should know that the intersection is a set composed of elements of two sets, so applying this concept to find the common part of two sets will solve the problem. Some students are confused because the concepts of intersection and union lie in. How to cultivate students' abstract generalization ability in mathematics teaching? I think we should start from the following aspects: 1. In teaching, the relationship between numbers and shapes reflected in mathematical materials is abstracted from concrete materials and summarized into concrete general relations and structures. To do a good job of abstract and generalized argumentation, we should pay special attention to the teaching of "analysis" and "synthesis". 2. In problem-solving teaching, we should pay attention to exploring the universality hidden behind all kinds of special details, find out its internal essence, and be good at grasping the main, basic and general things, that is, teach students to be good at using the methods of intuitive abstraction and ascending generalization. 3. Cultivate students' habit of induction, stimulate students' desire of induction, form a new type of question, often summarize this type of question, find out its essence, and be good at summarizing. 4. It is a long-term and hard work to cultivate students' abstract generalization ability. In teaching, we should always pay attention to training, consciously strictly train and require according to different situations, and gradually deepen and improve the requirements. (2) Logical reasoning ability Mathematical operation, proof and mathematical discovery activities are inseparable from reasoning. The knowledge system of mathematics is essentially a propositional system composed of logical reasoning methods. Therefore, reasoning is closely related to mathematics, and attention should be paid to the cultivation of reasoning ability in teaching. Logical reasoning is everywhere in mathematics, so we should pay attention to it. In addition to logical reasoning ability, we should pay more attention to the cultivation of intuitive reasoning ability, because intuitive reasoning makes mathematical thinking flexible, agile, creative and makes people guess. For example, for a straight line A and a plane α in space, it is known that the straight line is not in the plane α, and the straight line A is parallel to the straight line B in the plane α. It is proved that the straight line A is parallel to the plane α. Analysis: The straight line A is not in the plane α, and we know that the straight line A is parallel or intersects with the plane α. If a straight line intersects with the plane α, it must intersect with the plane α at a point A outside the straight line B (because the two straight lines are parallel), then the intersection point A is the parallel line C of the straight line B in the plane α. Reasoning: according to the parallel axiom, it is known that A is parallel to C and contradicts A ∩ C = A ... then the straight line A can't intersect the plane α. So the line is parallel to the plane. Through such a question, students are required to have the ability of logical reasoning. In teaching, we should attach importance to and guide students to think and analyze problems, and gradually cultivate students' ability. How to cultivate students' reasoning ability in teaching? I think it is very important to attach importance to the teaching of reasoning process. From the beginning, we should gradually develop a "step by step" reasoning process, strictly reason, and gradually train students to simplify the reasoning process on the basis of proficiency. We should make full use of the characteristics of geometry and other disciplines to gradually cultivate students' reasoning ability. (3) The ability to choose judgment is an important part of mathematical creativity. Selection and judgment are not only the judgment of the basic process and conclusion of mathematical reasoning, but also the estimation of the rationality of mathematical propositions, facts, ideas and methods for solving mathematical problems and the choices made on the basis of this estimation. Judgment ability is actually the thinker's self-feedback ability to the thinking process. Students with selective judgment ability are less disturbed by superficial non-essential factors, have higher accuracy and quick judgment ability, have a clear understanding of the judgment made, and can distinguish between logical judgment and intuitive guess. They have obvious psychological tendency, pursue the most reasonable solution and explore the clearest, simplest and most "beautiful" solution. How to cultivate students' ability of choice and judgment in teaching? I think we should start from the following aspects: 1. We know that intuitive judgment and choice often go through several links: obtaining information, information evaluation (judgment) and strategy selection. Therefore, we should first pay attention to obtaining information in teaching, which is the key to cultivate the ability of choice and judgment. 2. Students should gradually establish appropriate values in teaching, because this is the basis of choice and judgment. 3. In problem-solving teaching, to cultivate students' desire to choose the best solution, we should not only advocate multiple solutions to one problem, but also judge who is the best among several solutions. Where's the good news? (4) Mathematical inquiry ability Mathematical inquiry ability is a creative thinking ability developed on the basis of abstract generalization ability, reasoning ability and selective judgment ability. In essence, the process of exploration is a process of constantly putting forward ideas, verifying ideas, correcting and developing ideas. Mathematically, it is manifested in a series of meaningful discovery activities, such as putting forward mathematical questions, exploring mathematical conclusions, exploring problem-solving methods, and finding the law of problem-solving, while mathematical exploration ability is concentrated in the ability to put forward ideas and transform them. Mathematical exploration ability is the most creative element in mathematical thinking ability, and it is also the most difficult element to cultivate and develop. Students with strong exploration ability can quickly and easily switch from one psychological operation to another, showing strong flexibility, strong monitoring ability in the orientation, adjustment and control of thinking activities, strong self-awareness in the thinking process, good at asking questions and daring to guess. How to cultivate students' inquiry ability in teaching? I think we should focus on the following aspects: 1. Stimulate students' interest in learning, so that students are always in the active position of exploring the unknown world. 2. Be good at guiding students to scrutinize keywords in specific teaching. 3. Let students learn to "extend" what they have learned. 4. Give guidance to students from specific exploration methods. In the process of exploration, we should widely use various thinking methods, such as analysis, synthesis, generalization, specialization, induction, analogy, association and deduction. , and focuses on introducing the logical exploration method-synthesis and analysis to students. 5. Encourage students to be brave in exploration, be good at exploration, carry forward the spirit of innovation, put forward independent opinions and form exploration consciousness. Mathematics teaching is closely related to thinking, and mathematics ability is different from general ability. Therefore, developing mathematical thinking ability is an important task in mathematics teaching. When we strive to cultivate students' mathematical thinking ability, we should not only consider the general requirements of ability, but also deeply study the characteristics of mathematical science, mathematical activities and mathematical thinking, seek the laws of mathematical activities and cultivate students' mathematical thinking ability.