First, the cultivation of mathematical generalization ability in mathematics teaching, we should emphasize the balance between "process" and "result" of mathematics, so that students can experience the process of obtaining mathematical conclusions, rather than just paying attention to the results of mathematical activities. Here, what does it mean to "experience the process of getting mathematical conclusions"? In our view, its essence is to give students the opportunity to explore and discover the laws of mathematics through their own generalization activities. Generalization is the basis of thinking. Learning and studying mathematics, whether we can get correct abstract conclusions depends entirely on the process and level of generalization. Mathematical generalization is a process from concrete to abstract, from elementary to advanced, which is hierarchical and gradual. With the improvement of generalization level, students' thinking develops from concrete thinking in images to abstract logical thinking. In mathematics teaching, teachers should put forward higher-level generalization tasks to students in time according to their thinking development level and concept development process, and gradually develop their generalization ability. In the teaching of mathematical concepts and principles, teachers should create teaching situations, provide students with typical and appropriate specific materials, and provide appropriate steps for students' generalization activities. Make proper preparations to guide students to guess, discover and summarize abstract conclusions. Here, whether the steps paved by teachers are appropriate depends mainly on whether students can be in a state of "seemingly ignorant", "seemingly ignorant" and "half-baked". Guess is actually a tentative mastery of new knowledge by students in the process of interaction between old and new knowledge. When designing teaching situations, teachers should first analyze the old and new knowledge. Secondly, it is necessary to analyze the relationship between students' existing mathematical cognitive structure and new knowledge, determine the assimilation (adaptation) model, and thus determine the main content of the conjecture; Thirdly, we should try our best to design a variety of heuristic routes, so that students can guess at key steps and let their thinking really go through the process of generalization. The process of generalization has the characteristics of spiral rise and gradual abstraction. After students get a preliminary conclusion through generalization, teachers should guide students to concretize the summarized conclusion. This is a process of using newly acquired knowledge to solve problems and actively strengthening new knowledge. In this process, the contradiction between adaptation and inadaptability between students' cognitive structure and new conclusions is most likely to be exposed, and it is also most likely to cause students to form adaptation stimuli. In the process of generalization, we should pay attention to the role of variant training, so that students can achieve a comprehensive understanding of new knowledge through variant; We should also pay attention to the role of reflection and systematization. Through reflection, guide students to review the whole thinking process of mathematical conclusion generalization, check the gains and losses, and thus deepen their understanding of mathematical principles and general methods. Through systematization, the new knowledge is horizontally linked with the relevant knowledge in the existing cognitive structure, and the universal law is summarized, thus promoting the deepening of assimilation and adaptation. The expression of mathematics is a formal logic system, and the final establishment of mathematical theory depends on the ability to abstract and summarize according to assumptions. Therefore, teachers should guide students to learn formal abstraction, which is actually a process of advanced generalization. Students' logical reasoning ability can be well cultivated. Second, the key point is to cultivate students' thinking quality. Psychologists believe that cultivating students' mathematical thinking quality is a breakthrough in developing mathematical ability. Thinking quality includes profundity, agility, flexibility, criticism and creativity, which reflects the characteristics of different aspects of thinking. So there should be different training methods in the teaching process. The essence of mathematics determines that mathematics teaching should not only be based on the profundity of students' thinking, but also cultivate the profundity of students' thinking. The difference of mathematical thinking depth reflects the difference of students' mathematical ability. To cultivate the profundity of students' mathematical thinking in teaching is actually to cultivate students' mathematical ability. In mathematics teaching, students should be educated to see the essence through phenomena and learn to think comprehensively. Get into the habit of asking questions. For those confusing concepts, such as positive number and non-negative number, empty set f and set {0}, acute angle and the angle of the first quadrant, necessary and sufficient conditions, mapping and one-to-one mapping, sin(arcsinx) and arcsin(sinx), etc. It can guide students to understand the connection and difference between concepts through distinction and comparison, and at the same time assimilate concepts and divide old and new concepts. In this way, through variant teaching, we can deeply understand mathematical concepts, reveal and make students understand the essence and core of mathematical concepts and methods. In problem-solving teaching, we should guide students to carefully examine problems, find hidden relations, optimize the problem-solving process and find the best solution. The agility of mathematical thinking is mainly reflected in the speed problem under the correct premise. So on the one hand, we can consider training students' operation speed in mathematics teaching. On the other hand, we should strive to make students master the essence of mathematical concepts and principles and improve the abstraction of their mathematical knowledge. Because the more essential and abstract the knowledge they have, the wider the scope of their adaptation and the faster the retrieval speed. In addition, the operation speed is not only the difference in understanding mathematical knowledge, but also the difference in operation habits and thinking generalization ability. Therefore, in mathematics teaching, we should always ask students about speed, so that students can master it. Teach students some quick calculation essentials and methods in combination with the teaching content; Commonly used numbers, such as the square number of natural numbers within 20, the cubic number of natural numbers within 10, trigonometric function values of special angles, irrational numbers, π, е, lg2, lg3, should be "explained clearly"; Commonly used mathematical formulas, such as sum of squares, difference of squares, sum of cubes, difference of cubes, related formulas of quadratic equation in one variable, related formulas of logarithm and exponent, related formulas of trigonometric function, formulas of various areas and volumes, basic inequalities, formulas of permutation number and combination number, binomial theorem, related formulas of complex numbers, slope formula, standard equations of straight lines and quadratic curves, etc. , should be applied freely. Actually, it needs to be calculated quickly.