1. Grasping the basic knowledge of mathematics firmly is the most basic element of mathematical thinking. The basic concepts, definitions, properties, formulas, theorems and other knowledge required by the middle school mathematics syllabus are the basis of reasoning, judgment, calculation and problem solving. Only when students firmly grasp the basic knowledge of mathematics can they be clear-cut, open-minded, deeply understand mathematical knowledge and laws, and lay a solid foundation for improving their ability to find and solve problems. Second, cultivate students' mathematical thinking ability Professor Qian Xuesen pointed out: "The ultimate wit of education lies in people's thinking process." It can be seen that mathematics teaching is essentially a process in which students understand and finally solve problems through mathematical thinking activities under the guidance of teachers. Therefore, we should pay attention to cultivating students' mathematical thinking ability in mathematics teaching. There are three forms of mathematical thinking ability, including logical reasoning ability, intuitive thinking ability and divergent thinking ability. (I) Cultivation of Logical Reasoning Ability The logical reasoning ability in mathematics refers to the ability to comprehensively analyze and prove the attributes of mathematical objects or mathematical problems by using correct thinking rules and forms. It is one of the basic mathematical abilities that students must possess. Teachers should do the following in the teaching process: First, pay attention to the teaching of basic concepts and principles. Mathematical knowledge is not a definition or a rule. The accumulation of theorems, the content of each chapter and section is not only self-contained, but also includes the analysis and synthesis of learned knowledge, the comparison and contrast between abstraction and generalization, judgment and reasoning. , to further improve their analysis, judgment and reasoning ability. Secondly, seek the training of correct thinking direction. Mathematical reasoning process is composed of a series of processes, because the conclusion of the previous reasoning may be the premise of the next reasoning, and the basis of reasoning must be extracted from many points, theorems, conditions and known conclusions. Therefore, in the teaching process, teachers should first guide students to master the basic skills of reasoning, and then pay attention to cultivating them to think about problems by using the thinking of "whole-part-whole again", and enhance their ability to turn complex problems into simple problems and unknown problems into known problems. (II) Cultivation of Intuitive Thinking Ability Kadyrov, a scientist from the former Soviet Union, once said: "No creative action can be separated from intuitive activities". In teaching, teachers should first train students to pay attention to overall observation. Secondly, teachers should pay attention to cultivating students' thinking of combining numbers with shapes. Mathematics is composed of a lot of information such as mathematics, graphics, methods and patterns. Students will use this information repeatedly when solving problems, forming a knowledge module in their minds. Once they want to solve the problem, they will associate these knowledge modules, identify and analyze them intuitively, form a comprehensive judgment on the problem, and thus get the methods and ideas to solve the problem. (3) Cultivation of Divergent Thinking Ability The neo-Confucianism of modern education holds that innovative thinking depends on divergent thinking. Divergent thinking is a way of thinking that is unconventional, seeking variation and seeking answers to questions from many aspects. In teaching, first of all, when one method and one aspect can't solve the problem, students should take the initiative to jump to another method and another aspect, think from different directions, and associate known information from multiple directions and angles; Secondly, we should give students the conditions and opportunities to think and improve their own problems independently; Finally, appropriately carry out the teaching activities of "one subject is changeable", "one subject is multi-solution" and "one method is multi-purpose". To carry out "one topic is changeable", we can reveal the logical relationship between problems through the extension and change of topics. In the process of "one problem with many solutions", we can consider this problem from multiple angles and find out the relationship, advantages and disadvantages of each method. The implementation of "one method and multiple solutions" can help students understand the relationship between knowledge points, raise their thinking to a new height and improve their ability to analyze and solve problems. Third, cultivate students to develop reflective study habits. Modern educational theory holds that the essence of education is to guide students to learn, and teachers should let students learn, so that students not only know what to learn, but also know how to learn. Therefore, teachers should not only attach importance to the study of teaching methods, but also strengthen the guidance of students' learning methods, so that students can realize the importance of reflection and learn reflective teaching. First of all, reflection runs through the process of solving problems. Paulia, a famous American mathematician, believes that problem-solving activity is not a process of mechanically executing a predetermined program, but a process of constantly adjusting it, and reflection in the process of problem-solving is particularly important. However, in the actual problem-solving process, students are generally eager to do a lot of problems and are not good at reflecting on their own thinking process, which leads to the lack of systematicness and poor structure of the knowledge they have learned. Therefore, in the teaching process, teachers should guide students to reflect on how they found and solved problems, reflect on the gains and losses of the problem-solving process and their reasons, and learn from them, sum up the learning or problem-solving process from the height of giving thinking strategies, popularize and deepen the problem, and find the best solution to the problem. Secondly, promote students' reflection after solving problems. Reflection after solving problems refers to students' reflection on their teaching and learning behavior, problem-solving ideas and methods after completing staged mathematics learning. Through reflection after solving problems, students can consolidate their knowledge and methods and develop their ability to solve problems. After solving problems, teachers should guide students to do: 1 and reflect on their own problem-solving ideas; 2. Reflect on your own problem-solving methods; Finally, reflect on the conditions and conclusions of the original question and see if the conditions can be changed. Has the corresponding problem-solving method changed? Is the inverse proposition true? And so on, in order to cultivate their rigorous thinking and deeply understand mathematical knowledge and laws. In recent years, the direction of mathematics has embarked on the road of examining comprehensive quality and ability, which requires teachers to take improving students' mathematical problem-solving ability as the main goal of mathematics work, and let students know that mathematics learning is not only the study of knowledge and skills, but also the training of discovery and creation, and it is also an activity of reflection and renewal. Teachers should actively create a good teaching environment inside and outside the classroom, help students firmly grasp the basic knowledge of mathematics, cultivate students' mathematical thinking ability, make students develop reflective teaching and learning habits, make students naturally transition from "what to learn" to "how to learn", and constantly improve their ability to find and solve problems.