First, through setting question situations, improve the mathematical thinking ability of senior high school students.
Mathematics teaching is actually a process of asking and solving problems. It can be said that the problem is the key to mathematics and an important way to promote students to make greater progress. Under the background of quality education and new curriculum reform, in order to let students learn more knowledge and improve their ability to solve mathematical problems, we should attach importance to the cultivation of students' mathematical thinking ability, so that students' thinking ability can be greatly improved and the goal of mathematics teaching can be realized. In the process of mathematics teaching, we should attach great importance to mathematics problems, whether it is the whole teaching process or a certain link in teaching. According to students' actual level and teaching content, combined with real life, corresponding problem situations are set up. Through the creation of problem situations, the new knowledge learned by students is introduced into real life reasonably and effectively, thus stimulating students' interest in learning, activating students' mathematical thinking and their desire to learn mathematics, thus improving the quality of mathematics teaching and ensuring the continuous improvement of students' mathematical thinking ability.
For example, when teachers talk about "the application of function", they can teach relevant knowledge by setting problem situations, so as to better introduce teaching content and stimulate students' interest in learning function knowledge. For example, teachers can set questions such as "Do students know what a function is", "What's the use of a function in our real life" and "What's the role of learning a function" for students to explore. The process of discussion is the process of improving the mathematical thinking ability of senior high school students. In this process, teachers should give full play to their role and guide students appropriately and reasonably, so as to guide students to approach relevant teaching content more quickly. However, it is important that teachers should pay attention to cultivating students' thinking ability step by step from easy to difficult and from shallow to deep when setting up problem situations, so as to cultivate students' mathematical thinking ability to the maximum extent.
Second, improve the mathematical thinking ability of senior high school students by exploring problem-solving ideas.
Topic is the most important form of mathematics. Teachers should improve students' mathematical thinking ability by exploring problem-solving ideas, so as to achieve the purpose of cultivating students' mathematical thinking ability. In the process of high school students doing problems, some students don't pay much attention to the effective analysis of the problems. They usually take it and do it, and soon forget it. Therefore, as long as the problem changes, they should reconsider. In order to change this situation, teachers should cultivate students' mathematical thinking ability in a targeted way, give students some novel and typical problems from their specific conditions, encourage students to think actively and independently, and guide them to explore ways to solve problems. Some topics need strong thinking ability and innovative ability, and some topics need clever problem-solving ideas, which plays an important role in cultivating students' mathematical thinking ability. Therefore, teachers can make full use of such questions to cultivate students' thinking ability, stimulate students' desire to find the best way to solve problems, and thus improve teaching quality and students' mathematical thinking ability.
For example, in the section "Simple Linear Programming", the plane region represented by binary linear inequality is an abstract concept, which requires students to have strong mathematical thinking ability to better understand and master. Teachers can make full use of the exploration and analysis of solving some problems to improve students' mathematical thinking ability. For example, when talking about "drawing a plane area represented by the inequality 2x+y-6=0", because students have just come into contact with this knowledge, they have not established the relevant thinking ability. Therefore, teachers can guide students to explore problem-solving ideas first, and then draw their plane areas. This can not only improve students' mathematical thinking ability, but also improve teaching efficiency.
Thirdly, through the reflection and summary of the teaching content, the mathematical thinking ability of senior high school students is cultivated.
Constantly reflecting and summarizing the teaching content is an important guarantee to improve the quality of mathematics teaching. Teachers reasonably guide students to reflect and summarize the teaching content, which can deepen students' understanding of what they have learned, and then enable students to better complete the learning of the teaching content. Reflection and summary are the main motivation and core of thinking activities in mathematics teaching. Only when students reflect and summarize the new teaching content in time can they consolidate their knowledge and improve their mathematics knowledge. Therefore, in the process of carrying out mathematics teaching activities, teachers should guide students to reflect on the teaching content of each class, actively summarize each kind of examples, and establish the connection between old and new knowledge through continuous reflection and summary, so as to find out the scientific methods and laws to solve problems, further deepen the understanding of the formation process of learned knowledge, and ensure that methods to solve similar problems can be found quickly in the future. Improving and optimizing the ability to solve mathematical problems has greatly improved the mathematical thinking ability of senior high school students and achieved good teaching results.
For example, when talking about "arrangement", teachers should guide students to reflect and summarize relevant knowledge in time after finishing the teaching content, so that students can reflect on their own learning deficiencies by summarizing the definition of arrangement number, the difference between arrangement number and an arrangement, and the formula of arrangement number, so as to better grasp the basic principles of arrangement and successfully solve the application problems of arrangement. Improve their own mathematical thinking ability and lay a good foundation for improving the quality of mathematics teaching.
Fourthly, using retrospective thinking to improve senior high school students' mathematical thinking ability.
At present, high school students' math homework is mainly exercises. The purpose of correcting homework by teachers is to check whether students have mastered what they have learned, and to supervise students to consolidate relevant knowledge, so as to judge whether students are right or wrong in solving problems, and at the same time, to improve students' mathematical thinking ability by recalling thinking methods, so as to help students learn mathematical knowledge better. The mathematics knowledge learned by senior high school students is composed of numbers, symbols, words and letters, and the connotation and form of knowledge are abstract. Students need to fully mobilize their mathematical thinking to learn abstract knowledge, which is still difficult for high school students whose intelligence is still developing. Without retrospective thinking, all kinds of mathematical thinking methods are easier to forget. Therefore, in the process of mathematics teaching, teachers should make full use of retrospective thinking mode to help students learn, that is, teachers should help students regularly recall and summarize their own thinking mode, knowledge structure and thinking process, for example, let students recall relevant knowledge according to the textbook catalogue or a certain knowledge point. After a period of study, let students sort out and reprocess what they have learned in order to improve their abstract thinking and generalization ability. This can not only prevent students from forming fixed thinking patterns, but also help students form divergent thinking, so that the mathematical thinking of senior high school students can be greatly improved.
For example, when the teacher talks about "ellipse and its standard equation", the thinking mode of recollection is an effective way to improve the mathematical thinking ability of senior high school students. After talking about all the knowledge of ellipse and its standard equation, the teacher draws a knowledge structure diagram on the blackboard, so that students can recall what they have learned in this chapter according to the knowledge structure, such as the definition of ellipse and the form of elliptic standard equation, and promote the improvement of students' mathematical thinking ability.