1. In the initial teaching of high school mathematics, teachers must focus on understanding and mastering students' basic knowledge, especially when explaining new knowledge, they should strictly follow the staged characteristics of students' cognitive development, take care of students' individual differences in cognitive level, emphasize students' subjective consciousness, develop students' initiative spirit and cultivate students' good will quality; At the same time, we should cultivate students' interest in learning mathematics. Interest is the best teacher. Only when students are interested in mathematics learning can they have the excitement of mathematical thinking, that is, to prevent students from thinking obstacles to a greater extent. Teachers can help students to further clarify the purpose of learning, teach students in accordance with their aptitude according to their actual situation, and put forward new and higher goals for them respectively, so that students can have a feeling of "jumping up and touching peaches" and improve their confidence in learning high school mathematics well.

For example, when freshmen enter school, we usually review the content of quadratic function, but it is difficult for students to find the maximum and minimum of quadratic function, especially the maximum and minimum of quadratic function with parameters. Therefore, I have designed the following questions, which are of great help to break through this difficult problem of students, and in the whole operation process, students (including students with poor foundation) are generally excited and their thinking is always active. The design is as follows:

1 > find the maximum and minimum of the following function at x ∈ [0 0,3]: (1) y = (x-1) 2+1,(2) y = (x+/kloc-0)

2 > find the minimum value of the function y = x2-2ax+a2+2, x ∈ [0 0,3].

3 > Find the minimum value of the function y = x2-2x+2, x∈[t, t+ 1].

The above design is gradual, and the key points to solve such problems are pointed out in time after each problem is completed, which greatly mobilizes the enthusiasm of students and improves the classroom efficiency.

2. Pay attention to the teaching of mathematical thinking methods and guide students to improve their mathematical consciousness. Mathematical consciousness is the choice of students' own behavior when solving mathematical problems. It is neither the concrete application of basic knowledge nor the evaluation of application ability. Mathematical consciousness refers to what students should do and how to do it when facing mathematical problems. As for whether they are doing well or not, it is a question of skill. Sometimes some skills problems are not that students don't understand, but that they don't know how to do it. Some students face math problems, the first thing that comes to mind is to set up that formula, imitate that done problem, and are a little unfamiliar with the background. In mathematics teaching, while emphasizing the accuracy, standardization and proficiency of basic knowledge, we should strengthen the teaching of mathematical consciousness, guide students to drive the double basics with consciousness, and infiltrate mathematical consciousness into specific problems. For example, let x2+y2 = 25 and find the range of u=. If the conventional problem-solving ideas are adopted, the range of μ is not easy to find, but it is easy to find U ∈ [6 6,6] by appropriately deforming U, where the appropriate deformation of U is actually the transformation consciousness of mathematics. Therefore, in mathematics teaching, only by strengthening the teaching of mathematics consciousness, such as the teaching of "causal transformation consciousness" and "analogical transformation consciousness", can students answer mathematics questions easily and calmly. Therefore, improving students' mathematical consciousness is an important link to break through students' mathematical thinking obstacles.

3. Induce students to expose their original thinking frame and eliminate the negative influence of thinking mode. In high school mathematics teaching, we should not only impart mathematics knowledge, but also cultivate students' thinking ability, which should be a very important part of our teaching activities. Inducing students to expose their original thinking frame, including conclusions, examples and inferences, will play an extremely important role in breaking through students' mathematical thinking obstacles.

For example, after learning the "parity of function", students often ignore the problem of definition domain when judging the parity of function. Therefore, we can design the following questions: Judge the parity of the function in the interval [2-6,2a]. Many students immediately got f(x) from f(―x)=―f(x) as odd function. The teacher asked: ① What is the meaning of the interval [2-6,2a]? ②y=x2 must be an even function? By thinking about these two questions, students realize that a function is odd function only when a=2 or a= 1, that is, the domain is symmetrical about the origin.

There are many ways to expose students' views. For example, teachers can have a heart-to-heart talk with students, use well-designed diagnostic questions to understand students' possible wrong ideas in advance, and use the principle of delayed evaluation, that is, put forward contradictions after all students' views are fully exposed to avoid incomplete exposure and incomplete solution. Sometimes you can set up a difficult problem and discuss it. The problem is thought-provoking. Choose concepts that students can't understand, knowledge that can't be used correctly or confusing problems for students to discuss, and draw correct conclusions from mistakes, which makes students particularly impressed. Moreover, by exposing students' thinking process, the influence of negative thinking mode on solving problems can be eliminated. Of course, in order to eliminate the tendency of "step by step" in students' thinking activities, we should also encourage students to carry out different thinking activities in teaching and cultivate students to be good at thinking and think independently. They are not satisfied with getting the correct answers by conventional methods, but try and explore the habit of solving problems by the simplest and best methods. Developing the creativity of thinking is also an effective way to break through students' thinking obstacles.