1. Look at the example from another angle. Many students often read books and examples, often passing by, because they often feel that they know everything when they read them, but they don't understand them thoroughly. So when you look at the example, cover up the solution, do it yourself, and look at it when you have finished or can't do it. At this time, think about what you did differently from the solution, what you didn't expect, what you should pay attention to, which method is better, and whether there is another solution. After the above training, my thinking space has expanded and I have a comprehensive view of the problem. If the source of the topic is clear, it will be more beneficial to add a few comments at the back of the topic to explain the "vision" and ingenuity of the topic.

2. The purpose of exploring problems, the improvement of mathematical ability is inseparable from problems, and everyone knows the simple truth that "practice makes perfect". But the problem is not to engage in sea tactics, but to think of many problems through one problem. You should focus on the thinking process of solving problems, find out the significance and role of basic mathematical knowledge and basic mathematical ideas in solving problems, and study various ways to solve the same mathematical problem with different thinking methods. In the process of analyzing and solving problems, you should not only establish the horizontal connection of knowledge, but also develop the habit of thinking from multiple angles. The value of a question lies not in doing it right or doing it right, but in knowing what the question wants to test you. Understanding the problem from this angle can not only quickly find a breakthrough in solving the problem, but also not easily enter the trap set by the teacher. Instead of rushing in a class and sweating twenty or thirty repetitive questions, it is better to master a typical problem thoroughly. For example, deeply understand the various connotations of a concept and try to deal with a typical problem in various ways from various ideas, that is, multiple solutions to one problem; Try to use * * * to explore the law of problems, that is, to solve more problems; Constantly change the conditions of the topic and test your knowledge from all aspects, that is, a topic is changeable.

3. Learn to optimize the problem-solving process and grasp three words in solving problems: number, type and shape; Reading, examination and expression should realize the free conversion of three mathematics languages (written language, symbolic language and graphic language). Don't just be satisfied with the correct answer, but also learn to optimize the process of solving problems, pursue the quality of solving problems, spend less time and do more things, in order to win enough time to think and solve high-level problems. When making multiple-choice questions, try to make a mountain out of a molehill. In addition to the direct method, we should flexibly use special value method, exclusion method, test method, combination of numbers and shapes and estimation method to solve problems. When solving problems, the writing should be concise, to the point and standardized. Don't make a mountain out of a molehill, just write "score points".