1, analyze the relationship between conditions and conclusions.

After solving the problem, we should think about what knowledge points the problem involves, how the known conditions are deepened and related, what conditions are applied in ways that have not appeared in previous problems, how the conditions are related to the conclusions, and whether the results are consistent with the meaning of the problem or real life. Through this kind of thinking, we can understand the background of the topic, and urge us to explore boldly, and then discover the law and stimulate creative thinking.

2. Understand mathematical methods and ideas.

After solving the problem, we should pay attention to what kind of mathematical methods and ideas are used to achieve the purpose of drawing inferences from others. Commonly used mathematical methods mainly include collocation method, method of substitution method, undetermined coefficient method, definition method, mathematical induction method, parameter method, reduction to absurdity method, construction method, analytical synthesis method, special case method and analogy induction method. Regular thinking and analysis like this is conducive to the in-depth understanding and application of knowledge and improve the ability of knowledge transfer.

3. Multiple solutions to one question, multiple solutions to one question

When solving a problem, don't just satisfy and solve it, but also consider whether there are other solutions. Often trying a variety of solutions can exercise the divergence of our thinking and cultivate our ability to solve problems by comprehensively applying what we have learned and innovative consciousness. Thinking about ways to solve this problem can also solve those problems. The backgrounds of these topics may be very different, but the mathematical methods used to solve them are the same.

4. Change and expansion of the topic

After solving a problem, it can be changed and expanded appropriately. It can mainly change the conditions of the topic, including the strengthening and weakening of conditions, the exchange of conditions and conclusions, etc. The conclusion of changing the topic is mainly the deepening and extension of the conclusion. The diversity of a problem is conducive to broadening the horizon, broadening the thinking of solving problems, improving the ability to deal with emergencies, and effectively preventing the negative impact of mindset.

5. Summary and record of errors

After solving the problem, we should think about the confusing and error-prone places in the examination questions, sum up the experience of error prevention and the lessons of mistakes, and record the wrong questions when necessary. Make full use of the training function of a topic, and over time you will realize that there are not many topics but good ones.