Function thought refers to analyzing and studying the quantitative relationship in mathematics from the viewpoint of movement change, and analyzing, transforming and solving problems by establishing the functional relationship and using the image and nature of the function; The idea of equation is to solve the problem by transforming the problem into an equation or inequality model with mathematical language from the quantitative relationship of the problem. Students can use transformation ideas to transform functions and equations when solving problems.

Second, the combination of numbers and shapes.

The object of middle school mathematics research can be divided into two parts, one is number, the other is shape, but there is a connection between number and shape, which is called combination of number and shape or combination of shape and number. It is not only a "magic weapon" to find the breakthrough point of solving problems, but also a "good prescription" to optimize the way of solving problems. Therefore, it is suggested that students draw as many pictures as possible when solving math problems, which will help to understand the meaning of the problems correctly and solve them quickly.

Third, the concept of special and general.

This way of thinking is sometimes particularly effective in solving multiple-choice questions, because when a proposition is established in a general sense, it is bound to be established in its special circumstances. Accordingly, students can directly determine the correct choice in multiple-choice questions. Not only that, it is also useful to explore the problem-solving strategies of subjective questions with this way of thinking.

Fourth, extreme thinking problem-solving steps

The general steps to solve problems with extreme thinking are as follows: 1. Try to imagine a variable related to an unknown quantity; Second, confirm that the result of this variable through infinite process is an unknown quantity; Third, construct a function (sequence) and use the limit calculation rules to get the results or use the limit position of the graph to directly calculate the results.