Mathematical thinking methods include: function thinking, classified discussion thinking, reverse thinking, combination of numbers and shapes, function and equation thinking, transformation and transformation, whole thinking, transformation thinking, implicit condition thinking and limit thinking.

1. Functional concept

Functional thinking is a thinking strategy to solve "mathematics" problems. Since people used functions, after long-term research and exploration, the scientific community generally has a kind of consciousness, that is, function thought. When using this thinking strategy to solve problems, scientists found that they all have the same property, that is, the relationship between quantification and variables.

2. The idea of classified discussion

The idea of classified discussion is an important way of thinking. Its basic idea is to decompose a complex mathematical problem into several basic problems, realize the ideological strategy of the original problem by answering the basic problems, and classify and integrate the problems. The classification standard is equivalent to adding a known condition, realizing effective addition, decomposing the comprehensive problem into small problems, optimizing the thinking of solving problems and reducing the difficulty of solving problems.

3. The idea of reverse thinking

Reverse thinking, also known as divergent thinking, is a way of thinking about common things or opinions that seem to have become conclusive. It dares to "do the opposite", let the thinking develop in the opposite direction, explore deeply from the opposite side of the problem, establish new ideas and create new images.

4. The idea of combining numbers with shapes

Numbers and shapes are the two oldest and most basic research objects in mathematics, and they can be transformed into each other under certain conditions. The object of middle school mathematics research can be divided into two parts: number and shape. There is a connection between numbers and shapes, which is called the combination of numbers and shapes, or the combination of numbers and shapes