Mathematical thinking refers to what people usually call mathematical thinking ability, that is, the ability to think and solve problems from a mathematical perspective. For example, reduction, from general to special, from special to general, the idea of function/mapping and so on.

Ten ways of thinking in mathematical thinking;

1, control mode

According to the meaning of mathematical problems, the method of solving problems through understanding, memorizing, identifying, reproducing and transferring mathematical knowledge is called contrast method.

2. Formula method

Methods to solve problems by using laws, formulas, rules and rules. It embodies the deductive thinking from general to special.

3. Comparative method

By comparing the similarities and differences between mathematical conditions and problems, we study the reasons for the similarities and differences, so as to find a solution to the problem, which is the comparative method.

Step 4 classify

According to the similarities and differences of things, things are divided into different categories, which is called classification. Classification is based on comparison. According to the * * * similarity between things, they are grouped into larger classes, and the larger classes are subdivided into smaller classes according to differences.

5. Analytical method

The way of thinking that the whole is broken down into parts, complex things are broken down into parts or elements, and these parts or elements are studied and deduced is called analytical method.

6. Integrated approach

A way of thinking that combines all parts or aspects or elements of an object into an organic whole to study, deduce and think is called comprehensive method.

7. Equation method

Unknown numbers are represented by letters, and expressions (equations) containing letters are listed according to the equivalence relation. Column equation is an abstract and generalized process, and solving equation is a deductive process.

8, parameter method

A method of expressing related quantities by letters or numbers that only participate in formulas and operations without solving them, and listing formulas according to the meaning of the questions is called parameter method. Parameters are also called auxiliary unknowns and intermediate variables. Parametric method is the product of the extension and expansion of equation method.

9. Exclusion method

The result of eliminating opposition is called exclusion. The logical principle of exclusion is that everything has its opposite. In all kinds of right and wrong results, excluding all wrong results, the rest can only be correct results. This method is also called exclusion, screening or disproof. This is an indispensable method of formal thinking.

10, special case method

For topics involving general conclusions, the method of solving problems by taking special values, drawing special pictures or setting special positions is called special case method.