Mathematical thinking methods include:

1. Combination of numbers and shapes: It is the most important and one of the most basic thinking methods in mathematics. It is an effective idea to solve many mathematical problems. "When numbers lack shapes, it is less intuitive, but when there are countless shapes, it is difficult to understand the subtleties." This is the famous saying of Professor Hua Luogeng, a famous Chinese mathematician. It is a high-level summary of the role of the combination of numbers and shapes.

2. The idea of ??transformation: Throughout junior high school mathematics, the idea of ??transformation (reduction) has been running through it. Transformation thinking is to turn an unknown (to-be-solved) problem into a solved or easy-to-solve problem, such as turning complex into simple, difficult into easy, unknown into known, high order into low order, etc. It is the most basic idea for solving problems and one of the basic thinking methods of mathematics.

3. Classification ideas: classification of rational numbers, classification of integers, classification of real numbers, classification of angles, classification of triangles, classification of quadrilaterals, positional relationship between points and circles, positional relationship between straight lines and circles, The positional relationship between circles and so on are all discussed through classification.

4. Overall thinking

Start from the overall nature of the problem, highlight the analysis and transformation of the overall structure of the problem, discover the overall structural characteristics of the problem, and be good at using an "integrated" perspective , treat certain formulas or graphics as a whole, grasp the relationship between them, and conduct purposeful and conscious overall processing.

5. Analogical thinking

Compare two (or two types of) different mathematical objects. If you find that they are the same or similar in some aspects, then infer They may be identical or similar in other ways as well.

6. Combination method

Try to form a square formula into a formula, and then perform the required transformation. This method is often used when solving problems such as finding the optimal value of a quadratic function, saving the most money to solve practical problems, maximizing profits, etc.

7. Undetermined coefficient method

When the mathematical formula we are studying has a certain form, to determine it, we only need to find the values ??of the undetermined letters in the formula That’s it. To do this, you need to substitute the known conditions into the undetermined formula, and you will often get an equation or system of equations containing the letters to be determined. Then solving this equation or system of equations can solve the problem.