The commonly used mathematical thinking methods in mathematics mainly include: the idea of using letters to represent numbers, the idea of combining numbers with shapes, the idea of transformation (simplification), the idea of classification, the idea of analogy, the idea of functions, the idea of equations, the idea of no approximation and so on.

1. The idea of using letters to represent numbers: this is one of the basic mathematical ideas. This idea is mainly embodied in the first volume of Algebra, Chapter 2, Elementary Knowledge of Algebra.

2. The combination of numbers and shapes is one of the most important and basic thinking methods in mathematics and an effective way to solve many mathematical problems. "Less is not intuitive, but more is difficult to be nuanced" is a famous saying of Professor Hua, a famous mathematician in China, which highly summarizes the role of the combination of numbers and shapes.

3. Transforming ideas: In the whole junior high school mathematics, transforming (transforming) ideas have been running through it. Transforming thinking is to transform an unknown (to be solved) problem into a solved or easy-to-solve problem, such as simplifying the complex, changing the difficult to the easy, changing the unknown to the known, and changing the high order to the low order. It is one of the most basic problem-solving ideas and one of the basic thinking methods of mathematics.

4. Classification idea: The classification of rational numbers, algebraic expressions, real numbers, angles, triangles and quadrangles, the positional relationship between points and circles, straight lines and circles, and the positional relationship between circles are all discussed through classification.

5. Analogy: Analogical reasoning is of great significance in people's activities to understand and transform the objective world. You can learn from analogy and inspire thinking. It is not only the basis for solving a large number of problems in daily life, but also a powerful tool for scientific research and invention.

6. Function thought: Dialectical materialism holds that everything in the world is in the process of movement, change and development, which requires us to attach importance to the teaching of function thought and method in teaching.

7. Equation: It is the main content of junior high school algebra. Junior high school mainly studied several kinds of equations and their solutions, and junior high school will form the idea of equations. The idea of equation is to highlight the equal relationship between known quantity and unknown quantity, and achieve the purpose of evaluation by setting unknown quantity, listing equation or equation, solving equation or equation and so on.