The so-called method refers to the operable rules or patterns contained in the means, methods and behaviors that people take to achieve a certain goal. Through long-term practice, people have discovered many means, methods or procedures of applying mathematical ideas. The same means, approaches or procedures have been used repeatedly for many times, and all of them have achieved the expected purpose, which has become a mathematical method. Mathematical method is a scientific research method with mathematics as a tool, that is, mathematical language is used to express the state, relationship and process of things.

Mathematical methods have the following three basic characteristics: first, they are highly abstract and generalized; The second is accuracy, that is, the rigor of logic and the certainty of conclusion; The third is the universality and operability of application.

Mathematical method plays an important role in scientific and technological research: first, it provides a concise and accurate formal language; The second is to provide quantitative analysis and calculation methods; Third, it provides a tool for logical reasoning. The development of modern science and technology, especially the development of electronic computers, and the strengthening of the status and role of mathematical methods are exactly complementary.

Basic mathematical methods commonly used in middle school mathematics can be roughly divided into the following three categories:

(1) methods in logic, such as analysis (including reduction to absurdity), synthesis, induction, and exhaustive method (requiring classified discussion). These methods should not only conform to the basic laws and rules in logic, but also have mathematical characteristics because they are used in mathematics.

(2) General methods in mathematics, such as modeling method, elimination method, reduction method, substitution method, image method (also called coordinate method, which is often called image method in algebra, and we will learn coordinate method later in analytic geometry), comparison method (which mainly refers to comparison size in mathematics, which is different from many aspects in logic), scaling method, and vector method and mathematical induction to be learned later.

(3) Special methods in mathematics, such as collocation method, undetermined coefficient method, addition and subtraction (elimination) method, formula method, substitution method (also called intermediate variable method), decomposition method (including the mathematical idea of adding auxiliary elements to realize transformation), factorization method, parallel movement method, and folding method. These methods also play an important role in solving some mathematical problems, and we can't afford to wait.