Mathematical thinking refers to the spatial form and quantitative relationship of the real world reflected in people's consciousness, which is a result of thinking activities. It is the basic viewpoint of solving problems in mathematics, the essential summary of basic knowledge and methods of mathematics, and the guiding principle of creative development of mathematics. Mathematical thought has a higher level of abstract generalization than general mathematical concepts, the latter is more concrete and richer than the former, while the former is more essential and profound than the latter. Mathematical method refers to the operable rules or patterns contained in people's means, ways and behaviors to achieve a certain goal. Mathematical thoughts and methods are both unified and different. For example, junior high school algebra, using "elimination method" to solve multivariate equations; In order to solve the higher-order equation, the "order reduction method" is used; Solve quadratic equation. Use the "replacement method". The "elimination", "agreement" and "exchange" here are concrete mathematical methods, but they are not mathematical ideas. These three methods all embody the mathematical idea of "transformation", that is, the idea of transforming complex problems into simple ones. Specific mathematical methods cannot be marked with the word "thought". Such as "matching method", it cannot be called mathematical thought. Its essence is identical deformation, which embodies the mathematical thought of "transformation" However, every mathematical method embodies certain mathematical ideas; Every mathematical thought is expressed on different occasions through certain means, and the means here is mathematical method. In other words, mathematical thought is rational knowledge, and it is the spiritual essence and theoretical basis of related mathematical methods. Mathematical method is a practical, instrumental and technical means to realize related ideas. Therefore, people usually regard mathematical thoughts and methods as a whole concept-mathematical thoughts and methods. Generally speaking, there are three levels of mathematical thinking methods: low-level mathematical thinking methods (such as elimination method, method of substitution method, substitution method, etc. ), advanced mathematical thinking methods (such as analysis, synthesis, induction, deduction, generalization, abstraction, analogy, etc. ), as well as advanced mathematical thinking methods (such as transformation, classification, combination of numbers and shapes, etc. ). The lower-level mathematical thinking method can be upgraded to a higher-level mathematical thinking method through abstract generalization, and there is no clear boundary between all levels.