The understanding of mathematical thought and method can be discussed from two aspects: mathematical thought and mathematical method.

I. Overview

Mathematical thinking method is a basic concept and way of thinking to understand and solve problems in mathematics, which includes two levels: mathematical thinking and mathematical method. Mathematical thought is the essential understanding of mathematical theory and method, and mathematical method is the strategy and means to solve specific mathematical problems.

Second, mathematical thought.

1. Abstract thinking: Abstract thinking refers to the way of thinking that features such as * * * are extracted from concrete things to form abstract things such as concepts, symbols and models.

2. Inferential thinking: Inferential thinking refers to the way of thinking that a new proposition or fact is obtained through logical reasoning through a known proposition or fact.

3. Model thinking: Model thinking refers to a way of thinking that transforms real problems into mathematical models and solves problems by solving mathematical models.

4. Transformational thinking: Transformational thinking refers to the way of thinking that turns complex problems into simple problems and unsolved problems into solved problems.

5. extreme thinking: extreme thinking refers to the way of thinking that studies the changing trend and the changing limit state of things through the concept and method of limit.

Third, mathematical methods.

1, symbolic method: symbolic method refers to the way of thinking that mathematical concepts, theorems, formulas, etc. are expressed in symbolic language. , making the mathematical expression more concise and clear.

2. Structured method: Structured method refers to the way of thinking that a complex problem is decomposed into several simple problems, and the complex problem is finally solved by solving each simple problem.

3. Equation method: Equation method refers to the way of thinking to solve unknown quantities by establishing equations.

4. induction: induction refers to the way of thinking that summarizes general laws from specific examples and uses these laws to guide solving problems.

5. Analogy: Analogy refers to the thinking mode of reasoning or judgment by comparing the similarities or differences between two or more things.