Simply put, thought is the method in method, and method is the concrete realization of thought. Thought inherently unifies various methods, which is the embryonic stage of methods; Method must be guided by thought and is the concrete realization of thought. Based on the dialectical unity of thinking methods, here I will discuss the learning of mathematical thinking methods and the learning of basic mathematical knowledge together. The predecessors summarized and discussed many mathematical thinking methods for us. The question now is how to turn these other people's thinking methods into their own. First, collect and sort out a large number of mathematical thinking methods, whether online or in books. The problem is that the way of thinking is endless. When will this collection and sorting stage end? One way to judge is repetition, and repetition to a certain extent is enough. We can also judge the universality and importance of mathematical thinking methods by the degree of repetition. Second, preliminary classification and summary According to certain standards, a general system network framework is formed. Explain it in detail below. For example, according to the application fields, it can be divided into: mathematics research methods, mathematics learning methods and mathematics teaching methods. According to the degree of universality, it can be divided into philosophical methodology, general scientific methodology and specific scientific methodology. Mathematical methods include at least the above three fields and three levels. They are interrelated, showing a trend of mutual penetration and mutual transformation. We just want to grasp and reveal the relationship between them through preliminary induction, classification and summary. Such as abstraction and generalization, induction and deduction, classification and classification, comparison and analogy, analysis and synthesis, can be regarded as both philosophical methodology and general scientific methodology, and there is only a very thin line between them. If we stand on the height of philosophy to reflect and demonstrate, that is philosophical methodology; If we focus on how to apply perfection in science, it is the general scientific methodology. Abstraction and generalization are mainly manifested in the idealization and modeling methods in mathematics; In mathematics, induction and deduction are mainly manifested in mathematical induction, axiomatization and formalization; Comparative analogy is a very important mathematical conjecture method in mathematics; In fact, all kinds of mathematical methods are the combination of all kinds of philosophical methods, which are not as simple and linear as mentioned above. For example, axiomatic and formal methods mainly include deduction and abstraction; Mathematical model method also includes abstraction, classification, deduction and calculation. The preliminary summary is as follows: The basic thinking method of mathematics is 1. Idealized method and modeling method. Induction and deduction: mathematical induction, axiomatic method and formal method. Guess ideas in math. Analysis and synthesis: methods of analysis and synthesis. Classification: equivalent division, classification discussion is a unique way of thinking in mathematics 1 Thinking set law: 2. Mapping thinking method: correspondence, function, RMI (reflecting the principle of relational mapping) 3. Other thinking methods: reduction, construction, recursion, iteration, combination of numbers and shapes, equation method 4. Mathematical problem solving methods: reduction to absurdity, method of substitution, undetermined coefficient method, collocation method and elimination method. Third, break the foundation of mathematics. There are many attractive theories in modern mathematics. Every time I want to study deeply, I always feel that the foundation is weak and it is difficult to make progress. I really don't think I can move. We must concentrate on every stage of learning the basic knowledge of mathematics. Through the study of relatively simple basic knowledge, we can understand and master common and important mathematical thinking methods, and learn mathematics by doing mathematics. In the process of doing mathematics, we should deeply experience and understand the thinking method of mathematics. Only through this process can other people's mathematical methods become their own thinking methods. Fourth, gradually improve the optimization. To gradually form its own ideological methodology system, it is necessary to integrate various thinking methods and gradually systematize, network and enrich them. Therefore, we must strengthen our philosophical cultivation and mathematical cultivation. Through various channels, select some related master classics for research. "I've been thinking about it all day. It's better to learn it in an instant." "Listening to you is better than studying for ten years." Only by studying the master's classic original works can we play such a role and effect. In addition, we should continue to do mathematics in combination.

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