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Why is the problem the core of mathematics?
Abstract: When asked questions, doubts come from thinking. The process of mathematics learning is a complicated thinking process, and it is also a process of constantly "generating problems-questioning-solving doubts". Bold doubt is the characteristic of mathematical creation activities. Asking questions shows a thirst for knowledge and contains a spark of wisdom; Questioning is a spirit of exploration, which breeds creation. Aristotle famously said: "Thinking begins with doubt and surprise" How to understand "Problem is the core of mathematics" Balzac said: "The key to all science is undoubtedly a question mark. Most of our great discoveries are attributed to' how', and the wisdom of life probably lies in asking' why' everything. " "Problem is the core of mathematics" seems to have become a well-known "wisdom" in the field of mathematics education, and every mathematics learner can appreciate some truth from it. Halmos, a contemporary American mathematician, pointed out in the article "The Core of Mathematics": "It is true that without these components (axioms, theorems, proofs, concepts, definitions, theories, formulas and methods), mathematics would not exist; These are all necessary parts of mathematics. However, they are not the core of mathematics, and this view is tenable. Mathematicians exist to solve problems. Therefore, the real part of mathematics is to solve problems. " Some people may think that definitions, theorems, formulas and axioms are the core of mathematics, but the problem is only their application and consolidation. This is generally from a static and one-sided perspective, only seeing the existing mathematics. In fact, the emergence and development of mathematics is to answer people's demand for asking questions, but the constant raising and solving of problems is to transport "fresh blood" for mathematics and promote its "growth and development". So "the problem is the heart of mathematics". What is the role of correctly understanding "problem is the core of mathematics" in mathematics learning? We believe that since "problem is the heart of mathematics", the core of mathematics learning should be to cultivate the ability to solve mathematical problems. As Paulia pointed out: "Mastering mathematics means being good at solving problems, not only solving some standard problems, but also solving some problems that need independent thinking, rational thinking, unique insights and inventions. It can be considered that if all the computational exercises and theorems that tend to be proved or studied are listed as "problems", and if all the features of the learned mathematical concepts are established, the features that can explain the concepts are also called "problems", that is to say, if the term "problems" is understood in a broader sense, "problems are the heart of mathematics" will neither be distorted into "tactics of asking questions" nor be keen on delving into the dead end. In particular, problem-solving activities refer not only to the process of solving problems, but also to the process of asking questions. One of the most difficult parts of solving problems is to ask the right questions. When asking questions, doubts come from thinking. The process of mathematics learning is a complicated thinking process, and it is also a process of constantly "generating problems-questioning-solving doubts". Bold doubt is the characteristic of mathematical creation activities. Asking questions shows a thirst for knowledge and contains a spark of wisdom; Questioning is a spirit of exploration, which breeds creation. In the national college entrance examination in the 1980s, there was a calculation problem of solid geometry. Almost all the candidates worked out the "result" step by step according to the conditions, but one student pointed out that the spatial graph given according to the known data did not exist, so the problem was wrong. This is a typical example of questioning. Being good at questioning and asking questions helps to cultivate our independent thinking ability, especially when the internal language is transformed into an external language, the problems that were not very clear will become clear and the thinking process will become clear. It is not uncommon for a student to understand half of a problem when he expresses it in words. Some even asked half the questions before the other half "swallowed". Facts have proved that the problem itself was solved when he arranged the internal language with "abbreviated form" into an "extended" external language with logical structure. Aristotle famously said, "Thinking begins with doubt and surprise", but students can only ask questions when they are in doubt, which requires a process of self-learning and thinking. Zhang Hengqu, an educator in the Song Dynasty, said: "If you doubt, you will not learn, but you will doubt. "Zhang Hengqu believes that it is easy to treat all knowledge and realize that there are no suspicious people, and they must be people who have never learned. Because I haven't studied it, I don't know if there is a problem. This is indeed an empirical talk, and it is also in line with the general psychological process of learning. In this way, the psychological process of mathematics learning can be dissected into four necessary links: "learning-thinking-asking questions". Song Zhuxi said: "Those who learn without doubt will be taught to have doubts, while those who have doubts will have no doubt, and they will make progress when they come here." No wonder neil Pozmann, a famous educator, criticized: "Children are like a question mark when they go to school, but they are like a full stop after graduation. Because questions are the core of mathematics, each of us should always ask ourselves: "Did you ask today?" "? Always be a "question mark" in math learning. Jiang Wenbing, a bachelor of high school in Huainan No.1 Middle School, Anhui Province, was the first academic leader.