Mathematical thinking is a new concept created in the reform of mathematics curriculum. It has been widely popularized over the past decade with the forced promotion of new curriculum standards. It includes Mathematics researchers at of the Chinese Academy of Sciences, special mathematics teachers at Peking University , Tsinghua , and famous mathematical teachers on the Internet, all of which have taken cultivating mathematical thinking as their core goal, and extended to Mathematical Education . For example, the most popular internet celebrity in the science and technology industry also regards mathematical thinking as an important literacy in the workplace.
However, if you look closely, mathematical thinking is a typical pseudo-concept, which is a four-no concept that has no actual objects, no tradition of thought history, no clear definition, and no real needs: same as chess sports that improve thinking ability, there are also special thinking skills and methods in mathematical activities, but in logic, psychology, brain science and cognitive science, there is no mathematical thinking, Go thinking, and chess thinking outside of logical thinking. The concept of mathematical thinking has no actual objects, it is a pseudo-concept of object nothingness; from the history of human thought, the concept of mathematical thinking has no ideological history resources, it is just a new word invented in the recent mathematical curriculum reform, and there is no clear definition in theory; this concept is not naturally generated in teaching activities, but the personal claim of special scholars established by the new curriculum standards, it is an artificial product under specific conditions, and there is no real real needs.
stipulates mathematical thinking as the core concept of mathematics education. It comes from the "three meetings" theory proposed by Mr. Shi Ningzhong, Mr. Shi Ningzhong, who can observe the world with a mathematical perspective; he can think about the world with a mathematical thinking; he can express the world with a mathematical language. Mr. Shi Ningzhong's theory of "three meetings, four foundations, and four abilities" is the program of China's mathematics curriculum reform in the past 20 years. Its fundamental mistake is to replace logical thinking with mathematical thinking. For a detailed analysis of the discussion in the next issue, we will first sort out the main facts in this issue:
First. Regarding mathematical thinking and logical thinking, current mathematical theories cannot clearly define numbers and mathematics, and mathematical thinking is obviously also undefinable. In Chinese, logic in a broad sense is equal to Tao, and logic in a narrow sense is the way of thinking. Logical thinking is normal thinking, reasonable thinking, correct thinking, and scientific thinking. It covers advanced theoretical abstract thinking and ordinary daily abstract thinking, and also covers figurative thinking and intuitive thinking. Even lower animals' thinking to judge food and danger is primitive and intuitive logic thinking. Animal behaviors cannot survive if they violate logic. Obviously, there are only two basic categories of thinking: logical thinking and non-logical thinking. Non-logical thinking has specific criteria for determining psychiatric diagnosis. Apart from logical thinking, there is no category of mathematical thinking. The word mathematical thinking is at most an omitted word for "logical thinking in mathematics". Scholars' substantive explanations of mathematical thinking, such as abstraction, generalization, induction, deduction, etc., are all the contents of logical thinking.
Second, in the 2011 edition and 2022 edition of " Compulsory Education Mathematics Curriculum Standards ", the "three associations" with mathematical thinking as the core literacy are clearly stipulated as the ultimate goal of Chinese mathematics education .
Third, the new curriculum standards deliberately eliminate logical elements, completely blocking words such as logical thinking, concept definition, etc., and widely discussing mathematical thinking, scientific thinking, , rational thinking, normal thinking, reorganized thinking, divergent thinking, creative thinking, etc., just not mention logical thinking, the word logic only appeared accidentally once, and completely blocked the most basic logical concept of definition, replacing the "definition of mathematics" with "mathematical view".
shows that there are major mistakes in the mathematical curriculum standards, establishing false mathematical thinking as the ultimate goal of mathematics education, stifling the cultivation of logical thinking, and causing logical confusion in mathematics textbooks and teaching.
