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Mathematical ability refers to those unique psychological characteristics (mainly psychological activity characteristics) that Crouther, a Soviet psychologist, thinks can master mathematical knowledge, skills and habits quickly, easily and thoroughly. According to the characteristics of mathematical thinking, he thinks that mathematical ability includes: the ability to formalize mathematical materials; Summarize the ability of mathematical materials; Able to manipulate numbers and other symbols; Continuous and rhythmic logical reasoning ability; The ability to shorten the reasoning process;
The ability to reverse the psychological process; Flexibility of thinking, that is, the ability to transfer from one psychological operation to another; Mathematical memory; The ability of spatial concept. Since 1980s, there has been a popular view in China that mathematical ability is a necessary psychological feature for successfully completing mathematical activities, including mathematical operation ability, logical thinking ability and spatial imagination ability.
China's Feng Zhongliang believes that mathematical ability is a personality psychological characteristic that plays a stable role in regulating the process and mode of mathematical activities, and it is a generalized and systematic individual mathematical activity experience.
Its basic elements are two kinds of mathematical experience that regulate mathematical activities, namely mathematical knowledge and mathematical skills. Among them, mathematical knowledge plays a directional role in mathematical activities, and mathematical skills play a monitoring role in mathematical activities. They are interrelated and mutually restricted, which ensures the smooth progress of mathematical activities.
As a kind of classification experience, mathematical ability is formed in the acquired mathematical activities, and it is developed by students' continuous integration and classification of mathematical knowledge and skills through migration on the basis of mastering mathematical knowledge and skills. According to the different mathematical activities, it can be divided into counting ability, calculating ability, solving application problems, physical measurement ability and so on.