Visual-spatial Cognition And Reasoning Ability And Cognitive Structure For Mathematical Problem Solved

The research of Cognitive Psychology shows that to solve mathematics problems, one is influenced not only by factors like visual-spatial abilities and inferential capability detected from previous problem solving and studying experiences in a narrow range of knowledge, but also by the knowledge itself, namely mathematical cognitive structure involved in a wide range of knowledge. Mathematical cognitive structure forms and develops fast during one's childhood. A sound establishment of Mathematical Cognitive Structure is very important in promoting children's capabilities and cognition in other disciplines.We chose 244 primary school students from Grades 4 to 6 as subjects during the research,and adopted the traditional "visual spatial cognitive ability test," "Raven Standard Reasoning Test" as well as the cognitive structure of self-compiled math test. We started from characterizing capacity to probe the influencing factors of children's mathematics problem solving during their childhood. To begin with, we analized the features of characterization levels of students from different grades through complexity model of relation characterization. Then, we analized the effects of reasoning ability, visual-spatial ability and cognitive structure on mathematics problem solving. Last, according to the conclusions derived from experiments above, we undertook opposite experiment between good math learners and poor math learners to find out their discrepancies in reasoning ability, visual-spatial ability and cognitive structure, so as to give an in-depth analysis and inquiry of previous conclusions.Research was supported by a number of significant results. Generally speaking,the findings are as follows:(1)characterization capacity of students from Grades 4 to 6 increases with rising grades. Noticeable disparity lies in characterization level of students from different grades, so is within the same grade.(2)There is unevenness in the development of visual spatial ability and reasoning ability when children solve mathematics problems, which is related to cognitive structure. The integration of reasoning ability and cognitive structure starts earlier than visual spatial ability. Main effect is noticeable in all grades.(3)there exist significant differences among these three factors in good math learners and poor math learners.In comparison with normal students,these three factors have a staged influence on the mathematices problem solving of the three types of students. The high scores of banner students profit from an integrated development of the related capacities.