| Mathematical problem solving process is not only a highlight of research for developmental and cognitive psychological, but also an important trend of educational psychological research. Renowned scholars of both home and abroad have never neglected the function of visual-spatial ability, which is an important component of human intellectual structure, in mathematics study and never neglected the value of spatial factors in mathematics study and psychological research in recent years. Cognitive style, which is also known as Cognitive style of FDI (field dependence-indep-endence),is the ability of individual in identifying relationship between objects, organizing the non-structural scene and reestablishing cognition. Cognitive style of FDI has been widely concerned and much studied by Western scholars since middle ages of 20th century. The achievement not only spurred the development of human psychology in some degree, but also is widely applied in education, medical caring, business, and job selection. Chinese psychologists Mr. Xie Sijun and Zhang Houcan introduced this issue into mathematics education and made great achievement in the 1980s'.On the basis of the previous research ,this research mainly focus on observing the influence of various visual-spatial abilities, field dependence-independence and three different presentations to grade II, grade IV and Grade VI Primary Student's mathematical problem solving, and the influence of visual-spatial ability and cognitive style to mathematic representations strategy of students of these three grades. The students were given arithmetic word problems to be solved in three different presentations: words; with a picture; and with a diagram. Representations strategy observes only two kinds of visual-spatial representations strategies: they are pictorial representations strategy, schematic representations strategy.86 students participated in the formal study. They are from 9 classes of separately Grade II, Grade IV and Grade VI. Students of each grade will be tested and grouped in accordance with spatial ability and cognitive style. Test material for this research adopts Cognitive Laterality Battery (CLB) and Group Embedded Figure Test (GEFT);Experiment material adopts self-compiled practical primary school mathematic problems (Part from research by Thomas (2000) and part from co-compiling of researchers and senior primary school teachers). There are 6 kinds of problems and each kind includes three types of problems of the same homogeneity but of different presentations. The individuals were then interviewed during the experiments. And were asked to answer the problems the researcher proposes. Each student was required to report the representation strategy and method he used after he had finished one problem. Timing and audio record will be made for analyzing and marking his performance and representing strategy. Then SPSS 10.0 will be applied for statistics and analysis and the mathematics performance and representing strategy will be analyzed and marked for exploiting influential factors that influent the mathematical problem solving performance and representations strategies of primary school mathematics problems. Finally, the correlation between mathematics problem solving performance and representation strategy was examined.The results indicated:1.With the students growing in grades, their visual-spatial ability, field independency, figure representation ability and mathematical performance will all increase step by step.2.Spatial ability is an important factor affecting the students' mathematical performance. The higher the spatial ability, the higher the degree for the student to adopt visual-spatial representation. And the higher the degree of schematic representation strategy, the better the mathematical performance.3. Field dependence-independence is also closely connected with mathematics performance. The stronger the field independence, the better the mathematical performance.4.Problem presentation is one of the factors affecting the primary...
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