| Mathematical problem-solving is one of main projects of mathematical education. Many study focus on the factors that affect on mathematical problem-solving. With the development of cognitive style promote the study greatly. This article study from the relationship of cognitive style, mathematical representation and mathematical problem-solving, to reveal how the symbolic representation and graphic representation act on the process of mathematical problem-solving, otherwise the study provide the theory basis of symbolic-graphic combination.Symbolic representation and graphic representation are both external representation. In the psychological field, their homologue is visual representation and abstract representation, to the mode of thinking, they are corresponding to imagery thinking, and in the cognitive field, they are relation to cognitive style.The characters of symbolic are pithy, abstraction and better in logical expression, the characters of graphic representation are visual aids, easy grasping from whole and easy to operate.Students of versal style are like to choose symbolic representation, on the other hand, students of visual style are like to choose graphic representationSymbolic representation is of benefit to mathematical problem-solving to high school students in grade three, symbolic-graphic combination is great favorable of mathematical problem-solving.Graphic representation has no obvious effect on mathematical problem-solving, but it doesn't mean graphic representation is worse than symbolic representation. In face, graphic representation can reveal the mathematical nature of object more clearly than symbolic one. And it is able to help students think out the idea on how to solve the problem, then make the process of problem solving more successful. Moreover graphic representation can prompt symbolic-graphic combination.Students in different cognitive style have no difference in mathematical...
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