The Impact Of Cognitive Style On Problem Representation And Its Conversion

Problem representation is a kernel concept in problem-solution theory. With the development of Cognitive Psychology, many researchers pay a lot of attention to problem representation. The focus has gradually shifted to academic issues. This paper defines problem representation based on literature analysis, and summarizes its research situation in the field of general and academic issues, such as formation mechanism and influencing factors and hierarchy of problem representation. This paper also probes into the representation methods taken by the samples during dynamic problem solution process and reasons affecting problem solution, and further observes conversion process of problem representation.On the beginning of 1940s, the research on cognition originated by Witkin has undergone from differentiation to integration. Currently, Psychologists have plunged into the application of cognitive on education, vocational guidance. Cognitive style are widely concerned by psychologists at home and abroad, and the results had implications in many fields of education. However, in problem solution domain, the research which is involved the cognition style is not thorough enough, especially influence on problem representation conversion had not directly touched on. This paper intends to discuss the process of student problem solution in different cognitive styles, difference in representation mechanism and representation conversion after relevant clues are given. In addition, this paper also probes the difference of samples of different cognitive styles in different problem solutions, to explore structure and complexity of problems and interaction of cognitive styles. Based on the above experimentation and study, this paper proposed some feasible teaching strategies and methods.The study uses mixed experimental design of 3 (three problem types) x 2 (two cognitive styles) x 2 (clue hint or not): Embedded Figures Test is used to measure cognitive style of sample, based on which, field-independent sample group and field-dependent sample group are selected. All samples are required to complete the application of three problem types in two conditions of clue or not. The results are as follow:1. During problem solution, the mistakes that the samples often make in failure to solve the problem are very often problem presentation error.2. At the stage of non-hint problem solution, the samples in two cognitive styles have distinctly different achievements in math problem solution. At the stage of hint problem solution, the difference between groups is not obvious.3. At the stage of non-hint problem solution, the representation method chosen by the samples is related with their cognitive styles when the samples solved the problems with clear expression, implied information or misleading information. On the contrary, the difference isn't obvious.4. During non-hint problem solution, the samples in field-independence cognitive style more easily find implied information and distinguish misleading information.5. After the clue is given, their representation conversions are different when samples in two cognitive styles solve three problem types. Field-dependence individuals more easily realize representation conversion.Based on the above study results, we propose to conduct math teaching according to cognitive styles of students to promote the development of problem representation ability.