Research On The Effects Of Different Internal Structure Representation And External Structure Representation On Children's Solving Mathematics Subject Problems

By surveying the literature, this paper finds that the traditional problem-solving representation perspective has defects as follows: Studies are almost all focused on the part of the inner part of representation, emphasizing the analysis of its form and content. People view the representation as internal psychological structure by nature and a relatively static state., ignoring the significance of representation's dynamic developing in deciding to which degree it helps to solve problems. In studies of problem-solving representation, influence of external representation and the external structure of problems has been overlooked or ignored.A dynamic, holistic, systematic and structural representation perspective is being proposed in this paper. It is defined as the process and result of problem-solving based on the variables of problem-solving spatial information. That is, representation is an ever-changing process;it is both a process and a result, and there are both internal and external representations. The representation of primary students' subject problem solving can be examined from the dimensions of internal and external as well as structure and principle. It is of great importance of the match between internal representation and external representation for the solving of subject problems. Three studies are designed to check the assumption. They are preceding study, the study of children's internal representation and external representation in solving subject (mathematics) problems, and the study of effect of different external representations and memory task on problem-solving. All the three studies were practiced through interview, protocol analysis and didactic experiment method.The result of the study is of higher ecological validity and structural validity. Conclusions are drawn as follows:i. The level of children's external representation in subject mathematics problem-solving isrelatively lower and do not adapt to the level of their internal representation, which is a most important factor influencing their mathematics subject problem-solving quality. Good primary students have higher level integrated internal and external representation.ii. The more integrated external structure representation is, the more helpful it would be for problem solving.' Internal representation operation strategy training would help children enhance their capability of problem solving, especially for the problem-solving quality under the condition of word and complete external structure form.in. It is of great importance of the match between internal representation and external representation for the solving of mathematics subject problems.iv. Autonomous additional task may improve the problem-solving quality, and may notably improve the problem-solving quality conditioned by incomplete external structural form.v. More integrated external structural representation form would do good to the quality ofadditional memory task. A complete external structural representation form might conspicuously enhance the quality of memory conditioned by complicated and additional tasks.