The Effect Of Meta-cognition In Mathematical Problem Solving Transfer

Meta-cognition, which means cognition of cognitive activity, is a higher level of thinking activity by using cognitive activity as role of object. Mathematical problem solving is the core of mathematics education. The nature of mathematical problem solving is transfer, and transfer is one of the core indicators which reflect learning ability. Analyzing the effect of meta-cognition in mathematical problem solving is meaningful in improving students’transfer ability and problem solving ability.Based on the mathematical problem solving transfer process theory and meta-cognitive theory and transfer theory, this article analyzes the effect of meta-cognition in mathematical problem solving transfer from two perspectives of mathematical problem solving transfer—transfer in problem solving process and as the transfer of mathematical problem solving strategies.From the perspective of the transfer in problem solving process, the effect of meta-cognition is in the following three aspects:(1) In the stage of examining topics, with the guide of meta-cognitive knowledge, make students link with familiar mathematical structure and problems in cognitive structure, establish the correct mental representation, overcome the negative influence of negative transfer, review problems of inner structure and give it new meaning.(2) In the plan stage, through meta-cognition, mathematics problem solvers monitor and adjust their mathematics problem-solving activities, and control themselves when, where and how to transfer the previous strategies and patterns to resolve the problem. Problem solvers can effectively find the migration method, thinking mode and so on with the meta-cognitive knowledge.Meta-cognitive knowledge can improve the self-regulation ability of mathematics problem solvers. Once the deviation and error occurs, meta-cognitive experience and meta-cognitive monitoring can guide the problem solvers to change targets, focus on mathematical problems transfer and the target of problem solving, until establish the correct problem solving plan.(3) In the review stage, meta-cognition prompts problem solvers to take the initiative to reflect the existing cognitive activity, draw lessons from successful experience and failure, and be included in the cognitive structure, and summarize the problem solving and thinking about other more effective method experience, enrich their own cognitive structure and meta-cognitive structure, and create a bigger for future problem solving transfer.From the angle of transfer as a kind of mathematical problem solving strategy, the role of meta-cognition is embodied in the following three aspects:(1) Through meta-cognitive knowledge to help the problem solving person search "source" and realize the possibility of transfer.(2) Through meta-cognitive experience and monitor the correct use of "source problem", achieving successful problem solving transfer.(3) Through the meta-cognitive knowledge and experience to form a new problem solving strategies.