A Research On The Combination Of Multi-representation Of Mathematic Concept With Metacognition In The Process Of Solving Problems

To improve student’s mathematics grade, teachers would summarize the typical examples with key test points and assign lots of exercise for students which could be finished in certain time. But teachers didn’t give the useful advice for analyzing the condition or accordingly adjusting strategies in solving problems. So, an investigation about multi-representation of mathematic concept with the metacognition is theoretically and practically significant.In the process of solving math problems we need to extract the key information, then correctly represent it and the process should be monitored and adjusted by metacognition. The mathematics concept has a multi-representation and each of which could form a representation space. So choosing the best form of representation is very important, but I find it often ignored after talking with teachers and students. So I try to study it by means of literature analysis, investigation and interview, oral quantitative and qualitative analysis in order to understand multi-representation of mathematic concept with the metacognition and analyze influential factors of monitoring it. We define the multi-representation of mathematical concept on the basis of literature review as the multiple mathematical concept or expression of semantic units, which is different from generally defined multi-channel, multi-forms of representation. Thus this study by oral reports is to analyze multi-representation of mathematic concept with the metacognition including the act of metacognition, multi-representation space of mathematics and the control of metacognition on mathematical expressions. Finally, I obtain the following conclusions.(1) Metacognition has participate the activities of solving meth problems but not enough.(2) there is no perfect multi-representation space of mathematics.(3) the degree of the combination of multi-representation of mathematic concept with metacognition is low. According to the conclusions above, a teaching strategy is given in improving the ability of metacognition in monitoring multi-representation of mathematic concept which might enlighten us in teaching and learning mathematics, and solving math problems.