A Study On The Improveion Of The Metacognitive Level Of Mathematical Problem Solving

At present, the status of teaching and learning in the mathematical problem solving is not optimistic in grade 9. From the concept, the words and expressions of exams training and practice making perfect has been liberaled as a synonym for teaching and learning in the mathematical problem solving in grade 9.From the behavior, teachers generally adopt the mode which highlights the teachers’teaching and the students’passively accepting. The mode very emphasis on teachers’domination, but looks down on students’principal position. From theresult, although students have learned a lot of questions, but the effect often is geting half the result with twice the effort,which is very miserable.The related studies show that the influence factors of mathematical problem solving includes metacognitive factors in addition to the classic cognitive factors.The meta-cognition is different from the general abilityin problem solving. It is an independent structure in the process of problem solving, and it can make up for the inadequacy of general ability, which plays an important role in problem solving. And other studies have shown that the ability of mathematical problem solving is often associated with the metacognitive level,the higher meta-cognition level, the better ability of mathematical problem solving.The thought of George Polya’s problem solving has been generally recognized as scripture in the research of mathematics problem solving, which one’s essence major concentration is in "the table on how to solve problem". The table is mainly composed of a number of self-prompt problems. These self-prompt problems are not asked by someone else, but the problem solving oneself. They are actually the solvers self-heckling and self-examination, which actually contain the metacognitive components. In mathematical problem solving,although these self-prompt problems can’t direct effect on problem solving,but can indirectly influence problem solving. So it may be an important way to improve the students’mathematical problem solving level through diging into George Polya’s metacognitive thought and hereby improving students’ metacognitive leve.The research based on George Polya’s metacognitive thought in mathematical problem solving consists of theory research and practical research.In theory,the research had constructed "George Polya’s metacognitive training list",which based on the thought from meta-cognition and George Polya’s problem solving.And corresponding using strategies for it had been formulated.In practices, the thesis had choosed grade 9 students as the research object, and the "similar triangle unit" as the knowledge background.At the same time,the thesis had employed training experiment according to the’George Polya’s metacognitive training list’,which as a main method supplemented by investigation and interview.And the thesis had probe into the training experiment effect of the meta-cognition ability and ability in mathematical problem solving.Study show the following conclusions.(1)The grade 9 students’meta-cognition ability has significant positive correlation with the solving ability in mathematical problem solving.(2)The metacognitive training based on the the "George Polya’s metacognitive training list" can improve the grade 9 students’metacognitive ability of mathematical problem solving,especially for the poor student.(3)The metacognitive training based on the the "George Polya’s metacognitive training list" can improve the grade 9 students’mathematical problem solving ability,especially for the poor student.