Developing Metacognitive Training Junior High School Students To Solve Mathematical Problems Capability

Mathematics problems solving or solving problems means the process of using mathematics knowledge and methods to solve mathematics or practical problems creatively. metacognition means self-consciousness or control, is about cognition's cognition. Mathematics metacognition is the opinions of the mathematics cognition activity and self-adjustment. From the late nineteen eighties, people paid attention to problem solving and in mathematics teaching, people emphasize cultivating the ability of solving practical problems. And almost at the same time, mathematics teaching begin to pay attention to the research of metacognition. At present, the deficiency of the research of metacognition and problem solving is how to improve the ability of problem solving. There are more introduction of the correlated knowledge of metacognition, or prove the existence of metacognition by the research of authentic proof. The probing of how the metacognition has the effect on the problem solving.Main conclusions: (1) Students can have the ability of solving problems by doing more exercises, but thisdoesn't mean students have high ability of solving problems. (2) The method of doing more exercises will press students' metacognition. But suitableteaching of problem solving will develop students' metacognition.(3) We don't pay attention to the relation between metacognition and other variables of teaching. The original results of metacognition are scare in mathematics teaching.(4) There is low relation between junior students metacognition and the scores of easy problem solving. There is high relation between junior students metacognition and the scores of difficult and more difficult problem solving and open problems.(5) Students can improve the ability of mathematics problem solving by the consciously training.(6) In the teaching of developing students metacognition, we should pay attention to: cultivate the consciousness of metacognition in the process of problem solving; improve the efficiency of problem solving; shift teachers' teaching to students' studying; cultivate students' better study habits.(7) The higher the grades are, the effects of metacognition in the problem solving aremore obvious. Work hard has fewer effects on junior students than pupils. In junior, scientific study methods are more important than working hard. Junior play an important role in forming the habits of metacognition. In junior, pay attention to develop metacognition, and form the habits of metacognition, students will benefit from it in their whole life.