The Cognition Diagnosis Research Of Plane Geometry Problem Solution Of Minority Junior Middle School Students Of Karshgar

Mathematical problem solving has undertaken the task that ensure the mathematical diathesis of students to develop completely and be demanded by the society of the 21 st century. Plane geometry problem solving as a subclass belong to mathematical problem solving, it has the generality of mathematical problem solving, and has features of strict deduction. When we attach importance to knowledge, it is a necessary constituent part of mathematics knowledge hierarchy; when we pay attention to mathematical capacity, plane geometry is a kind of important material that develop the mathematical thought ability for students who are in the critical period of developing this ability. But, because of some reasons, minority junior middle school students of Xinjiang has leaved much to be desired in the studying of plane geometry problem solving, and it is very hard to analyze the reason deeply to utilize existing methods of evaluation,so teachers can’t improve their teaching method effectively.Because of above reasons, this research analyze the microcosmic reasons of the problem that minority junior middle school students had bad fruit in the studying of plane geometry problem solving, so we can clarify the character of the problem,and design some measures to alleviate the problem.This study had built a cognitive system of common mathematical problem solving with the document research method and extracted the cognitive attributes of plane geometry problem solving based on the features of plane geometry. Appropriate degree of cognitive attributes had been tested and the hierarchy relationships among the cognitive attributes had been built in a verbal protocol. The result of the comparison between the date of minority students and Han students, which gained with the tool that constituted based on the hierarchy relationships of cognitive attributes and analyzed by the DINA model, had shown the drawbacks of minority students in plane geometry problem solving. Base on the reasons of those drawbacks, this paper had presented some strategies to improve the instruction of minority plane geometry problem solving. Below words are the research content.The mission of the chapter 1 is that analyze the research about the common mathematical problem solving、plane geometry problem solving and the theory of cognitive diagnosis to clarify the current situation and the fault. In the chapter 2, it commence from representation of problem、concerning model、conversion problem and metacognition of problem solving, and infer the system of cognition base on the theory of mathematics model. we can ascertain that the process of plane problem solving contain six cognitive attribute like comprehension of problem information 、geometry deduction 、space imagination、recognition of model、transfer of model and recognition of ‘invisible’ model from the relationship between the generality and the features of plane geometry problem solving. Something can be ascertained from problem solving thinking of eight students by verbal protocols: at first, the precision of six cognitive attribute had been attested; the second, the hierarchy relationship of cognitive attribute that established base on the level of fundamental had been ascertained. In chapter 3, it had compiled the diagnostic tool based on the hierarchy relationship of cognitive attribute and reflected that there are many minority students had the first hierarchy mistake by the comparison between the minority and Han students. The patterns of the first hierarchy mistake contain that at least one cognitive attribute of the three that include comprehension of problem information 、geometry deduction and space imagination are not mastered. So we can know that minority students were instability in plane geometry studying. In chapter 4, it had presented the main reasons that cause the three kind of mistake for the diagnostic result. From the case that minority students solved the plane geometry problem, we can infer that: firstly, the main reasons of the first hierarchy mistake is that minority students had bad mathematical reading and trait of mathematical thinking; secondly, the deficiency of mathematical summarization and metacognition had caused the second hierarchy mistake; final, the imperfection of the mathematical diathesis result in the third hierarchy mistake. The chapter 5 had proposed some measures for the trait of minority students to help them have a perfect development in four aspect that include mathematical language 、 mathematical cognitive structure 、 trait of mathematical thinking and metacognition.