A Study On Differences Of Mathematical Problem Representation Between Excellent Students And Ordinary Students In 10 Grade

Characterization is the central link of problem solving; it has been studied by many researchers with the development of cognitive science. In mathematical problem solving, since the level of characterization is too low or not comprehensive of other reasons, students can’t reasonably and accurately transform the problems into the schema of familiar formula and concepts, which finally influence the solution to the problems. The research done in the subject’s field can improve students’ capacity to solve the problems; therefore research is gradually focusing on the problems of all kinds of subjects students are learning in normal schools.On the basis of document analysis, this paper gives an overview of the problem representation and also points out the significance of the research. Providing an overview of the problem representation research situation in the general subject’s field and Mathematics, it points out the direction for the research. Based on the research in the field of general mathematical problem-solving steps and problem representation level in other disciplines, my research finally puts forward the level of characterization of mathematical problem solving.This paper adopts the method of literature research, verbal reports to discuss the subject. Firstly, analyze different situation of characterizing the implicit question information between Excellent and Ordinary students. Next, compare the results of different types of students experiencing to characterizing the same math problem(Dynamic differences and Static differences) and the correlation between the various levels. Meanwhile, the research also compares and analyzes external representation forms’ application of different examines. Finally, provide some reasonable and effective teaching suggestions for the difficulties arose from problem-solving for students.The conclusion is:(1) the excellent students can characterize the implied information more comprehensively and can translate the implicit information successfully, while most of the ordinary students can’t complete this.(2) Students in 10 grade will experience the same level of characterization(text characterization; context characterization; mathematical characterization; number characterization); Characterization level exist the dynamic and static differences; Characterization is no significant difference in context characterization and Mathematics characterization, the subjects of different levels exist significant differences in context characterization; Text and number characterization exist significant differences with the context and mathematics characterization, so the process of whole problem solving context representation and mathematical characterization dominates the Mathematical problem solving; Static differences are the differences in knowledge structure, characterization conversion and the construction of the problem space.(3) The Excellent students accustomed to various application and transformation of external representation, while most Ordinary students accustomed to characterize the problem by the form that the problem title has given, so the form of external representation is limited.Teaching suggestions: achieve overall optimization of cognitive structure; Promote students to form problem schema; Guide students to dig implied conditions; To improve the student’s CPFS structural system; To cultivate student’s transformation ability about characterization.