Comparative Study On Eighth Graders Errors Of Problem-solving About Congruent Triangles

The research analyzed the outstanding students and the underachiever’ problem solvingerror。Compared errors of both phenomena, analysis the differences and similarities betweenthe two classes of students then provide some basis for teaching the two types of students.Related researches about problem solving errors are abundant. Through literatureanalysis to review the studies on the existing to find a direction for the research. Based on theknowledge of congruent triangles and the students’ mathematics level and curriculumrequirements to a write test paper. Through the investigation on students’ solving congruenttriangles exercises error to get the real data about students’ errors. Based on Polya’s theory andthe perspective of the problem solving process, analysis error phenomenon in the process ofproblem solving of two classes of students. By interviewing students for errors to understandthe specific idea of students’ problem solving and grasp the real situation of the error. By thisway, count the distribution and proportion of the total error. The study chooses someoutstanding students and underachievers in junior middle school in Dalian as the researchobject then compare the two classes of students’ problem solving the phenomenon of errorhorizontal and vertical.’’ The result display:(1) The two classes of students’ errors in the process of distribution are the same. Fromstudents’ problem solving process of longitudinal perspective the two classes of students’problem solving error in the distribution of each process are the same. Most errorsconcentrated in the first three processes, especially for the planning process.(2)The two classes of students’ performance are different in problem solving errors.From the point of each process of problem solving, the two classes of students behavedifferent in the first three process, they only have the same performance in the process ofreflection.(3) Two classes of students have different proportion in the same errors. There’redifference ratio between two classes of students in understand the question and the reflectionprocess.According to the research results, the article proposed suggestion for teaching two kindsof students’ in problem solving respectively, and points out the direction in the future.