The Influence Of Problem Representation In Solving Circle Problems By Junior High School Students

Modern cognitive psychologists believe that the process of problem solving can be divided into four stages: problem representation,the formation of problem solving strategies,the implement of problem solving strategies and review and evaluation.Problem representation,as the first step,is crucial for the entire procedure.The research on problem representation is generally conducted as the cognitive psychology develops.During the two years of my internship teaching,the author have found that junior high school students felt very difficult to solve geometric problems,which are the difficulties for mathematics learning,among which the circle problems play an important role of planar geometry.Their are relatively concentrated and abstract.Circles has high requirements for junior high school students' spatial imagination,logical reasoning and thinking skills.Although students are able to memorize the relevant formulas of circles,when encountering circle-related solutions,they may fail to read the questions and the formulas cannot be flexibly applied,which will result in failure to solve the problems.This shows that junior high school students have some difficulties in characterizing problems.Therefore,the author choose to study the impact of problemrepresentation on junior high school students solving on the the pre-designed circle problems.This study takes 80 students in the third grade of a middle school in Changsha as the sample,and uses a combination of questionnaires,data analysis and oral reports as the method.The questions to be studied in this thesis are:1.Is there a correlation between the problem representation and the circle problem?2.How does the problem representation affect the problem of junior high school students' solution?3.How the students' ability to represent problems can be improved in the teaching process?This article first stated the definitions of circular problems,problem representations,and problem solving.According to the classification of various representation forms by researchers in mathematics education,and the characteristics of the circle problem itself,the author proposes a three-level conception of the external representation experience when junior high school students are solving the circle problem: textual representation,graphic representation,and symbolic representation.The questionnaires were distributed to the students for analyzing the correlation between the problem representation and the solution to the circle problem,and the differences in the problem representation ofand analyzing students' thoughts in the process of solving the circle problems as the oral report method.Three methods of the impact on problem representation for the circle problems are analyzed by collecting and analyzing the integrated data,the following conclusions are drawn:there is a positive correlation between the students' ability to represent the mathematical problem and the solution to the circle problem;there is a difference in the ability to represent the problem between the male and female students;factors such as comprehension,figure recognition,and original cognitive structure all affect the ability of problem representation.Through the research report and the combination of teaching practice,the corresponding teaching suggestions are ought to be implemented pay great attention on the cultivation of students' good question review habits;foster students' problem representation ability;help students improve the geometric knowledge network structure.