Research On Problem Representation And Its Influence On Mathematics Problem Solving Of Eighth Grade Students

At present,problem-solving teaching is the focus of mathematics education researchers,and it is also the goal of mathematics education and teaching at this stage.It is very important to cultivate students' mathematics problem-solving ability,and it also has deeper requirements for teachers' teaching.In recent years,with the deepening of research on problem representation in psychology,people have paid more attention to the impact of problem representation on student problem solving.At present,research is mainly focused on internal representation,while there is little research on external representation of problems and knowledge domains..This article takes the internal and external representation of the problem as a research perspective,taking into account different knowledge fields,selecting eighth grade students from several schools in Dazhou City,Sichuan Province as the research object,using questionnaire testing and interview methods to analyze the overall situation of the eighth grade students' problem representation ability.The status quo of each dimension of student's problem representation ability,explore the influence of different problem representations on the solving of math problems of eighth grade students,in order to make useful suggestions for mathematics teachers' teaching.The main conclusions of the study are as follows:1.The problem representation level of the eighth graders is generally poor,and the development of the problem representation ability of the eighth grade students needs to be solved urgently;the problem representation ability of the eighth grade students is significantly positively correlated with the student's performance,and the level of its representation ability has a greater impact on the student's performance.2.The status quo of each dimension of the question representation of the eighth graders(1)Extraction of problem information;the overall level of the eighth grade students' ability to extract problem information is low,the gap between good students and poor students is large,and the polarization is serious;among them,the ability to extract text information is significantly better than graph information,and men and women are in the extraction of problem information There are no significant differences.(2)The conversion of different representation methods;eighth grade students lack the ability to convert different representation methods,lack the idea of combining numbers and shapes,and it is difficult to construct diagram representations when the problem of text representation and text+ symbol representation is present.(3)The knowledge and experience of the problem solver;the mathematics knowledge and experience of the eighth grade students are better,and there is no significant difference between men and women.3.The impact of different problem representations on student problem solving(1)Number and algebraThere are significant differences in the impact of different problem representations on the problem-solving of eighth grade students.Students have the best performance in solving symbolic representation problems,followed by text representations,and graph representations the lowest;there is no significant difference between male and female problems.(2)Graphics and geometry fieldsDifferent problem representations have no significant differences in solving mathematical problems.Among them,there are significant differences between men and women for the topics of text+symbol representation,text+symbol+chart representation,and there is no significant difference between men and women for the topics of text representation,symbol+chart representation.(3)Statistics and probability fieldThere are significant differences in the impact of different problem representations on students' mathematical problem solving.The scores of text + symbol representation are higher than text + graph representation,indicating that in the part of statistics and probability,students are better at solving the problem of combined representation of text and symbols,but their analytical skills for statistical graphs are relatively low.There is no significant difference between male and female genders.(4)Comprehensive and practical partThere are significant differences in the impact of different problem representations on students' mathematical problem solving.The topic score of the word representation is significantly higher than that of the combination of text and graphics,and there is no significant difference between male and female genders.Finally,in view of the specific situation of students' problem representation ability and the results of different external representations on students' problem solving,corresponding teaching suggestions are put forward from the perspective of problem representation.Cultivate students' problem representation ability in a targeted manner,pay attention to the important role of diagram representation,pay attention to the two-way communication between number and shape,and use a variety of representation methods to teach according to the specific content.