The Research On The Representation Ability Of Plane Geometry Problems Of Junior Middle School Students

Problem solving is the core of mathematics education.In recent years,it has been widely valued by mathematics education circles at home and abroad.It is a trend of international mathematics education to closely link it with mathematics courses.Problem representation is a key part of problem solving.Researching problem representation in subject teaching is of great significance for improving students' problem-solving abilities.Cognitive psychology researchers usually think that problem representation is understanding problems,and is about problem solving constructed by problem solvers.Cognitive structure is the interpretation of the initial conditions and constraints of perceived problems.Geometry learning is an important part of mathematics.With the deepening of the reform of the education system,people pay more attention to geometry learning.At the same time,geometric proof questions can effectively train students 'thinking ability,which is an important content in the textbooks,and is also a hot spot in the middle school exam questions in recent years.It provides effective suggestions for teachers' teaching through the study of the problem representation ability of junior high school students.Formally,problem representations are mainly divided into internal representations and external representations.Internal representations are learners' transformation of external problem information into internal propositional forms in their minds.Their external performance is the conditions under which the learner states the problem in his own words and goals;and external representations represent problems in words,symbols,diagrams,models,and other specific things.External representations are based on internal representations.External representations can greatly reduce the burden of working memory and help solve problems.Based on the research of Li Guangzhou,Shi Yanfei,Liu Xiaotong and others on the level of problem representation of students,during the experiment,the students were divided into students with good grades,middle grade students,and poor grades according to their usual grades.There are three levels of students,mainly for three studies: one,the representation level experienced by the students in the third grade of junior high school students in the process of solving plane geometric problems;What are the correlations between the different representation levels of problem representation;Third,what are the reasons for the differences in students' problem representation abilities at different levels.This article uses literature research method,oral report method,comparative research method,interview method and data analysis method to study.First,by reading relevant literature,we will understand the concept of problem representation,research process and Van Hill 's geometric thinking level,mathematical multiple representation,etc The theoretical basis provides the basis for the following research;using the oral report method when studying the representation level of the students' representation experience of planar geometric problems,through the student 's oral report to understand the students 'problem-solving thinking and record and analyze;Students of different levels study together to compare and analyze the differences between them;the interview method is to analyze the reasons for the differences between students of different levels,exchange interviews with students,understand the students' specific thinking and psychological activity processes;and finally use SPSS software Analyze the research data and draw conclusions.The findings are as follows:1.Students of different levels will experience three levels of representation: text representation,graphic representation and symbols,and principle representation when solving geometric problems;2.In the process of solving the plane geometry problem,the students in the third grade are better at representing geometric problems than the students with lower grades.At the level of text representation,the differences among students at different levels are not very large;At the level of graphic representation,students with higher grades have significantly better representation ability than students with lower grades;at the level of symbolic and principle representation,students with better grades have significantly higher representation ability than students with lower grades,and the difference is Sex is greater than the level of graphical representation;3.The students with better grades have a significant correlation between the scores of the text representation level and the figure representation level at the level of0.05(both sides),and the scores of the figure representation level,the symbol,and the principle representation level are at the level of 0.01(both sides).There is a significant correlation.The correlation between the level of graphic representation and the symbol and principle representation level is higher than the correlation between the level of text representation and the level of graphic representation;4.Students with poor grades have no significant correlation between the scores of the text representation level and the graph representation level,and the scores of the graph representation level,the symbol,and the principle representation level have a significant correlation at the level of 0.05(both sides);5.The reasons for the differences in the representation of geometric problems of students at different levels are: poor reading ability in mathematics,inadequate understanding of mathematical concepts,poor ability in geometric intuitive thinking,and poor ability in geometric logical thinking.Finally,based on the results of the study,the reasons for the differences in the problem solving of the students in different representations are analyzed,and the author tries to pass the causes of the differences and seek teaching measures to improve the problem solving of the students,and puts forward specific suggestions for teachers' teaching.