Investigation And Teaching Research On Geometric Language Representation Of Middle School Students

Currently we strongly advocate quality education.However,the main method about the detection of students' knowledge of mathematics is still examination,which has higher requirements for students' written expression.The geometric part is the key point of entrance examination for secondary school or college in mathematics.So representation of Geometrical language is very important for students to present their own acquisition degree.Therefor,it is very important to strengthen the research on the representation of geometric language.In this paper,based on the basis of existing research,the geometrical language representation was constructed by means of literature analysis,test volume investigation,interview and questionnaire survey.This thesis delves into the characteristics of geometric language representation,geometric error types and reasons of language representation.This paper is divided into chapters,and the chapters are arranged as follows:The first chapter raises questions.This chapter thinks of the important position of geometry knowledge in middle school mathematics,the value of geometry language in mathematics education and the representation in the application of mathematics as the background of this article,raising issues and research of this paper which is on this basis,then describes research methods which used in this article.Chapter II is the review.This chapter mainly divided into two sections.The first section is the geometric language's review,and the second part is the review of representation theory.Most of the current researches on geometry language are used as a part of the study of mathematical language.The research and analysis of the problems need to be deepened,Moreover,the combination of mathematical language and representation is seldom explored.Chapter III is the theoretical analysis about the geometrical language representation of middle school students.Based on the existing relevant definitions,this paper combines with my own understanding and relevant contents of this study to define the related concepts such as "geometric language","mathematical language","representation" "geometric representation of language" and "geometric language representation error".The paper also discusses the classification,functions and features of geometric language,classification and characterization of geometric language,and errors of geometrical language representation.Chapter IV is the empirical study on errors of geometrical language representation in middle school students.In this chapter,in order to grasp the wrong types of middle school students in the representation of geometry language,we compile the test volume of the error types of the geometrical language representation of middle school students,and then draw the following conclusions: there are five types of language representation errors in middle school students: the answer is not clear,Leakage content,writing more content,the writing is not standard,and it is completely wrong;there are five types of sign language representation errors: signs writing errors,symbol confusion,letter writing errors,irregular symbols writing,and irregular letter writing;there are five types of graphics language representation errors:dotted lines are confused with solid lines,letters marked wrong,graphics and text descriptions are not exactly the same,graphics and text completely false,leakage standard symbols.Chapter V is an empirical study on the reasons for the misrepresentation of the geometrical language of middle school students.According to the theoretical analysis and interview results of students,a questionnaire about the reasons for the misrepresentation of the geometrical language of middle school students was prepared.The following conclusions are drawn from the statistical analysis of the survey results:(1)The leading cause of high school text representation mistakes is learning habit,and there exists significant difference between male and female students.There was no significant difference between excellent students,general students and poor student.(2)The primary reason for the errors in the representation of characters in junior high school students is the study habit,and there is a significant difference between male and female students.There is a significant difference between students with excellent students,general students and students.(3)The primary reason for the emergence of symbol representation errors in high school students is the difficulty of knowledge.There are significant differences between male and female students and there is a significant difference between students with excellent students,general students and students.(4)The primary reason why junior high school students are wrong in symbolic language is the degree of knowledge acquisition.And there is no significant difference between male and female students.There are significant differences between excellent students,general students and poor students.(5)The primary reason for the errors in the graphic language representation of high school students is the degree of acquisition,and there is no significant difference between male and female students.There are significant differences between the excellent students,general students and students.(6)The primary reason for the errors in the graphic language representation of high school students is the degree of dependence on textbooks,and there is no significant difference between male and female students.There is no significant difference between excellent students,general students and students.Chapter VI,teaching suggestions.Based on the analysis of the types and attributions of errors about geometric language of middle school students,corresponding teaching suggestions are given respectively.Finally,this paper summarizes the research and points out the shortcomings.