An Investigation On The Level Of Linear Function Understanding Of Junior Middle School Students

Mathematical understanding is the foundation of the cultivation of mathematical core literacy,and the functional understanding is one of the important and difficult contents in mathematical understanding,and the understanding of the linear function is the basis of the functional understanding,so these show that the linear function is important in mathematics teaching and learning research.At present,the research of the linear function is mainly from the angle of teachers’ "teaching",for example teaching design,teaching strategy and so on,but seldom from the angle of students’ "learning".In view of the fact that students’ level of understanding is not only a window for teachers’ teaching feedback,but also a basis for students’ follow-up study,so it is necessary to deeply study the students’ understanding level of the linear function.On the basis of dividing the understanding level of linear function,this study designs the survey tools to carry out investigation,then analyzes and discusses the present situation of the students’ understanding level of the linear function.The main contents of this paper are as follows:In the first chapter,the question is raised.This chapter mainly introduces the research background,summarizes the concept,process,evaluation of the mathematics understanding and teaching research of linear function,determines the starting point of the research based on the investigation of the understanding level of the linear function of junior high school students,and draws up the research contents,methods and ideas.In the second chapter,it is mainly the construction of the understanding framework of the linear function.Through combing the literature on the level of the mathematical understanding,it is found that the instrumental and relational understanding of R.Skemp can clearly divide the level of students’ understanding.Through combing the literature on the functional understanding,it is found that the functional understanding framework based on David Tall theory can not be directly applied to the linear function,but it is worth learning the way of construction from content and level.On this basis,according to the content of the textbook and themathematics curriculum standard of compulsory middle school,this study constructs the " understanding framework of the linear function"(Figure 2.5)from three dimensions,two levels.In the third chapter,it is mainly the division of the understanding level of the linear function.In the understanding framework of the linear function,by analyzing the specific performances about conceptual form,the representation method at two understanding levels about instrumental and relational understanding and then the division of the conceptual understanding level of the linear function is obtained(Table3.2);by analyzing the specific performances about four types of modeling at two levels of understanding and then the division of the model understanding level of the linear function is obtained(Table 3.3);by analyzing the specific performances about the relationship among the content of the linear function itself and the relationship among the content of different sections at two levels of understanding and then the division of the relationship between the linear function and related knowledge understanding level of the linear function is obtained(Table 3.4).In the fourth chapter,it is mainly the selection of investigation methods and development of tools.According to the characteristics and level division of understanding about the linear function,this study selects the traditional test and concept map combined with the survey method,and the traditional test paper and the composition of a picture test paper are developed.To examine the students’ understanding level of the concept and model of the linear function,this study preliminarily designs the traditional test paper(Appendix 1)with examples and exercises in textbooks,and after two pre-tests,a formal test paper with Cronbach’s Alpha coefficient of 0.801 is formed(Appendix 2);to examine students’ understanding level of the relationship between the linear function and related knowledge,this study preliminarily designs the composition of a picture test paper(Appendix 3)with the concept map of the linear function,then through forecasting and expert advice,the formal test volume is formed after revision(Appendix 4).In the fifth and sixth chapters,it is mainly about investigation and analysis of results.In January 2018,junior high school students in C school are investigated by using two survey tools(Appendix 2,4)and the results are analyzed.In the time of "mathematical weekly test",by using the 452 traditional test paper,this study gets 408 effective samples,and through analyzing the data by spss16.0,this study gets the understanding level of the concept and the model of the linear function about Junior high school students tested,and gets the difference about students of different genders or about different class levels;in the "self-study class" time,by using the 452 composition of a picture test paper,this study gets 412 effective samples,and then through counting the number of lines,inconsistency,acceptable proposition ratio in the concept map made by the students,the understanding level of the relationship between the linear function and related knowledge of junior high school students is obtained.In the seventh chapter,it mainly includes findings and discussions.Firstly,to understand the linear function systematically,the linear function understanding framework is constructed.It provides a reference for teachers to understand the linear function and also brings enlightenment to the evaluation of function understanding.Secondly,in order to comprehensively and effectively test the students’ understanding level of the linear function,the traditional test and concept map are used in the investigation,and then the traditional test paper and the composition of a picture test paper(Appendix 3 / 4)are developed.They provide the reliable tools for evaluating students’ understanding level.Finally,according to the analysis of the data,we find that the junior middle school students’ understanding level of the linear function is low.So this paper discusses the reasons from the two aspects of the students’ test paper and the teaching of the linear function,and puts forward some corresponding suggestions.It is hoped that it will bring enlightenment to the improvement of teaching.