Research On The Organizational Characteristics Of Mathematical Cognitive Structure Of High School Students Based On Network Analysis

There is no doubt that mathematical cognitive structure plays an important role in the process of students' mathematics learning.Therefore,the research on mathematical cognitive structure is of vital importance,especially the study on the characteristics of knowledge organization,because it can help people to find out the optimal mathematical cognitive structure,so as to perfect the mathematics teaching and improve the quality of mathematics teaching.Review the existing studies,however,the vast majority are based on the thought of teaching activity experience combined with theory,there is little direct detection and quantitative research of students' mathematical cognitive structure,especially in terms of the organizational characteristics of the knowledge in mathematics cognitive structure.Based on this,this article will carry on the research mainly from the quantitative angle,with the aid of concept maps and social network analysis method,detect the organizational characteristics of the high school students' mathematics cognitive structure intuitively,and then find out the organizational characteristics of the high school students' good mathematical cognitive structure,so as to put forward relevant teaching suggestions and guide the teaching of high school mathematics.About the methods of study,the dissertation mainly uses the method of literature,investigation,social network analysis and so on.The order of this paper is: first,study the related theory and write research review.Analyze the existing research related to the knowledge in(good)mathematical cognitive structure and its organizational form,study the theory of concept map and social network analysis and related software.Second,write the questionnaire,and verify the effectiveness and stability.Third,choose several representative of high school students to investigate.Fourth,sort out and count the result of the investigation,analyze the data using Excel preliminarily.Fifth,use the network analysis software UCINET6.0 to analyze the data and get the network index of the mathematics cognitive structure.Sixth,compare the differences of organizational characteristics of mathematical cognitivestructure between top,middle,general students and boystudents,girlstudents and find the organizational characteristics of the good mathematical cognitive structure.Seventh,put forward teaching suggestions combining the reality of mathematics teaching.The main conclusions of this study are: First,from the network analysis point of view,the organization of high school students' mathematical cognitive structure is a network,it can't be confirmed if there is a link between the knowledge,even if there is contact,the strength is also different.Different knowledge may be in different places in the network,some are in the core,with the larger density and centrality,some are at the margins,even isolated position.From the macro point of view,the whole network can be divided into different blocks according to the related degree,the densities are different inside a block and between blocks,and because some knowledge in the network link closely,there are many small subgroups in the network.The number and size of subgroups in different network will have difference,in addition,the density and degree of condensation of the entire network will be different too.Second,by comparing the organization of knowledge in mathematical cognitive structure of top,middle and general students in senior high school,it can be seen that top students' knowledge network has more contact and therefore it is more dense;The members' distance of the whole network is small,and therefore it is more cohesive;put the network into different blocks according to the correlation,its blocks have larger scale,that is there are more members in each block,and the strength of the contact between and within blocks is larger;the members in subgroup can almost cover the whole internet,the number of the subgroups is also big relatively.In the top students' knowledge network,there are more concepts with high centrality,even if the requirement of connection strength is high,the connections between these concepts and others are still stable,these concepts in the center always have highest general level and the package level,concerning the objective relationship between knowledge,they are more scientific;the concepts with higher betweenness is less,the communication of information in the knowledge network isnot particularly dependent on some specific concepts.However,the middle students are relatively weak in all the above aspects,the general students are the weakest.The difference will be more obvious when the requirement of connection strength become higher.Third,the knowledge organization of a good mathematical cognitive structure should be such a structure: The strength of connection between the knowledge is large,high intensity of contact is more likely to be activated actually;the mutual contact is more,the macro performance is the network is dense;The path of contact is longer,the macro performance is that the members in the subgroup is more.In addition,the accumulation point in network is more,and the general level and the package level is higher,structure hole is less,there are relative more blocks,the size of block is large,the knowledge in network where contact inside block and between blocks are more intensive is easier to associate.Finally,based on the above research results,in the daily mathematics teaching,students' cognitive structure can be cultivated from the following aspects:First,increase the number of connection between mathematical content;Second,enhance the strength of connection between mathematical content;Third,increase the interrelated mathematical knowledge block;Fourth,increase the size of mathematical knowledge block;Fifth,optimize the quality of center mathematical point.From the aspects of specific operational measures,something can be done from the following aspects: First,use concept map during the mathematical teaching;Second,summarize the knowledge structure multi-dimensionally to establish rich connect;Third,repeat the key mathematical knowledge,pay attention to the students' fuzzy mathematical knowledge;Fourth,catch the appropriate timing,comb the relationship between mathematical knowledge.