Research On The Balance Process Of College Students' Mathematical Cognitive Structure Based On Network Analysis

Mathematical cognitive structure plays an important role in students' mathematics learning.Therefore,the study of good mathematical cognitive structure is of great significance,especially the process of balance of good mathematical cognitive structure,because this aspect of research can understand the formation process of good mathematical cognitive structure more deeply,and then improve mathematics teaching to promote students' mathematics learning.However,looking back on the previous studies,most of them are aimed at the static characteristics of mathematical cognitive structure,and a few are based on the dynamic development of cognitive structure,the qualitative research on the balance process of individual students is simply expounded,so far there is no basis for the balance process of good mathematical cognitive structure a quantitative study of in-depth analysis by combining data with theory.Therefore,this study will use concept map and social network analysis to quantify and analyze the balance process characteristics of college students' mathematical cognitive structure,and finally analyze and get the balance process characteristics of college students' good mathematical cognitive structure,so as to put forward scientific and reasonable teaching suggestions.The order of the study is as follows: first,using the literature method to find out the relevant(good)mathematical cognitive structure balance process theory and review research,comprehensive and in-depth study of concept maps and social network analysis of the relevant theory and supporting software.Second,make the research design,select the relevant research materials,write the corresponding investigation materials,and ensure its effectiveness.Third,according to the requirements of the study,select a suitable number of representative college students as a research sample.Fourth,the use of concept maps to collect data,and through the Excel of the survey data for preliminary collation and analysis.Fifth,using the corresponding software U of social network analysis method CINET6.216 do further quantitative analysis of the collated data.Sixth,with reference to the characteristics of the balance of cognitive structure in mathematics of middle and general students,focuses on analyzing the characteristics ofbalance of top students,so as to find out how the balance process of good mathematical cognitive structure is and its characteristics.Seventh,based on the research conclusions,put forward the corresponding targeted teaching suggestions.The findings of the study include:(1)in the original mathematical cognitive structure of the overall network changes.First,from the point of view of the number of links,the number of links between the "old mathematical concepts" in the original mathematical cognitive structure has increased.That is to say,more and more "old mathematical concepts" are connected,the overall mathematical concepts are more and more closely linked,and the flow of information is becoming more and more easy.Second,from the point of view of connection strength,the average strength of connection between "old mathematical concepts" in the original mathematical cognitive structure has been enhanced.In other words,in the good mathematical cognitive structure of higher algebra,the correlation between concepts becomes more and more The greater the relationship,the stronger the understanding and memory of the concept.Third,from the point of view of position,the position between the "old mathematical concepts" in the original mathematical cognitive structure is getting closer and closer.That is to say,the distance between "old mathematical concepts" is getting smaller and smaller,and to some extent,the concepts can be linked together by fewer and fewer edges,and the information transmission between each other is more and more smooth.(2)aspects of individual changes in the original mathematical concept of cognitive structure.First,from the point of view of the number of links,the number of other mathematical concepts(including the new mathematical concepts that are constantly being incorporated)connected by the original mathematical concept is based on the concept Body situations correspond to additions or subtractions,but concepts are becoming more logical.That is to say,with the study of the new mathematical concept,the original mathematical concept is related to the more relevant mathematical concept,the original mathematical concept related knowledge system is constantly merged or expanded,the relationship between concepts is more and more clear,and the top students consider more in-depth and comprehensive in solving specific mathematical problems.Secondly,from the point of view of connection strength,the connection strength of the original mathematical concept andother mathematical concepts with greater relevance will become stronger and stronger.In other words,top students not only retain the more relevant mathematical concepts,but also remember more and more.At the same time,the relationship between mathematical concepts is stable and maintainable.Third,from the point of view of position,the position of the original mathematical concept in the mathematical cognitive structure tends to be more and more central,that is,the original mathematical concept is closer to other concepts,and the "distance" is very short,and the information transmission between concepts is more unobstructed.Based on the relevant conclusions of this study,in normal mathematics teaching activities,the teaching requirements of cultivating college students' good mathematical cognitive structure are as follows: first,to increase the interrelation between mathematical concepts;second,to change the number of concepts corresponding to the original mathematical concepts;third,to strengthen the connection between mathematical concepts;fourth,to narrow the distance between mathematical concepts;fifth,to gradually put the original mathematical concepts in a more important position.The concrete teaching measures are as follows: first,using concept map to assist teaching;second,introducing mind map;third,sorting out the original mathematical knowledge;fourth,constructing reasonable mathematics Knowledge structure.The term teaching plan is as follows: first,before the semester--to update the concept of education and teaching;second,during the semester--to guide college students to build a good mathematical cognitive structure;third,after the semester--to improve the mathematical cognitive structure of college students.