Study On The Relationship Between The Structure Of Plane Vector CPFS And Representation Ability Of Senior Three Students

Vector has the dual properties of "number" and "form" and plays an important role as a bridge between geometry and algebra geometry.Plane vector,as an important part of vector,is difficult to build a perfect cognitive system because of its various concepts and propositions,and complex relationship with each other,which has become a major difficulty in mathematics teaching and learning.CPFS structure is a unique and excellent cognitive structure in mathematics learning,especially suitable for knowledge points with multiple representational modes such as plane dimension.The study of the relationship between CPFS structure and representation ability of plane vector can help students build knowledge system,improve mathematical problem-solving ability,and provide theoretical reference for teachers to carry out the teaching of plane vector.In this study,literature survey was used to determine the research ideas,questionnaires were used to collect the data needed for the study,and SPSS software and Excel software were used for statistical analysis.The purpose of this study is to investigate the structure and representational ability of plane vector CPFS of senior three students,and to study the relationship between them.The author determines the research problems and theoretical framework by combing the literature.Plane Vector CPFS Structure Test paper and Plane Vector Representation Ability Test paper were compiled,and the predictive test analysis was carried out and the test papers were modified successively.Finally,two sets of formal test papers with good difficulty,reliability and validity were obtained.Then,four classes of grade three in a school in Chengdu were tested in the evening self-study time.After sorting out and analyzing two sets of papers,the following conclusions were drawn:(1)The construction of plane vector CPFS structure of senior three students is generally at a medium level,and there is a great difference in the perfection degree of CPFS structure among students.(2)The plane vector representation ability of senior three students is average,and there is a great difference between students.(3)There is a significant positive correlation between the structure excellence of plane vector CPFS and the representation ability of senior three students,that is,the more perfect the CPFS structure is,the stronger the representation ability of students,and the worse the CPFS structure is,the weaker the representation ability of students;The stronger the students' representation ability,the more perfect the CPFS structure;Vice versa,the weaker the students' representation ability,the worse the degree of perfection of CPFS structure.In the unitary linear regression analysis of plane vector CPFS structure and representation ability of senior three students,with the CPFS structure score of senior three students as the independent variable and the representation ability score as the dependent variable,the standardized unitary regression equation between the two is.The results showed that the structural excellence of CPFS in senior three students directly affected the students' representation ability,and there was an obvious causal relationship between them.This study provides a new idea for the teaching of plane vector,that is,by helping students build CPFS structure system to enhance their representation ability,so as to improve their ability to solve plane vector problems;At the same time,the CPFS structure can be improved by training students' representation ability,so as to deepen the connection and understanding of plane vector knowledge points.