Investigation And Research On CPFS Structure Of Spatial Vector For High School Students

As an important vehicle for developing students' mathematical core literacy,spatial vector and stereo geometry have always been an important module in high school mathematics.However,in reality,the development of students' cognitive structures is not given sufficient attention,resulting in incomplete knowledge of this part of the content and difficulties in its application.The CPFS structure is a unique cognitive structure of mathematical learning,which provides a more accurate method for students' mathematical understanding.Optimizing students' CPFS structure is an important way to address this issue.According to the Senior Secondary Mathematics Curriculum Standards and spatial vector teaching content,the test paper is designed based on the structure theory of CPFS,and the structure of the spatial vector CPFS of high school students is investigated.The survey found that the current status of the spatial vector CPFS structure for high school students is as follows:(1)An overall satisfactory level,with 18.28% of students have a good spatial vector CPFS structure,62.58% have a moderate spatial vector CPFS structure and 19.14% not have a good spatial vector CPFS structure.(2)18.71% of students do not able to screen conceptual extrapolations well,15.70% of the students do not understand the nature of the concept and fail to form a good concept field;74.84%of the students have a medium level of concept system and can better link spatial vector with other mathematical knowledge,17.20% of the students have a poor level of concept system;the overall level of the student's proposition field is poor,with significant differences in the level of proposition field between individuals;55.70% of the students fail to form a methodological system in their minds for the application of spatial vector,and their proposition system are not well developed;(3)Gender is not an influential factor of the spatial vector CPFS structure of high school students;sophomores have a better spatial vector CPFS structure and better stability of performance than juniors;science students have a higher level of spatial vector CPFS structure than arts students,but the stability of performance of arts students is better than that of science students.The structural causes of CPFS of students' spatial vector are analyzed from both students and teachers:(1)Students lack the awareness of optimizing their cognitive structure and their knowledge system is scattered;they are not interested in learning about spatial vector and have negative learning emotions.(2)In terms of knowledge integration,teachers lack systematic guidance to students;teaching focuses on examination points rather than the development of students' abilities,and ignore the use of educational information technology.Based on the analysis of the survey results,the teaching suggestions for improving the CPFS structure of the spatial vector of high school students are proposed,which helps teachers improve teaching efficiency and promote the development of students' mathematical ability.