Research On The Correlation Between Mathematical Modeling Ability And Cpfs Structure Of Senior Two Students ——Taking Analytic Geometry As An Example

The widespread use of mathematical models in life has made mathematical modeling a long-standing interest in all walks of life.Since mathematical modeling has become one of the core literacies in high school mathematics,developing students’ mathematical modeling skills is on the agenda.Previous studies have shown that cognitive structure is an important factor affecting mathematical modeling ability,and CPFS structure,as an excellent mathematical cognitive structure,is there a connection between the two? Based on analytic geometry knowledge,this paper explores the correlation between CPFS structure and mathematical modeling ability of grade two students through empirical research.There are two perspectives on the understanding of mathematical modeling capabilities: the macroscopic perspective and the microscopic perspective.Based on the microscopic perspective and "process theory",this paper divides the mathematical modeling ability into four modeling sub-capabilities: model building ability,model calculation ability,model interpretation ability and model inspection ability.The purpose is to explore the characteristics of the analytic geometric modeling sub-ability of senior two students.In this paper,we compiled the "Analytic Geometry Modeling Ability Test Paper for Sophomore Students" and the "CPFS Structure Test Paper for Sophomore Students’ Knowledge of Analytic Geometry",and selected two representative schools in the capital city and prefecture city of Yunnan Province for investigation.The purpose is to explore the characteristics of analytic geometric modeling ability of senior two students,the characteristics of CPFS structure of analytic geometric knowledge,and the correlation between the two.The analysis of the survey data led to the following main findings:For the analytic geometry modeling ability of sophomore students,from the overall characteristics,sophomore students’ analytic geometry modeling ability is poor,75.4% of the students’ analytical geometric modeling ability is at level zero and level one,and only 6.5% of the students.At level three,18.1% of students are at level two.The development of the four modeling sub-capabilities is uneven The best developed is the model building ability,the second is the model computing ability,the third is the model interpretation ability,and the least developed is the model testing ability.From the perspective of gender characteristics,there were no significant differences between the analytic geometry modeling（sub）abilities and their levels among the sophomores of different genders.From the perspective of school characteristics,there were significant differences between the analytic geometry modeling（sub）abilities of sophomore students and their levels in different schools.For the CPFS structure of analytic geometry knowledge of senior two students,from the overall characteristics,the CPFS structure formed by the analytic geometry knowledge of senior two students is not perfect,16.3% of the students are in the low CPFS structure group,68.8% of the students are in the middle CPFS structure group,14.9% of the students were in the high CPFS structure group.From the perspective of gender characteristics,there is no significant difference in the CPFS structure formed by the knowledge of analytic geometry between boys and girls.From the perspective of school characteristics,there are significant differences in the CPFS structure of students’ analytic geometry knowledge in different schools.A Pearson correlation study was conducted on the analytic geometric modeling ability and the CPFS structure of analytic geometric knowledge of senior two students.The results（R=0.851,p≈0.000<0.01）indicated a strong positive correlation between the two.A univariate linear regression equation was developed using the scores on the CPFS structure test of analytical geometry knowledge as the independent variable and the scores on the analytical geometry modeling ability test as the dependent variable: y =0.71x-2.307.