The Influence Of CPFS Structure On Mathematical Modeling Ability Of Senior High School Students

The related psychological research on mathematics learning shows that the foundation of mathematics learning is the cognitive structure of students,and an effective mathematical cognitive structure should be hierarchical and networked.The CPFS structure is formed based on concept field,concept system,proposition field and proposition system.It is a unique cognitive structure in mathematics that students internalize mathematical knowledge into their own minds.Therefore,in mathematics learning of senior high school,developing students’ CPFS structure in mathematics teaching is one of the effective ways for teachers to effectively cultivate students’ mathematical learning thinking,strengthen students’ deep understanding and summarizing abilities in mathematics,and strengthen students’ awareness of mathematical application.Mathematical modeling,as a link between mathematical theoretical knowledge and real life,is one of the ways that mathematics moves from students’ real life to mathematical abstraction.Mathematical modeling ability reflects the ability of students to correctly and flexibly use their mathematical knowledge to solve practical life problems and is one of the important criteria for measuring the effectiveness of students’ mathematical learning and teachers’ teaching.Based on the existing research on the CPFS structure theory,this article combines the CPFS structure theory with the teaching of high school functions,and demonstrates the teaching design of the section "Exponential Function" based on the CPFS structure theory.Two classes with basically the same level of CPFS structure,mathematical modeling ability and mathematical academic performance are used as experimental objects,and they are respectively set up as an experimental class and a control class.The CPFS structure theory is integrated into the mathematics teaching of the experimental class,and the control class carries out traditional mathematics teaching,conducting a half academic year teaching experiment.After the experiment,there were significant differences in the CPFS structure level,mathematical modeling ability and mathematical academic performance between the experimental class and the control class,demonstrating that the establishment of the CPFS structure had a promoting effect on students’ mathematical modeling ability and mathematical academic performance.Based on the practical teaching experience of combining CPFS structure theory with function teaching and the guidance of senior high school mathematics teachers,this article provides four suggestions for function teaching based on CPFS structure theory.The purpose is to provide some reference for the way of cultivating students’ mathematical modeling ability in senior high school mathematics teaching.(1)Repeatedly emphasizing to establish knowledge connections;(2)Connecting nodes to achieve knowledge correspondence;(3)Concept map to present the composition of knowledge;(4)Independent divergence to promote structural formation.