Research On The Evaluation Of Trigonometric Function CPFS Structure In High School Students

The process of mathematics learning is essentially the formation,development and perfection of the mathematic cognition structure.Therefore,the perfection degree of individual cognitive structure directly affects the students' mathematics learning effect and achievement.In order to perfect students' cognitive structure,it is necessary to make scientific evaluation and remedy under theoretical guidance.CPFS structure theory,as a cognitive theory of mathematics,is a whole integrating mathematical concepts,propositions and mathematical thinking contained in abstract relations between concepts and propositions.Meanwhile,trigonometric function is an important part of mathematics course in senior high school.It involves a great number of abstract concepts,and the application of formulas is flexible and changeable.Students need to construct a good cognitive structure to learn trigonometric function and achieve good results in mathematics learning.Therefore,examining high school students' cognitive structure of trigonometric function based on CPFS structure theory is of practical significance to improve the trigonometric function learning of high school students and the teaching effects of teachers.Based on the theory of CPFS structure,this research attempts to test the trigonometric function CPFS structure of high school students.The following three tasks are completed: Firstly,in order to ensure the scientific and effective development of the test,good trigonometric function CPFS structure is discussed based on the theory of CPFS structure.Secondly,based on the investigation of the trigonometric function CPFS structure of 110 senior high school students in M Middle School and the questionnaire survey of trigonometric function learning among 180 senior high school students,the characteristics and causes of the trigonometric function CPFS structure of the senior high school students are studied.Thirdly,some teaching suggestions on perfecting the trigonometric function CPFS structure of senior high school students are proposed according to the test results.This study expects to assist teachers to understand the characteristics and causes of trigonometric function CPFS structure of high school students,and help students construct a good trigonometric function CPFS structure and improve the efficiency of trigonometric function learning.The main conclusions of the study are as follows:Secondly,high school students' trigonometric function CPFS structure is ideal.15.69% students' trigonometric function CPFS structure is at a high level,63.73% students' trigonometric function CPFS structure is at a moderate level,and 20.58% students have poor trigonometric function CPFS structure.From the perspective of grade,individuals' CPFS structure gradually improves with the increase of grade.From the gender point of view,there is no significant difference between male and female students in the CPFS structure;In addition,individuals' CPFS structure is significantly related to the academic achievement of trigonometric function.In other words,students with good CPFS structure have better academic achievement,while the academic achievement of students with poor CPFS structure is unsatisfactory.Thirdly,the teaching proposal for the formation of good trigonometric function CPFS structure among high school students is proposed.(1)Reveal the connotation of concepts from multiple perspectives;(2)form the concept of trigonometric function,propositional system;(3)Emphasize the application of concepts and propositions in trigonometric function;(4)set question string and build a bridge between propositions;(5)pay attention to variant training and highlight the connection between concepts and propositions;(6)improve students' divergent thinking in proposition domain(system)through classroom communication and discussion;(7)pay attention to students' independent inquiry,and promote the independent construction of the knowledge network.This study uses the CPFS structure theory to examine the cognition of trigonometric functions among senior high school students,which enriches the research results of specific mathematical modules based on CPFS structure theory to a certain extent.The survey results are analyzed from two perspectives of the characteristics and quantification of CPFS structure.The combination of the two analysis methods provides a new idea for the study of CPFS structure.The study also has some shortcomings such as small sample size and narrow coverage,which may affect the generalization of the study conclusions.In addition,because of the abundance and diversity of CPFS genetic data,the possibility of one-sided inference may exist in data analysis,leading to the one-sidedness of study conclusions.