A Survey Of Senior High School Students' Trigonometric Formulas Cognition Based On CPFS Structure Theory

CPFS structure theory is a cognitive theory of mathematics,which is an individual cognitive network composed of mathematical concepts,propositions and mathematical thinking methods contained in their abstract relations.At the same time,trigonometric formulas are important contents of trigonometric fuctions and the application of trigonometric formulas is flexible,so students' cognition in the contents will appear different degrees of problem.Therefore,it is of great significance for teachers to have a deep understanding of students' cognitive improvement in classroom teaching design to measure senior high school students' cognitive structure of trigonometric formulas based on CPFS theory and get their cognitive characteristics of trigonometric formulas.This paper investigates senior high school students' CPFS structure on trigonometric formulas from two senior high schools in G city and D city,to understand senior high school students' CPFS structure status on trigonometric formulas.Based on the results of the survey,effective teaching suggestions are put forward to improve the senior high school students' cognitive structure on trigonometric formulas.The main conclusions of this study are as follows:On the whole,17.19% of students have relatively perfect CPFS structure on trigonometry formulas,64.06% have medium level of CPFS structure on trigonometric formulas,and remainng 18.75% have low level of CPFS structure.Through the difference analysis,it is concluded that there is no significant difference in the structure level of CPFS on trigonometric formulas between senior high school students and their genders.However,there is a significant difference between students selecting physics and students selecting history in the level of CPFS structure on trigonometric formulas,indicating that students selecting physics are better than students selecting history in the construction of CPFS structure on trigonometric formulas.It is found that the excellent degree of CPFS structure is correlated with academic performance.Secondly,senior high school students' CPFS structure features forming on the learning of trigonometric formulas are as follows: students form the concept domain of trigonometric formulas with its own characteristics,but the understanding of the trigonometric formulas is not deep enough.On the construction of the concept system of trigonometric formulas,students are not clear about the relationship between trigonometric formulas and the others,failing to express the connection between them very well.Some trigonometric identities are stored in the students' cognitive network,forming a certain proposition field of trigonometric formulas,but the knowledge nodes are not extensive enough and there are still some problems among the derivation of some formulas.The properties reflected by trigonometric formulas are not well expressed,so there is no relatively good proposition system.In the application of knowledge,problem-solving thoughts of some students are not clear enough,for they haven't formed a good system of thoughts and methods on trigonometric formulas.Finally,some teaching suggestions are put forward to improve senior high school students' CPFS structure on trigonometric formulas.(1)Pay attention to the generation and proof of mathematical concepts and propositions.(2)Use multiple solutions to one problem to mobilize students' cognitive network to solve problems.(3)Use variable training to promote the development of students' mathematical thinking.(4)Infiltrate mathematical thinking and methods to reinforce students' cognitive structure.