| Functions is an important mathematical model for describing variable relationships.It’s an important component of senior high school mathematics curriculum.In recent years,the teaching of function concepts has always been the focus of research in the field of mathematics education.However,in practice,many students cannot use the concept of function flexibly to solve mathematical problems due to their inperfect cognition of the concept of function.The CPFS structure theory proposed by Professor Yu Ping can solve the above-mentioned educational problems effectively.The CPFS structure is a unique cognitive structure of mathematics learning composed of concept field,concept system,proposition field and proposition system.It can help students absorb new knowledge faster,assimilate new knowledge,establish excellent cognitive structure,improve learning efficiency and achieve good results in mathematics learning.Therefore,it is important to investigate the cognitive structure of the function concept based on the CPFS structure theory and the implementation of teaching practice.It has important research value.Taking the CPFS structure as the theoretical guide,this paper designed the CPFS test questionnaire and the understanding level test questionnaire to understand the current situation of the senior high school students’ cognition of the concept of function.This paper compiled the teaching design of the function chapter for teaching practice.Therefore,this paper put forward some teaching suggestions to improve students’ cognitive structure of function,aiming at providing effective help for senior one students’ learning of function.Based on the perspective of CPFS structure theory,this study analyzes the cognitive status of the function of the senior high school students of Xi’an L.Middle School in Shaanxi Province.This paper analyzed the cognitive status of their functions,and used SPSS25.0 to statistically analyze the valid questionnaire,and drew the following conclusions.①The CPFS structure of the function of senior high school is at the medium level as a whole.②There was no significant difference in the structure and comprehension level of students’ CPFS structure of function in gender,and there were significant differences between classes at different levels.③ The superiority of the CPFS structure of the first year of senior high school affects the level of understanding to a certain extent,and the better the CPFS structure of the relevant functions,the higher the level of understanding of the students’ functions.In addition,this paper took two classes of L.Middle School students as experimental subjects,used CPFS structure theory to compile the function teaching design and conducted practical empirical analysis,and concluded that function teaching based on the CPFS structure theory will have a positive impact on students’ mathematical performance.Based on the above research results and teaching practices,the following teaching suggestions are put forward to improve the cognitive structure of student functions.① Pay attention to the connection between new and old knowledge,and pay attention to the growth points of students.② Pay attention to the concept generation process and deeply reveal the concept connotation.③ Sort out the context of knowledge and construct cognitive structure. |
