Investigation And Research On CPFS Structure Of High School Students' Function Concept

Function is one of the four main themes in high school mathematics curriculum,the teaching of function concept has been the key research object of mathematics education for the past few years.A great deal of studies have shown that forming a good cognitive structure is contributive to students mastering learning methods and improving learning efficiency.CPFS structure theory put forward by Professor Yu Ping provides a scientific basis for studying students' cognitive structure.CPFS structure is a good cognitive structure for mathematical research,which is composed of Concept Field,Concept System,Proposition Field and Proposition System.Making an investigation of the status quo of students' CPFS structure will play a guiding role in the construction and improvement of students' good cognitive structure.The core question of the study: what is the current situation of CPFS structure and what are the current problems of Grade One students? What are the main contributing factors?In order to investigate the CPFS structure of functional concepts of senior high school students,literature analysis was firstly adopted,which was divided into two directions: functional concept teaching research and CPFS structure theory,and relevant literatures were sorted out respectively.The concept and properties of functions in the new textbook are analyzed and the knowledge framework is sorted out to lay a foundation for the compilation of the questionnaire.Next,based on the CPFS structure theory,the questionnaire prepared by Professor Yu Ping was adapted based on the measurement method of CPFS structure,and the final questionnaire was revised by solicting the opinions of prominent teachers and professors,and the investigation was carried out.Finally,data processing was carried out on the questionnaire,and test questionnaires were issued as well as interviews which are directed against students and teachers.The current situation of CPFS structure of senior middle school students was comprehensively analyzed from both quantitative and qualitative aspects,and the elements impacting on the current situation of CPFS structure of students' function concept were analyzed from multiple perspectives.Conclusion :(1)The CPFS structure of the function concept of senior middle school students presents a intermediate level.(2)From the perspective of the concept field,concept system,proposition field and proposition system of function,students have a better grasp of the function concept field and proposition field than that of concept system and proposition system.(3)Students lack a clear knowledge framework in their minds and a sense of perfecting the structure of mathematical cognition.(4)Students of Grade One are not accurate enough to grasp the essence and connotation of functions,and their mathematical language conversion ability and rigor need to be improved.Through the research and analysis,there are three factors that impact the formation of CPFS structure of the concept,that is,curriculum knowledge,teachers and students themselves.The improvement of teaching mainly focuses on the course dimension,teacher dimension and student dimension,and attaches importance to the processing of course content to promote knowledge cohesion and structural integrity.As the leader of education,teachers improve the students' adaptability from many aspects and apply theories of education to teach the concept.Students,as the major learners,excavate the essence of concept proposition and take the initiative to construct and perfect the structure of CPFS.