Research On Function Teaching And Practicing Based On CPFS Structure In Senior Middle School

Function is the most basic mathematical language describing the laws of the objective world.In the 17 th edition of the new curriculum,function is an important part of the high school mathematics curriculum.Based on the important position and effect,function has always been the focus of high school mathematics teaching.Due to the characteristics of the function itself(such as high abstraction,extensive application,etc.),it is difficult to understand for the students who are in the senior middle school.Therefore,the function teaching is also the difficult content in the senior middle school mathematics teaching.It is a common problem for students to understand the concept of function and to be weak in solving practical problems.In 2003,professor Yu Ping proposed the CPFS structure theory based on the students' mathematical cognitive structure,which provided a new way to solve the problems in the above teaching.Based on the theory of CPFS structure,this paper studies the problems of function teaching in high school and the relationship between individual CPFS structure and students' understanding of function.the author did the following work:First,relevant literature review and combing.By referring to a large number of literatures,the current research status of function teaching and CPFS structure theory was sorted out,and the relevant concepts and theoretical basis were analyzed and discussed.Second,investigate and analyze the structure level of function CPFS in senior high school students.By means of test paper and interview,this paper studies the current situation of high school students' learning function.By analyzing the test results,the following conclusions can be drawn:(1)The CPFS structure of functions in most high school students is at an intermediate level,and most high school students have an average understanding of functions.(2)On the whole,there are significant differences in the CPFS structure level and understanding level between the students in grade one and grade two,and the students in grade two are better than the students in grade one.This indicates that the abundance of knowledge of students contributes to the enhancement of CPFS structure and knowledge understanding of individuals.(3)Gender has little relation to the excellence of student learning function.(4)There was a positive correlation between students' CPFS structure level and their understanding of the function.Then the influence of teaching and learning on students' CPFS structure was further analyzed through teacher interviews.Thirdly,the design and implementation of function practice teaching based on CPFS structure.Based on the CPFS structure theory,the function teaching was designed,and the students of two parallel classes in a high school in changchun city of jilin province were selected as the object to conduct a period of teaching practice and collect statistical materials.Fourth,the analysis and suggestion of teaching practice results.The results show that the average score of the experimental class is higher than that of the control class,and the average score of the middle-level students in the experimental class is higher than that of the middle-level students in the control class.Based on the above research,the conclusion is drawn that the function teaching based on CPFS structure is more conducive to helping students to understand functions comprehensively and to their learning of functions.On the basis of the above investigation and experimental analysis,the author puts forward some Suggestions on the function teaching from four aspects: the attention of students' growing point,the guidance of concept formation,the use of variation and the systematization of concept.Finally,the author summarizes the research of the paper,analyzes the shortcomings of the research,and prospects the future research.