Investigation On The Present Situation Of CPFS Structure Of The Concept Of Higher Student’s Function

The concept of function not only is one of the problems in the mathematics learning of the senior high one,the idea of function also runs through the whole high school mathematics learning.in recent years.the study of the concept of function has been a hot topic in teaching research.However,many high school students only understand the concept from one side in the concept of learning teaching reality.it is difficult to form a complete concept system,which leads the students will not be able to solve the problem,even if it is only one side of the transformation of the problem in the specific application of the concept.Yu Ping pointed out that the perfect CPFS structure is an important way to solve the above phenomenon,therefore,to improve the CPFS structure is of great significance to solve the above phenomenon.but the relevant research must base on the current situation of CPFS structure.A survey on the existing concept of function analysis found that most research perspective combined with APOS,SOLO,Fan Xier.Cognitive.Concept map theory,there was no study in combination with the CPFS structure perspective.the research on the concept of function from the perspective of CPFS structure is the research topic of this paper.CPFS structure is composed of concept field.concept system,proposition field and proposition system.Among them,all equivalent definitions of mathematical concept C are called the conceptual domain of concept C,a group of conceptual networks with mathematical abstract relations is called a conceptual system,the propositional set equivalent to a proposition is called the propositional domain of the proposition,in a set of propositions,any proposition has at least one pushing relation with the other proposition,the set of propositions is called a proposition system.In order to have a more objective understanding to present of CPFS structure,this study mainly base on the test method of CPFS structure to design the CPFS function test,investigation to the two different levels high school senior one students’ CPFS structure,and through related teaching cases and case studies analysis the causes of the current situation of CPFS structure.Through investigation and study finds that the current situation of the high students’ CPFS structure are as follows.First point,only 18.44%students CPFS structure reached an excellent level,having 66.23%students CPFS structure are better,and the CPFS structure is poor in 15.33%.Second point,80%students correctly represent the function from the perspective of the image,most students don’t form a good concept field;up to 87%students don’t form a complete functional concept system,84.42%students know the function range meaning,most students haven’t formed a complete method system to solve questions about function range,about 70%students can make changes three languages for the function of increasing or decreasing,nearly half of the students can infer the monotone of the new function after operation of the function calculation of increasing or decreasing.67.01%students form the concept field and proposition field of parity,more than half of students haven’t formed the concept field and proposition field of odd function,few students can use the original proposition and the converse negative proposition to construct the conceptual field,but it is still necessary to improve the method of solving the related problems.The third point,the school with a good level of aggregation is also good in the overall situation of the CPFS structure,the number of poor level is less,the independence test of contingency table shows that different school levels have an impact on the excellent performance of student function CPFS structure.Fourth point,the independence test of contingency table shows that the gender doesn’t affect the excellent situation of CPFS structure.Fifth point,Han students functional CPFS is poor than Zhuang and Miao,but the overall the functional CPFS structure situation of Zhuang and Miao is not significant,the final test of the independence of the contingency table shows that the nation doesn’t affect the excellent situation of functional CPFS structure.The teaching cases analysis and case studies shows that the reasons for the above situation of high school students are as follows.Firstly,teachers doesn’t reveal the growth point of correspondence theory from variable theory;ignoring the strengthening of the nature of the function concept,there is no multi angle to explain the concept of function of correspondence theory;without guiding students to reflect on the function and its related concepts.Secondly,students usually ignores number of keywords of function in specific application,which is confused with the concept of mapping,and students also easy to ignore the unique correspondence;students understand the concept of function better from the perspective of the image,but can not understand the idea of mathematical methods;students are not able to organization structuring to function concept.Based on the analysis of the reasons for the current situation of the high school students’function CPFS structure,there are suggestions to improve the present situation of the CPFS structure of high school students.To reveal the growth point of correspondence theory from variable theory.Using the teaching method of variation to explain the concept of function from multiple perspectives.Structuring organization to function concept by Concept map or Mind map.To strengthen the understanding of number set and unique correspondence in the nature of function concept.Students should also pay attention to the idea of combination of number and shape with acquiring the function image language.Students should pay attention to the classification in the process of solving problems.