Research On Teaching Strategies Of Function Concept In Senior Middle School Based On CPFS Structure Theory

Mathematics concept is the cell that forms the subject of mathematics,which is the base that leads students to carry on activities of mathematical thought and the key content of mathematical learning as well.With the development and constant depth of education reform,the complete propelling and developing of cultivating education puts forward higher requirement to the learning and understanding of mathematics concept.Having a thorough look at the common senior "mathematics course standard",one can see that emphasizing the understanding of mathematics concept is one of its basic concepts.On the other hand,the original knowledge structure has significant influence on mathematics learning.As for students,a good knowledge structure could help them much more quickly learn new matters,understand new substances,apply new methods and solve new problems as well.Therefore,the research of excellence on individual knowledge structure,the understanding level of mathematics concept as well as the relations between the two is of great value to mathematics education.Function,whose thinking method infiltrates the math study of whole senior grades,is regarded as one of the core concepts of mathematics contents for senior grades.Students' understanding level of function concept can be representative of the understanding level of important concepts for senior grade mathematics.It is well known the importance of the concept understanding for function.Thus,it is quite meaningful to help students improve understanding level of function concept.In another aspect,structure of CPFS is formed by concept field,concept system,proposition field,and proposition system,which is a special and excellent knowledge structure for mathematics learning,which is the precondition for the learners to develop good CPFS structure.Based on the analysis above,selecting CPFS structure as the entering point,the relativity between function CPFS structure and its understanding level of function concept that students are building is further discussed.Through the test of the excellence of structure of function CPFS and the test of understanding level of function concept to students of senior grade one and two from M School,Kunming,Yunnan province,this research has analyzed the present situations of function CPFS structure and understanding level of function concept which students who tested have built.Presuming on software SPSS19.0,its relativity between the two has been further analyzed.The research finds:(1)From the whole view,function CPFS structure that senior students have built is not perfect yet in the present stage.(2)Function CPFS structure students are building is to become perfect with the grade rising.(3)Function CPFS structure built by students of the same grade shows no obvious difference between male and female.(4)It's not ideal for senior students to understand function concept in general in the present stage.(5)Students' understanding level to function concept is to improve gradually with grades rising.(6)There is no obvious difference to students of same grade on sex towards understanding level of function concept.(7)Individual understanding level of function concept has close connection with its function CPFS structure.Therefore,students of building good function CPFS structure are to surely get higher understanding level of function concept.Meanwhile,the higher understanding level of function concept students have gained,the better function CPFS structure they build.Based on the analysis of the investigating result above,teaching strategy towards function knowledge of senior grades is put forward in further step.And on this basis,teaching design is carried out on three typical topics related to functional knowledge,so as to offer certain reference to present teachers.