Research On The Relationship Between CPFS Structure And Mathematical Abstraction

With the proceeding of the course reforming,people started to show broader concerns on literacy development of math,in which the mathematical abstractions ability has stepped into the public insight.The CPFS structure,a particular quality cognitive structure,also has deep impact in math-learning.Therefore,to determine the relationship between the complementary level of CPFS structure and the math abstraction could contribute to finishing the teaching strategy.The essay bases on experiment researches,with the CPFS structure quiz and math abstraction quiz from relevant high-school function,by measuring two classes from different grades in high school in Chengdu.According to the data from the 240 examples,the essay tries to answers questions in: the current structure of CPFS,the current ability of student math abstraction,the relationship between both,the influence of higher or lower CPFS structure,also to analyze: whether the sex and grades could affect them.The conclusion is as followed:(1)The general CPFS structure of high-school student is medium.There is no difference in sex.With the increasing in age,the complementary level of CPFS goes upward.(2)The ability of strong abstraction and math abstraction is medium,while the weak abstraction is below average.There is no difference between sex,even female have greater performance than male.Paralleled with CPFS,the ability increases with higher grade.(3)The CPFS structure use positive correlation with math abstraction,with their regression equation: Y=1.753X+2.911.The quiz result has shown great differences among different structures.(4)The effect of external regulation on the high CPFS structure group was not obvious.(5)The results of strong abstraction,weak abstraction,and mathematical abstraction of the low CPFS structure group with hints were still significantly different from those of the high CPFS structure group without hints.(6)After being prompted,the low CPFS structure group showed great progress in strong abstraction and mathematical abstraction ability,but the progress in weak abstraction ability was not obvious.(7)According to the experiment,this essay has released three teaching strategy in CPFS structure: infiltrating the diverse of knowledge performance,strengthening the training of multi-solution to same question and emphasizing the review.At the meantime,it has created four teaching strategy in normalizing math abstraction: creating proper question situation,specifically training of induction reasoning,experience the origins of knowledge and deliberately infiltrating mathematical mind.