Research On Analytic Geometry Problem Solving Ability Based On CPFS Structure

With the new curriculum reform,the modern concept of students are paying more attention to teacher,The modern concept of students emphasize student is in the development of people,to know students with the development of perspective;students are unique;students are independent significance.Therefore,when the students learning new knowledge,which require the teacher to understand the cognitive structure of students that the knowledge structure in the brain from learner rather than from textbook or cognitive structure in the brain from teacher.Teaching practice and experimental study show that it can play a positive sole in effective learning and problem solving by take a certain method to understand the cognitive structure of the student and has the destination to improve students' cognitive structure of availability,stability and clarity,and the degree of distinguishable.And cognitive structure here is aimed at students all the knowledge in the mind is concerned,the professor of Yuping from china point out that the mathematics knowledge structure in students mind is a special kind of cognitive structure,put forward the cognitive structure of mathematics in our country,CPFS structure.The author inspired by it,who think that a specific mathematical module also has the core of the CPFS structure.Therefore,this paper are based on the relevant analytic geometry CPFS structure,problem solving,research results,using the method of questionnaire and interview survey of high school mathematics problem solving ability and analytic geometry CPFS structure correlation and explore the influencing factors,and according to the research conclusion,develop based on the analytic geometry teaching under the CPFS structure,better service to education practice.The research of this paper are as follows: First,in combination with the research background of the “problem solving”,and the status of analytic geometry in high school mathematics knowledge,put forward the point in this paper that study main problem and the research significance;Secondly,this paper summarize the current related research from the two aspects of the CPFS structure theory and the analytic geometry problem solving;Thirdly,the core concept of the paper is expounded;Fourth,refer to the previous studies of CPFS structure theory,combined with the high school mathematics analytic geometry learning,make the high school students of plane vector learning questionnaire,questionnaire investigation,and spss19.0 survey results;The questionnaire analysis,eliminate invalid questionnaire,data processing and analysis,and make the corresponding research conclusion;Finally,according to the conclusion,to find analytic geometry problems existing in the teaching and learning,and work out teaching strategies,specific teaching design.In this study,the students of Grade Two and Grade Three are the main research subjects,and the following conclusions are drawn:Firstly,Whether the student of science or arts,the test scores of analytic geometry CPFS have high correlation with the ability of problem solving of analytic geometry,and have good linear regression modeling.Secondly,the student of science or arts,CPFS structure test score variance analytic geometry under the condition of equal,the different subjects has a significant effect on analytic geometry CPFS structure,that is to say,the subjects is the influence factors of analytic geometry CPFS structure.Thirdly,the boys and girls,CPFS structure test score variance analytic geometry under the condition of equal,the different gender has not a significant effect on analytic geometry CPFS structure,that is to say,the gender is not the influence factors of analytic geometry CPFS structure.Fourthly,the students of Grade Two and Grade Three,CPFS structure test score variance analytic geometry under the condition of equal,the different Grade has a significant effect on analytic geometry CPFS structure,that is to say,the Grade is the influence factors of analytic geometry CPFS structure.The survey show that the students of Grade Two who has just learned of analytic geometry knowledge has a better scores of CPFS structure than the students of Grade Three who has yet to review the related knowledge of analytic geometry,it show that the knowledge points in just learned if not timely review,the student has the most forgotten.Finally,on the basis of the theoretical analysis of predecessors' research results and this paper,based on CPFS structure,this paper put forward analytic geometry concepts and propositions teaching strategy,for the concept of analytic geometry teaching this paper put forward:(1)fully understand students CPFS structure of analytic geometry;(2)from different sides to reveal the connotation of the concept;(3)from the various structure reveals the connotation of the concept;(4)the examples proper arrangements,to deepen the understanding of the concept;(5)introduce the history of mathematics to understand the occurrence,development process of knowledge;(6)let the students try to use own words to describe the definition of the concept,properties,and so on;(7)feedback timely,scientific evaluation.For analytic geometry proposition teaching,the teaching strategies are given respectively by combining the three stages of learning.In the end,With the example of “simple geometric properties of the oval”,gives a concrete teaching design.