A Case Study On Diagnosis And Intervention Of High School Students With Conic Curve CPFS Structure

CPFS structure theory is a special cognitive theory in mathematics.Under the guidance of CPFS structure theory,it is of practical significance for students' learning and teachers' teaching to explore the cognitive structure of conic curve.In this paper,the test method and interview method are used to select the cases needed for the study,and the problems existing in the conic CPFS structure of the cases are diagnosed and analyzed.Then,according to the existing problems of the case and CPFS structure theory,the case was guided for two months.The results show that there are two main problems in the conic CPFS structure.Firstly,the conceptual domain and conceptual system of the case are not perfect,which are mainly manifested as :(1)the definition of conic curve and the generation of standard equation;(2)Incomplete understanding of relevant properties of conic curves,which cannot form a certain knowledge network.Furthermore,the propositional domain and propositional system of the case are not perfect,which are mainly manifested as :(1)weak ability to derive and understand propositions related to conic curve;(2)The application ability of conic curve knowledge is poor,and knowledge extraction cannot be carried out efficiently.In view of the existing problems of the case,this paper gives two aspects of intervention measures.First of all,the intervention measures in concept domain and concept department are as follows :(1)let students experience the derivation process of definition and standard equation;(2)Proper arrangement of positive and negative examples;(3)Reveal the connotation of the concept from different aspects.Secondly,the intervention measures in the propositional domain and the propositional system are as follows :(1)introduce propositions in a variety of ways to help students integrate old and new knowledge;(2)Guide students to independently prove propositions;(3)Guide students to conduct appropriate exercises,so as to develop students' divergent thinking and help them gradually internalize new knowledge into the existing cognitive structure.