The Parallelogram CPFS Structure

The basic task of mathematics teaching is to lay a good foundation for students' study and development.The key to realize this basic task is to let students obtain a good mathematical cognitive structure which is conducive to their further learning and development.CPFS structure is a good mathematical cognitive structure.CPFS structure is a complete system composed of abstract concepts,propositions and mathematical thinking methods.Research shows that the perfect CPFS structure is conducive to students' better mathematics learning,and it is more conducive to improve their mathematics grades.Based on the CPFS structure theory,this paper tests the parallelogram cognitive structure for junior high school students,which can help students to master knowledge better,and also can put forward corresponding teaching suggestions for teachers' reference.This study mainly completed three tasks: in-depth study of CPFS theory,definition of a good parallelogram CPFS structure;preparation of a questionnaire and test paper,and test 141 subjects,reasonably selected,analyze 270 valid test results,and get the current situation and formation reasons of parallelogram CPFS structure of junior high school students;according to the analysis results,This paper puts forward some reasonable teaching suggestions to improve the parallelogram CPFS structure of junior high school students.The specific research results are as follows:The parallelogram CPFS structure is a cognitive structure system composed of multiple elements and multiple relations under the support of CPFS theory.It consists of three parts: the conceptual domain and conceptual system composed of the concept of parallelogram and the concepts with abstract relations(such as triangle,parallel line,real number,etc.);the properties and judgment of parallelogram(including special parallelogram)As well as the propositional domain and propositional system composed of propositions with abstract relations(such as Pythagorean theorem,the nature and determination of parallel lines,etc.);the teaching method system composed of mathematical ideas(such as the combination of number and shape,transformation ideas,etc.)involved in the parallelogram part.Through the multi angle statistical analysis of the survey results,the current situation of the parallelogram CPFS structure of junior high school students is obtained.Generally speaking,students' learning interest,learning methods and teachers' teaching methods affect the construction of the parallelogram CPFS structure.The statistical results show that only 19.72% of the students have constructed a relatively perfect parallelogram CPFS structure,and 26.76% of the students have not established or established a low-level parallelogram CPFS structure.The current situation of the structure is not very ideal;the establishment of CPFS structure has no significant correlation with the gender of learners;the establishment of CPFS structure has significant correlation with the mathematics grades of learners.The higher the level of construction of CPFS structure is,the better the mathematics grades are.According to the current situation of the parallelogram CPFS structure of junior high school students and the reasons for its formation,several teaching suggestions are put forward:(1)pay attention to enhancing the students' interest in learning(create the situation,use the technology and methods wisely;work stratification,and obtain the successful experience);(2)teach the system knowledge in the beginning of a good chapter;(3)simplify the knowledge points(pay attention to the reasoning between propositions,and the relationship between concepts);(4)Pay attention to the knowledge structure chart;(5)pay attention to the connection between the new and old knowledge;(6)clarify the thoughts of solving problems and dredge the knowledge vein.In this study,CPFS theory is applied to the field of parallelogram for the first time,which enriches the research content based on CPFS structure theory in junior high school to some extent.It is hoped that the results of this study can promote the teaching of parallelogram and other modules.