Teaching Research Of "Number And Algebra" Module In Junior Secondary School Under CPFS Structure

"Number and Algebra" is listed at the top of the curriculum in the Compulsory Mathematics Curriculum(2022 Edition)(hereafter referred to as "the new curriculum")and occupies an important position in the teaching of Mathematics in junior secondary schools.However,due to its large conceptual system,complex interlocking knowledge and scattered teaching materials,students have not yet formed a good cognitive structure.The CPFS structure theory proposed by Professor Yu Ping is an effective way to help students construct a conceptual knowledge system in mathematics.Therefore,this study intends to explore the following two questions:First,what is the knowledge system of the Number and Algebra module under the CPFS structure theory? Secondly,what is the current status of students’ construction of the CPFS structures in the Number and Algebra module?In response to question 1,we refer to a large amount of relevant literature,analyse the core concepts in the new curriculum and the junior high school textbook,and construct the knowledge system based on the abstract relationship between concepts,and come to the following conclusions: 1.the six operations have reciprocal and conversion relationships;2.integral exression are the core of the knowledge system of the number and algebra module;3.equations and inequalities have correspondence and conversion relationships;4.functions and equations,functions and inequalities are inextricably linked.In response to Question 2,test papers were prepared and statistically analysed with the help of SPSS software to empirically investigate the current status of students’ constructs in the CPFS structure of the Number and Algebra module.The following conclusions were drawn: First overall status,students’ CPFS structures varied widely,with most students’ CPFS structures being at an intermediate level;students’ CPFS structures were more related to their usual academic performance,the teaching methods of their teachers and the level of their schools.The second specific neutral status is that the operations and results of the operations often appear in pairs in the student’s mind;students’ learning of the same type of content is effectively facilitated when they have developed a better CPFS structure in a particular module.The third specific problematic status quo,the study found that students had a poor grasp of detailed concepts and lacked variation training and consolidation exercises;there were still structural problems with the perception of some concepts: 1.incomplete construction of the six operations,2.unclear construction of the real number system,3.unclear ideas for solving equations,and 4.unsound construction of the relationship between functions and equations and functions and inequalities.Finally,it returns to the CPFS structural theory and conceptual system to design targeted teaching cases.This study sorts out the knowledge system of the number and algebra modules,it helps teachers and students use abstract logical relationships between concepts to effectively construct systematic CPFS cognitive structures;Empirical research to understand students’ construction of CPFS structures in the Numbers and Algebra modules,the research conclusions have a certain level of universal applicability,front-line teachers can use problem-oriented teaching cases to better understand teaching materials and solve teaching problems.