Research On High School Mathematics Teaching Based On CPFS Structur

Function is the key and difficult point in high school mathematics learning,and is one of the four main lines of high school mathematics course content,occupying an unshakable position in high school mathematics.Among them,"The concept and properties of functions" is the first chapter of function content,and it is also the foundation of learning functions.This chapter covers a lot of knowledge and the content is relatively general,which students cannot comprehend in the process of study.In the teaching process,due to the tight time and heavy tasks,most students are difficult to obtain the clear meaning of knowledge,and cannot unify the new knowledge with the original knowledge,so that the students’ knowledge of this chapter is not thorough enough to form a complete system.Professor Yu Ping of Nanjing Normal University in China clarified that CPFS structure theory is a unique mathematical cognitive structure for learning.This provides a new idea for solving the problems of students’ lack of deep understanding of knowledge,inability to form a complete system,and difficulty in flexible application of knowledge in the learning of functional knowledge.Based on CPFS structure theory,this paper studies the teaching design and implementation of "the concept and properties of functions".The main contents are:Chapter 1: Introduction.Introduce the review,ideas,structure,etc.of this study.Chapter 2: Related concepts and theoretical foundations.Introduce the concepts of CPFS structure;The two theoretical foundations of this study are summarized.Chapter 3: Instructional Design Construction Based on CPFS Structure.Firstly,the teaching strategy is summarized on the basis of the predecessors,and secondly,the overall and partial analysis of the "concept and properties of functions" is carried out to create the corresponding CPFS structure diagram.Chapter 4: A Case Study of "The Concept and Properties of Functions" Based on CPFS Structure.The teaching design of "function concept","monotonicity","parity" and "power function" under CPFS structure is carried out respectively.Chapter 5: Teaching Implementation and Results Analysis.First,the teaching is implemented according to the teaching design,then the test results of students are analyzed,and finally the teachers are interviewed and analyzed.Chapter 6: Conclusions and Reflections.Draw conclusions based on statistical analysis results and reflect on the shortcomings in the study.Through the above research,three conclusions can be obtained: First,the teaching design of "the concept and properties of functions" based on CPFS structure theory can help students build a good CPFS cognitive structure and enhance students’ understanding and application of function knowledge.Second: In the comprehensive application of the topic,the more complex the topic,the better the teaching under CPFS structure theory than the traditional teaching.Third: CPFS structure theory has a positive effect on teacher teaching.