Research On Teaching Strategy Of Optimizing The CPFS Structure Of Derivative Concept In Senior High School Students

Calculus is the cornerstone of modern mathematics.With the development of the new round of curriculum reform,it is not only the requirement of social science and economics on mathematics courses,but also the requirement of realizing the goal of quality education in high school to offer some calculus contents in high school.Some knowledge of calculus in college is transferred to senior high school ahead of schedule,considering the cognitive development law of senior high school students and the realistic requirements of the age,senior high school students can and should learn calculus.High school students' learning calculus can understand mathematical thoughts and common methods,which is helpful to build a rigorous and logical thinking,and lay a good foundation for future learning.The new curriculum standard emphasizes that the essence of derivative should be emphasized in the teaching of calculus,and the infiltration of mathematical thinking method should be emphasized clearly.The study of derivative concept by educators has been a hot topic in teaching research in recent years.However,there are too many high school students who lack a complete concept system in the practice of concept teaching in reality.Therefore,when students apply concepts,even if only one expression of the problem is changed,they will have no idea and can't see the essence of the problem.Professor Yu ping points out that the perfect CPFS structure is an important way to solve the above problem,which can help students walk out of difficulties.Therefore,the improvement of CPFS structure plays an important role in improving the above phenomenon,but relevant research must be based on a clear understanding of the current situation of CPFS structure.The author collects and analyzes the existing related research literature of the high school derivative concepts,findiing that most studies are based on the theory of APOS and the mind map,while less researches are carried out from the perspective of the CPFS structure.With theoretical requirements and realistic demand,research on derivative concept of high school based on the theory of the CPFS structure comes into being at the historic moment,which is also the innovation of this article.In this paper,three teaching strategies are put forward to optimize the CPFS structure of derivative concept of senior high school students,they are visual strategy of concept formation,diversified strategy of concept understanding and variable strategy of concept application.This paper combines theoretical research and practical research.Theoretical research is mainly based on experience summary and theoretical speculation,after an overview of the CPFS structure theory,derivative concept,teaching strategy and other related core concepts and the related research of the CPFS structure,then taking the CPFS structure theory as a guide,this paper explores the basis of three teaching strategies for optimizing the CPFS structure of derivative concept of students in senior high school,specific content of the strategy and related application cases.Practice research adopts the research method of combining "experimental teaching","test survey" and "case interview",applys visual strategy of concept formation,the diversification strategy of concept understanding and the variable strategy of concept application under the guidance of CPFS structure theory to teaching practicethe to examine its impact on students' learning process and outcomes.Research result shows that experimental class students' math score has improved significantly,the CPFS structure of the student's derivative concept has been optimized to a certain extent,experimental class student's understanding ability,problem-solving ability,emotional attitude,learning method is improved,the core qualities of mathematics,such as intuitive imagination and mathematical abstraction,have been cultivated,The effectiveness of visual strategy of concept formation,diversification strategy of concept understanding and variant strategy of concept application under the guidance of CPFS structure theory is verified.