Research On The Teaching Of Derivative Concept Based On APOS Theory

The importance of calculus is self-evident.It is called a milestone creation in the history of mathematics,and it has played a role as a bridge in the development of mathematics.As one of the core concepts of calculus,derivative is also a meeting point of knowledge.It has an important position in high school mathematics.However,the concept of derivative is very abstract,which makes it a difficult point in high school mathematics teaching.In the teaching process,teachers are easily affected by test scores.They focus on test-taking skills and calculation skills and lack attention to the understanding of derivative concepts.This is not only detrimental to the cultivation of students' core mathematics literacy,but also violates new education idea.This paper mainly takes APOS theory as the carrier,carries out in-depth investigation and analysis of the teaching of derivative concepts,and puts forward reasonable teaching suggestions.Starting from the source,connotation and model of the APOS theory,this article conducts an in-depth analysis of the teaching status quo of the concept of derivative through surveys and interviews.The survey is divided into two parts.One part uses a questionnaire to conduct a comprehensive survey on the three aspects of learning,teaching and difficulties;the other part uses test papers to investigate the four aspects of the rate of change,the meaning of the derivative,the derivative function and the application of the derivative.The knowledge dimension examines the students' specific mastery of the concept of derivative,so as to conduct an in-depth analysis of the students' learning of the concept of derivative.Based on the APOS theory,the article makes a series of discussions on the teaching of derivative concepts,and compiles a teaching design suitable for students' cognitive development.Finally,in view of the problems and causes analysis of the students' learning of the concept of derivatives,the teaching suggestions on the concept of derivatives are put forward: pay attention to the concept formation process,pay attention to improving students' ability to use derivatives to solve practical problems,stimulate students' interest in learning,change teachers' traditions and use information technology to strengthen the teaching of derivative concept.The teaching concept is hoped to provide a reference for teachers in front-line teaching.