The Teaching Research Of High School Mathematics Derivative Based On HPM

The derivative plays a very important role in high school mathematics.It is a very important way to study the properties of functions.Moreover,the derivative also occupies a large proportion in the college entrance examination.However,due to the limited level of students' thinking development,teachers do not guide students to understand the concept of derivative from the perspective of limit in high school and focus on the application of derivative in the teaching derivative and its application of high school mathematical.Therefore,how to grasp the essence of the concept of derivative and flexibly apply the nature of derivative to study the original function on this basis and solve practical problems has become a difficult point for students and also a difficult point for teachers in the teaching process.In 2013,the Ministry of Education launched a new round of curriculum revision for ordinary high schools.The general high school mathematics curriculum standard(2017 edition)(hereinafter referred to as the standard)was officially published in January 2018.There are 4 basic ideas in the "Standard","to grasp the essence of mathematics,to inspire thinking,to improve teaching" is one of them.This idea requires high school mathematics teaching to develop students' core quality of mathematics subject as the guidance,to create a suitable teaching situation,to inspire students to think and to guide students to grasp the essence of mathematics content.In recent years,there have been more and more researches on HPM,and the educational value of HPM in teaching practice has been more and more recognized by researchers.The practice of HPM provides ideas and directions for the practical teaching of derivative.By expounding the occurrence and development history of derivative,integrating the history of mathematics into the actual teaching,creating the appropriate teaching situation,let students know the origin of derivative,so as to better grasp the essence of derivative concept and use the derivative more flexibly to solve practical problems.Through literature research,this paper sorts out the research on HPM and the derivative,including the development process of research related to HPM,the research on HPM applied teaching,the development history of derivative and derivative teaching.On this basis,the concept of derivative and the application of derivative based on HPM were designed and implemented.Through statistical analysis of the data collected from the questionnaire survey and analysis of the interview results,the following conclusions are drawn:(1)Derivative teaching based on HPM can promote students' understanding of the essence of derivative concept.(2)Derivative teaching based on HPM can promote students to flexibly apply the properties of derivative to study the original function.(3)Mathematics teaching research based on HPM can improve the comprehensive ability of researchers.