Research On The Teaching Design Of High School Function Concept From The Perspective Of HPM

Function is the main thread that runs through the high school mathematics curriculum.The concept of function is one of the widely used mathematical concepts.Its significance is indispensable.“General high school mathematics curriculum standard(2017 edition)” points out that function is the basic concept of modern mathematics,and the basic mathematical language and tool to describe the relationships and laws of variables in the objective world.It plays an important role in solving practical problems.The concept of function in senior high school is an extension of the concept of function in junior high school,which lays a solid foundation for the study of the properties of function,reference to function,trigonometric function,derivative and limit.In the literature review and practical operation,the researchers found that there were various problems in the teaching and learning of the concept of function in senior high schools,and the students’ understandings of it needed to be improved.In recent years,the educational value of mathematical history has been widely recognized by many mathematicians and front-line teachers.Based on the relevant knowledge of function concept and the existing HPM theoretical research framework,this study developed and designed the teaching design of function concept from the perspective of HPM,hoping to provide some references for front-line teachers,improve the teaching status of function,and deepen students’ understanding of function concept.On the basis of the existing research,this paper conducts interviews and exchanges with in-service teachers from the perspective of mathematics history,combining with the existing HPM research cases,and carries out the teaching design of the concept of high school function in combination with the teaching practice,and practices it in the classroom teaching.Based on that,a variety of research methods are used to collect data for qualitative and quantitative analysis,in order to explore the influence of teaching from the perspective of HPM on teachers’ teaching and students’ learning function concept knowledge.The research questions of this paper are as follows:Question 1: Do students have historical similarities in their understanding of functions?Whether students show the similar understanding of functions as historical researches?Question 2: Compared with the traditional function concept teaching,can high school function concept teaching from the perspective of HPM promote students’ understanding of knowledge?What are the effects on students’ feelings,attitudes and values?Question 3: Does the high school function concept teaching from the perspective of HPMchange the teachers’ teaching belief? Can the history of mathematics contribute to the improvement of teachers’ teaching skills?Main conclusions of this study:(1)students’ understanding of the concept of function is highly similar to that of mathematicians in different time and space in history;(2)function concept teaching from the perspective of HPM improves students’ mathematical literacy,deepens their understanding of function concept to different degrees,and cultivates their emotional attitude and values.(3)function concept teaching from the perspective of HPM transforms teachers’ teaching beliefs and promotes the development of teachers’ professional ability.