Teaching Design And Practice Research Of Radian System From The Perspective Of HPM

The history of mathematics is of great value in mathematics education,and teachers' understanding of mathematics history is not only good for their systematic knowledge of mathematics,but also for teachers to understand the cultural value of mathematics.However,there are still many misunderstandings about why and how to apply the history of mathematics.Therefore,the HPM field on the "history of mathematics" related issues have come into being,for mathematics teachers to make more rational use of mathematical history to provide a theoretical basis."Radian" is an important teaching content in high school.Many teachers shift the teaching focus to the conversion formula of radian and angle,so that students think that radian is a symbolic game with angle system conversion.The history of mathematics is an important tool to understand the concept of radian system and introduce necessity,so this study will give the design of HPM teaching for reference on the basis of the theory of mathematical history and mathematics education(HPM).The research questions of this thesis are followings:(1)How to explore the teaching design of the "Radian" case under HPM's perspective,(2)How radian teaching under HPM's perspective affects students' conceptual understanding,and(3)How radian teaching under HPM's perspective affect students' emotional attitude.Finally,this study collects literature and data by means of literature analysis,questionnaire survey,teaching record,experimental research,etc.,and through quantitative and qualitative analysis of data,draws the conclusion of the study:(1)After comparing the teaching of parallel classes,found that students using HPM teaching methods,their conceptual understanding level is significantly higher than the normal teaching methods not integrated into the history of mathematics,and emotional attitude has a more positive impact on students;(2)Students show some historical similarities in the process of exploring the generation of radian system,that is to say,the mathematical history of radian system can be used as a teaching guide for radian system.(3)The radian teaching under HPM's perspective generated under this study is of reference significance to mathematics teachers,and the students' questionnaire results show that there are some suggestions worth improving under the original design to make radian teaching more perfect.For example,highlighting the role of arc length in arc teaching;The idea of penetrating the number of forms in the exploration of radian system;Pay attention to the students' understanding ? of "society";In the follow-up triangulation function study,students can further appreciate the advantages of radian system and so on.