Research On Teaching Design Of Arithmetic Sequence Based On HPM

Equivariant series as one of the two special series,is an important object of study in high school mathematics,in the college entrance examination also occupies a certain proportion,and in real life also often use the knowledge related to the equivariant series.However,due to the knowledge related to the equivariant series is more logical and computational,students have some difficulty in understanding,so the actual learning effect is not satisfactory.The General High School Mathematics Curriculum Standards(2017 edition)particularly emphasizes the importance of mathematical culture and requires teachers to appropriately integrate elements of mathematical culture in the classroom.The history of mathematics is one of the most common ways to reflect mathematical culture,and the integration of mathematical history knowledge into mathematics teaching can improve students' interest in learning and deepen their understanding of mathematical knowledge.However,in the current high school textbook "Equivariant series",the material of mathematical history is very limited,and the educational value is thus limited.In this paper,we study the teaching design of HPM based on the history of mathematics and the existing HPM case studies.The research questions of this paper are as follows.Question 1: What attitudes do students and teachers hold toward the integration of the history of mathematics into the equivariant series?Question 2: What difficulties do teachers perceive in integrating the history of mathematics into the teaching of the equivariant series?Question 3: How can the history of mathematics be naturally integrated into knowledge related to the equivariant series?The main findings of this study are as follows.(1)Students and teachers were quite interested in the integration of the history of mathematics into the equivariant series and wanted to integrate knowledge of the history of mathematics into the teaching of the equivariant series.(2)Most teachers felt that there was too little history of mathematics in the textbook and were unsure of the ways in which it could be incorporated.(3)Based on reading a lot of literature and books,this study gives the principles of integrating the history of mathematics into the equivariant series,the ways of integrating the history of mathematics into the equivariant series,and on this basis,the basic steps and models of the HPM-based equivariant series are designed.Based on the above research findings,three teaching design cases are given in this paper,"Teaching Design of the Concept of Equivariant Series Based on HPM","Teaching Design of the Sum of the First n Terms of Equivariant Series Based on HPM" and "Teaching Design of Exercises Based on HPM",for the reference of front-line teachers.