Research On Number System Development And Teaching Practice From The Perspective Of History & Pedagogy Of Mathematics

In recent ten years,mathematics educators have attached great importance to the penetration of mathematics culture in mathematics teaching,especially the applied research on the History & Pedagogy of Mathematics(HPM).More and more people are aware of the educational value of HPM.Questions or applications related to the history of mathematics and mathematics culture have appeared one after another in the college entrance examination and middle school entrance examination,and the teaching case studies from the perspective of HPM by mathematics education scholars have gradually increased.The development of the mathematics system has taken a long time in the history of mathematics,and it is a highlight in the long history,and it is the foundation and key to the development of mathematics.If the development history of the mathematics system is integrated into the expanded chapter teaching of the mathematics system,not only allows students to experience the long and hardships of mathematics development,but also allows students to understand and master relevant knowledge from a historical perspective.It can also provide effective case support for the integration of mathematics history and mathematics education and the teaching of middle school mathematics.At present,there are relatively many studies on the number system,but there are few studies from the perspective of HPM alone.There are only 27 documents in CNKI that use "number system" + "HPM" as keywords(as of March 2021.31),these articles generally have problems such as incomplete research on the history of the development of the logarithmic system,and insufficient systematic combing of the system.Therefore,the author intends to use the literature review,case analysis and other methods to further sort out the development history of the number system through this article.By comparing the teaching effect of the normal teaching mode and the teaching mode integrated with the HPM teaching mode,we study the teaching of HPM integrating the concept of mathematics,clarify the educational value and significance of HPM,and provide HPM education materials for frontline teachers.This thesis has six components in general.The first chapter is the introduction,which introduces the research background,the significance of the research and the teaching means and methods of the practical application of the educational theory in the subject research.Through the review of Related Literature,this paper discusses the development of HPM at home and abroad and the methods of Educational Research Integrated into the history of mathematics.The second chapter is the definition of related concepts,which mainly summarizes the definition of historical similarity and genetic pedagogy.The third chapter summarizes the emergence and historical development of the number system,laying a theoretical foundation for the writing of the next chapter.The fourth chapter summarizes the order and methods of the number system teaching arrangement in the textbook.Chapter 5 is a practical case study,summarizing the steps of HPM's integration into mathematics teaching,taking the "Expansion of Number System and the Introduction of Complex Numbers" in the new high school human education version A mathematics compulsory 2 in 2019 as an example to conduct a comparative experiment to clarify the number In the course of the development of the department,students have obstacles to the cognition of the mathematics department,and use historical similarity to explore the influence of the integration of mathematics history into mathematics teaching on teachers and students.The sixth chapter is the research enlightenment,which summarizes the innovation and shortcomings of the research in this paper.Through the above research,the following two goals have been achieved:The first is to integrate HPM into the mathematics class.When students experience the formation and development of mathematics concepts firsthand,they understand the source of mathematical concepts,notation and their application in life,and experience the connection between mathematics and real life.Cultivate the habit of actively trying various methods to solve problems.Through reading mathematics stories,students understand that mathematics scholars face difficulties in the process of researching problems and still face difficulties.Looking back on themselves,they bravely face and solve difficulties in learning and life,strengthen their confidence in mathematics learning,and build self-confidence and self-improvement.View of life.Second,by integrating HPM into mathematics teaching,teachers can master teaching methods such as copying,additional,and reconstruction.In the process of consulting related mathematics historical materials,establish the concept of lifelong learning,strengthen the overall grasp of mathematics culture,and activate the classroom atmosphere.In the process of selecting historical materials,we should clearly grasp the cognitive barriers of beginners,quickly seize the "opportunity",give more guidance to students' difficulties and difficult to understand,slow down and give pointers frequently,so that students can quickly understand and master knowledge.