| It is pointed out in the "Mathematics Curriculum Standards for Ordinary high School(2017edition,2020 revision)" that we should attach importance to the subject concept as the core,make the curriculum content structured,theme-oriented,contextualize the curriculum content,and promote the implementation of the subject core literacy.The history of mathematics has a high educational value,and both the history of mathematics and big ideas can promote students’ understanding of knowledge,and there is an inevitable correspondence between them.The history of mathematics is an important carrier to promote students’ understanding of big ideas,but there are few studies on the combination of the two.Therefore,this thesis aims to make use of the close connection between the history of mathematics and big ideas.This thesis studies the teaching design of big ideas unit permeating the history of mathematics,and gives specific teaching design cases in combination with the trigonometric function unit of high school mathematics,so as to enrich the research of big concept theory in mathematics,and provide methodological reference for the research of the combination of the history of mathematics and the teaching of big ideas unit.Through the research of existing literature,this thesis reviews the research status of big ideas,unit teaching and mathematics history,and finds that there are few literature on the research of big ideas combined with high school mathematics,and few research on the combination of big ideas unit teaching and mathematics history.Therefore,this thesis further investigates and studies high school mathematics teachers and students by means of questionnaire survey and interview,providing a realistic basis for this research.Through the questionnaire survey of students,the conclusions are as follows:(1)At present,high school mathematics classroom is generally integrated into the history of mathematics teaching;(2)Most students think that learning the history of mathematics is beneficial;(3)Students learn the history of mathematics mainly through mathematics class;(4)The types of mathematical history that students are interested in from high to low are the stories of mathematicians,the thoughts and methods of mathematicians in the process of solving problems,the classical mathematical problems in history,and the mathematical history of related concepts;(5)Most students hope to integrate into the history of mathematics through multimedia such as videos or pictures.Through interviews with teachers,the conclusions are as follows:(1)Some teachers are not very clear about the concept of big ideas,but they agree that it is necessary to carry out big ideas teaching in high school mathematics teaching;(2)Senior high school mathematics teachers’ understanding of unit is generally limited to the given chapter in the textbook,and they will carry out unit teaching to some extent;(3)Most teachers recognize the educational value of the history of mathematics and will selectively integrate the history of mathematics into classroom teaching.Based on the above investigation and analysis,this thesis puts forward the strategy of infiltrating the history of mathematics into Ub D:(1)Extracting big concepts and clarifying basic problems through the history of mathematics;(2)Determine the authentic task of performance evaluation from the history of mathematics;(3)Effective integration of mathematical history and WHERETO elements.Based on this strategy,the general process of teaching design of large concept units of high school mathematics,which permeates the history of mathematics,is put forward,which are "clear unit theme,sort out mathematical historical materials","analyze teaching elements,screen mathematical historical materials","Grasp key links,design unit objectives","Adapt mathematical historical materials,design unit evaluation","reconstruct mathematical historical materials".Design unit activities "five key links,and in the link" Grasp the key links,design unit objectives ",put forward the strategy of extracting big concepts from the history of mathematics:(1)Grasp the key historical development steps in the history of mathematics;(2)Screening big concepts by curriculum standards and learning conditions;(3)To inquire about the big concept,and finally express the big concept with accurate language.In order to apply the general process of the teaching design into practice,this thesis combined trigonometric function unit,sorted out the history of related mathematics,carried out specific unit teaching design,and put forward three big concepts of trigonometric function unit:(1)in the process of solving mathematical problems,unified unit of measurement and base can simplify operations;(2)trigonometric function is a typical mathematical model describing periodic motion;(3)Circle is an important tool to study trigonometric functions.Finally,the concepts of preamble class,arbitrary Angle and radian system and trigonometric function are selected for specific teaching design. |
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