Research On Reaching Design Of Analytic Geometry Infiltrating Mathematical Culture

Since the 21 st century,with the reform and development of education,it has become an inevitable trend to infiltrate mathematical culture in the classroom.And analytic geometry is an important part of mathematics,so it is indispensable to infiltrate mathematical culture in high school classrooms.Besides,because instructional design will directly affect the teaching quality of a class,it is very necessary to design instructional design of analytic geometry from the perspective of mathematical culture.Under this background,this paper makes an in-depth study on the present situation of mathematics culture infiltration in senior high school mathematics classroom,the presentation mode of mathematics culture in senior high school mathematics textbooks and the instructional design of analytic geometry infiltration of mathematics culture.In this paper,firstly,the theoretical basis of analytic geometry instructional design which permeates mathematical culture is reviewed and analyzed by using literature analysis method,which is mainly reflected in three aspects: mathematical culture,analytic geometry and instructional design.Secondly,the questionnaire survey is used to study the current situation of mathematics culture infiltration in high school classrooms.It is found that only a few teachers can infiltrate mathematics culture into students frequently in high school mathematics classrooms,so most students are in a state of ignorance of mathematics culture.Then,it is found that mathematics culture is mainly reflected in four aspects: mathematics history,mathematics beauty,mathematics thinking method and mathematics application,while analytic geometry mathematics culture is mainly reflected in four aspects: origin and simple application of analytic geometry in the first chapter,mathematics history in "reading and thinking",mathematics thinking method in "exploration and discovery" and mathematics demonstration experiment in "application of information technology".After that,it summarizes and puts forward the conditions that should be met in the teaching design of analytic geometry,and the arrangement of each link in the teaching process.The instructional design should meet the conditions of reflecting mathematical culture in six aspects such as teaching material analysis: first,teaching materials should be dug deep;second,the academic situation should be deeply analyzed;third,the teaching goal should reflect the mathematics culture;fourth,teaching methods should be flexible and changeable;fifth,teaching materials should be taken from real life;sixth,the teaching process should be innovative and diverse.It should be noted that the expression of mathematical culture is not only in the history of mathematics,but also in the beauty of mathematics,mathematical thinking methods and so on.The teaching process should include five teaching links: situation introduction;explore new knowledge;consolidation exercises;summarize and summarize;assign homework.It should be noted that teachers must not stick to the rules and be trapped in this framework in actual teaching.Instead,they should break through the framework according to the actual situation and integrate mathematics culture in the appropriate places.Finally,according to the conditions that the teaching design of analytic geometry should meet and the arrangement of each link in the teaching process,two teaching cases,"Ellipse and its Standard Equation" and "Position Relationship between Line and Circle",are designed and analyzed.