Research On The Content Selection Of School-Based Curriculum Of "Symmetry And Groups" In Senior High School

The new round of mathematics curriculum reform requires high school mathematics curriculum to face all students,to achieve that everyone can get a good mathematics education that different people get different development in mathematics.This kind of mathematics course is basic,selective and developmental,which shows that the compulsory courses are oriented to all students in order to build a common foundation;the selective compulsory courses and elective courses fully consider the different growth needs of students and provide a variety of courses for students to choose independently.Among them,elective courses are divided into five categories: A,B,C,D and E,which have credit requirements for students."Group" is a very important concept in modern mathematics.Can some excellent secondary school students,who have taken part in high school mathematics competitions,learn the knowledge? In the last round of mathematics curriculum reform,"group" has entered the high school textbooks.Symmetry and groups,an elective course of senior high school mathematics,has introduced some elementary knowledge on group theory to students,but it mainly refers to some concepts.It does not show students the profound thoughts and application value of "group" and cannot serve the students having taken part in mathematics competitions well.In the new curriculum standard,"symmetry and groups" is put into class E curriculum,which is developed or selected by schools according to their own needs.And the new curriculum standard does not elaborate on the specific requirements of this part of the content,which leaves room for teachers and students to explore this course.The purpose of this paper is to provide a school-based course of "symmetry and groups" for high school students who have taken part in mathematics competitions.On the basis of referring to the existing senior high school textbooks,popular science books,some undergraduate textbooks and analysis of learning situation,the author puts forward some suggestions on the selection of the course content of group theory and designs three teaching programs.We hope to provide help to the teachers and students who will join this course in the future.