Teaching Research On The Knowledge Of Circle In Middle And High School

This paper mainly studies the knowledge of Circle in junior and senior high school,and uses the content analysis method,questionnaire survey method,statistical analysis method and comparative analysis method to study the distribution,curriculum difficulty of Circle.What's more,four feasible strategies and cases are given.Firstly,the Introduction explains the background,main problems,significance and thoughts of this paper.There are three main problems:what are the characteristics of the distribution of Circle in junior and senior high school?What is the change in the difficulty of Circle in junior and senior high schools?What help can the study provide for teachers?Secondly,the evolution process of Circle in the syllabus(curriculum criterion)from 1949 to 2018 is arranged.It is found that the knowledge of Circle in junior and senior high school can be divided into two categories:one is the Circle's own elements and the relationship between them,and the other is the relationship between the Circle and other geometric objects.After the promulgation of the new curriculum criterion(the 2017 version),the former kind of knowledge is only studied in junior high school,while the latter kind exists both in junior and senior high school.But the difference is the learning method.In addition,the type,quantity and function of column in teaching material are studied based on the chapter of Circle.The column can be divided into three types:to ask questions,to give explanation and to expand knowledge,among which the quantity of the column to ask question is the most.As the function of each kind of column is different,teachers should make rational and full use of them.Thirdly,the paper analyzes the absolute difficulty of Circle in junior and senior high school through four quantitative analysis models of curriculum difficulty,and finds that the absolute difficulty of Circle in senior high school is higher than that in junior high school.The study on the absolute difficulty of the exercises in the textbook shows that,except for the background and reasoning level of the exercises,the comprehensive difficulty of exercises in senior high school is higher than that in junior high school especially in the operation level.Then the result of the questionnaire survey investigating junior and senior high school teachers is regarded as the relative difficulty of Circle.It is found that the relative difficulty of Circle in senior high school is basically consistent with the absolute difficulty,while the relative difficulty in junior high school is lower than the absolute difficulty.The study of difficulty of Circle can provide a basis for the division of students' mathematical literacy in teaching.Finally,four teaching strategies from four dimensions are put forward,which are structural strategy,instumental strategy,generative strategy and reflective strategy,respectively.Besides,four cases containing mathematical literacy are given to explain these strategies.