The Change Of The Content Setting Of "Basic Inequality" In The "PEP Edition" Textbook(1952-2019)

Basic inequality is one of the important contents of high school mathematics,which plays an important role in proving inequalities and maximizing value.Basic inequality have been included in "PEP" high school math textbooks since 1952.With the continuous improvement of textbooks,the content setting of basic inequality is also changing.In this paper,11 sets of "PEP edition" high school mathematics textbooks from 1952 to 2019 were selected,and the content setting of basic inequality was taken as the research object.The literature research method and comparative research method were used to study and analyze the characteristics of the changes of basic inequality from three aspects,namely,the introduction of basic inequality,the concept expression and the setting of examples and exercises.The reasons for the changes are discussed from the aspects of syllabus and textbook construction history,etc.Finally,the changes about the introduction,concept expression,the setting of examples and exercises of the basic inequality in 11 sets of "PEP edition" high school mathematics textbooks from 1952 to 2019 are obtained respectively.While sorting out the changes of the arrangement of basic inequality,according to the preference of the introduction of basic inequality,this paper uses questionnaire survey method and interview method are used to survey senior high school students and interview senior high school mathematics teachers,in order to put forward more objective and reasonable suggestions on the arrangement of basic inequality in textbooks and teaching suggestions for senior high school mathematics teachers.This paper puts forward the following suggestions for textbook compilation: First,in the introduction of basic inequality,pay attention to the generation of knowledge while taking into account the psychological characteristics of students;be good at using the actual background of basic inequality.Second,in the concept expression,be good at using the essential characteristics of basic inequality;Third,in the setting of examples and exercises,focus on a variety of types of problems;pay attention to the combination and integration of scientific situation.What's more,the following teaching suggestions are put forward for the teachers: first,in the introduction of basic inequality,it is also worthwhile to "occupy" class hours occasionally.Second,in the concept expression,teachers should make use of the Sketchpad to demonstrate dynamically,so as to deepen students' understanding of equal conditions;teachers should integrate Mathematics Culture into teaching,expand students' vision and improve their quality.Third,in the setting of examples and exercises,teachers should cut down and add problems appropriately according to the actual situation.