A Comparative Study On The Difficulty Of Trigonometric Functions In The Old And New Textbooks Of High School Mathematics In The People's Education Edition

Mathematics textbooks are important resources to achieve the goals of the mathematics curriculum and implement the concept of curriculum reform.They are also the basic materials for teachers and students to carry out teaching activities.Therefore,the difficulty of the textbooks affects the teaching effect,and the difficulty of the examples and exercises in the textbooks can reflect the difficulty of the textbooks to a certain extent.Mastering the difficulty level of examples and exercises in teaching materials,and selecting the appropriate difficulty topic for classroom teaching will help teachers teach students in accordance with their aptitude.In 2017,the Ministry of Education of the People's Republic of China promulgated the Standards for General Senior High School Mathematics Curriculum(2017 Edition),which made suggestions on the compilation of textbooks.New versions of the textbooks of version A of people's Education Press,version B of people's EducationPress,and Beijing Normal University Press came into being.Studying changes in old and new textbooks is important for effective teaching.This thesis intends to select the examples and exercises in the trigonometric function section of the 2007 and 2019 editions ofthe high school mathematics textbooks of version A of people's Education Press as the research object.Through the methods of literature,content analysis,and comparative research,quantitative research and qualitative analysis are combined.The differences in the three difficulty factors of background,knowledge content,required level and comprehensive difficulty of examples and exercises of trigonometric functions in the two editions of textbooks are compared.First of all,this thesis makes a statistical analysis on the examples of trigonometric function in the two editions of textbooks.The results shows that:(1)The background level of the new edition is slightly lower than that of the old edition,and more than 90%ofthe examples in the two editions of textbooks are pure mathematical situations;(2)The knowledge content level of the new version is higher than that of the old version.At the same time,the number of examples involving one knowledge point is the most in the two versions of textbooks,while the number of examples involving four or more knowledge points is the least;(3)The required level of the new version is higher than that of the old version,and the number of examples at the understanding level o f the two versions is the highest;(4)The comprehensive difficulty of the new version is higher than that of the old versionSecondly,the three types of exercises in the trigonometric function of the two editions of textbooks were statistically analyzed.This thesis founds that:(1)The background level of the practice questions and review reference questions in the new version is higher than those of the old version,and the background level of the afterschool questions in the new version is lower than that of the old version.The exercises of the two versions are dominated by background less questions;(2)The knowledge content level of the practice que stions and after-school questions of the new version is lower than those of the old version,but the knowledge content level of the reviewre ference questions of the new version is higher than that of the old version.In addition,more than 70%of the exercises involve no more than two knowledge points,and the proportion of exercises that involve four or more knowledge points increases comparedto the example problems;(3)The required level of the practice and after-school questions of the new version are higher than those of the old version,while the required level of the reference questions of the new version are lowerthan those of the old version.Meanwhile,the practice questions and after-school questions of the two versions are mainly imitative and understanding level questions,while the review reference questions are mainly of understanding and application level questions;(4)The comprehensive difficulty of the practice questions and the review reference questions of the new version is higher than those of the old version,and the comprehensive difficulty of the after-school questions of the new version is lower than those of the old version.On the whole,the comprehensive difficulty of the exercises of the new version is lowerthan that of the old version.Finally,this thesis considers the research about textbooks,and then puts forward suggestions to teachers:make full use of the background of examples and exercises in textbooks to expand the function of example and exercises;make full use of the functions at expanding and extension of the examples and exercises in textbooks to improve the mathematical knowledge system;make full use of the examples and exercises in the textbook to strengthen variant training;make full use of the modular design of exercises of textbook to effe ctively teach students according to their aptitude.This thesis research the changes in the difficulty of examples and exercises of the trigonometric functions of the old and new textbooks,and it is hoped that they can be used to help teachers understand the changes of the new textbooks and improve the teaching effect.At the same time,it is also an intent to provide some references for the study of longitudinal comparison of examples and exercises in the textbooks.