Research On The Changes Of The Content Of Trigonometric Functions In Chinese Middle Schools(1950-2019)

As the key learning content of mathematics in junior and senior middle school,trigonometric functions not only exercise students' functional thinking,but also a model of combining number and shape.In the past 70 years from1950 to 2019,with 8 educational reforms,People's Education Publishing House issued 29 sets of mathematics textbooks(12 sets for junior high schools and 17 sets for high schools).Nowadays,the trigonometric function course has been gradually systemized,the content layout is relatively complete,and the development is continuous.Without the experience of writing textbooks in the past,there will be no improvement and optimization of the subsequent textbooks.Therefore,this article sorts out the changes in the content of trigonometric functions in the junior and senior middle school mathematics textbooks from 1950 to 2019 in the "People's Education Edition",and studies the characteristics of the changes in order to provide a reference for the compilation of future textbooks.This article takes the trigonometric function content in 29 sets of junior and senior high school mathematics textbooks published by the People's Education Society since 1950 as the main research object,with the mathematics curriculum standard(syllabus)as the background,using literature research methods,comparative research methods and statistical analysis The method analyzes the changes in the content of trigonometric functions in 29 sets of textbooks,from the definition and related concepts of trigonometric functions,the images and properties of trigonometric functions,induced formulas,the transformation and application of trigonometric functions(theorems of sine and cosine,examples and exercises)And the chapter on trigonometric functions.The history of mathematics integrates six aspects to conduct macro and micro research on the changes of trigonometric functions in 29 sets of middle school mathematics textbooks(12 sets for junior high school and 17 sets for high school)published by the People's Education Edition from 1950 to 2019.On the basis of the rich original literature,show the evolution of the trigonometric function content in Chinese textbooks since the founding of New China 70 years ago,better grasp the trigonometric function content,and provide reference for others to learn and study the trigonometric function content in mathematics textbooks.Provide reference for the construction of Chinese mathematics textbooks.This paper draws the following conclusions: On the macroscopic research of trigonometric functions,it is concluded that: ?.The teaching objectives are gradually and specifically optimized;?.The field of trigonometric functions changes repeatedly;?.The content of the course is cut and strengthened.In the microscopic study of trigonometric functions,it is concluded that in terms of the changes in the definition of trigonometric functions and the content settings of related concepts: ?.Focus on the integrity of the content;?.Emphasize the conciseness of the teaching content.In terms of the changes in the setting of images and properties of trigonometric functions: ?.The setting of content has gradually shifted from passive acceptance to independent exploration;?.The tendency to emphasize the subject status of images and properties of trigonometric functions.In terms of the changes in the content of the induced formula: ?.From "scattered" to "centralized";?.The proof of the formula is gradually biased from intuitive perception to logical argument.In terms of the changes in the setting of the changing content of the trigonometric function: ?.from the application of memory to the use of reasoning;?.to explore the economic tendency of thinking in the process of proof.In terms of the changes of sample questions and exercises in junior and senior high schools: ?.The sample questions and exercises are arranged in multiple types and ways;?.Set according to the syllabus(curriculum standard)and the changes of the times;?.Based on simple symbolic operations,focusing on the examination of computational ability.In the trigonometric function chapter,the history of mathematics is integrated into the changes: ?.Compiled in accordance with the requirements of the syllabus(curriculum standard);?.The layout position is from the beginning to the end of the section;?.The content is changed from general to specific;?.Transition from patriotism to multiculturalism.