A Comparative Study Of Trigonometric Functions In High School Of Chinese And American

As a concentrated expression of the will of the country,textbooks are a carrier for concretely presenting the established teaching content under the guidance of the country’s educational philosophy and teaching goals.To a certain extent,there will be what kind of textbooks there will be,what kind of young generation will there be,and what kind of country and future will there be.Therefore,textbooks play a vital role in the development of basic education.By studying the ideas and content of textbook compilation in different countries,we can discover the advantages and teaching value of different versions of textbooks,make up for the unreasonable parts of the current textbooks,and make further adjustments and implementations for the reform and implementation of high school mathematics courses and teaching.guide.This paper mainly selects Chinese teaching materials,Shanghai teaching materials and American"Nu-Strength" course materials as textbook research texts,and selects trigonometric function,a key high school knowledge content,as the object of comparative study,designing structure and content from two perspectives The comparative research framework of the three different editions of the textbooks has conducted a comparative study on the curriculum framework,teaching links,knowledge structure,chapter introduction,situation introduction,concept definition,example exercises,chapter summary and legends,etc.,and in-depth exploration of the three editions of the textbook The characteristics and deficiencies of the macro and micro aspects of the compilation,and finally the following research conclusions:(1)In terms of structure,in the curriculum framework,the knowledge structure of trigonometric functions in the three versions of the textbook is mainly divided into three sections:algebra,geometry,and function.The content of the PEP version is relatively scattered,and the geometry section As an application of the plane vector in another chapter,the content of the Shanghai Education Edition and the American"Nuclear-Strength" course materials are arranged more compactly.All chapters are concentrated together.In addition,in terms of section division,the PEP textbook is based on trigonometric functions.The knowledge hierarchical structure and logical sequence of the chapters are obviously not as clear as the Shanghai teaching materials and the American "Nuclear-Strong" course materials.In terms of knowledge structure,there is no obvious difference in knowledge structure between PEP textbooks and Shanghai PEP textbooks.The American"Nu-Strength" course textbooks are more knowledgeable than PEP textbooks,adding secant and cosecant.For the image of the secant and cosecant functions,more trigonometric identities transformation formulas are proposed,and the Helen formula is introduced,and students are required to master the formulas of product and difference,and product of difference.Although the three editions of textbooks differ greatly in the order of arrangement,they all retain the basic knowledge of trigonometric functions.(2)In terms of content,in terms of concept definition,the three editions of the textbooks have made scientific and strict definitions of trigonometric functions from different angles.The PEP textbook uses the unit circle method for the definition of trigonometric functions.At the same time,the coordinate definition method of trigonometric functions is mentioned in the sample questions.The Shanghai education textbook starts from the acute triangle ratio learned in junior high school and infers the sine from the coordinates.,Cosine,and tangent,and put forward the case of unit circle when r=1;the American "Nuclear-Strong" course establishes a connection between the arc length of the unit circle and the coordinates,circumventing the problem of the radian system,and can be purely from Looking at trigonometric functions from the perspective of real numbers is of reference to domestic textbooks.In terms of chapter summaries,the American"Nuclear-Strong" course textbook does not have chapter summaries.The chapter summaries of the Shanghai Education Edition textbooks summarize the concepts and knowledge points,but in various forms,including written text,tables and other forms,specific knowledge will be listed.content.The PEP textbook sets up two sections:chapter knowledge structure,review and thinking.The chapter knowledge structure is given in a hierarchical directed graph,while review and thinking will raise some in-depth questions from a higher perspective.The summary of knowledge points is missing,and the content of solving triangle positions has not received enough attention in the chapter summary.In terms of legend annotations,the legends of the teaching materials of the People’ s Education Edition and the Shanghai Teaching Edition are obviously more abundant than those of the American"Nuclear-Strength" course materials.The main functions of the legends of the three versions of the textbooks are explanations,and Both have the role of annotations.There are quite a few illustrations in the teaching materials of the People’s Education Edition and the Shanghai Education Edition,which play a role in questioning and learning guidance.The teaching content is designed in the legend to assist the teaching of the textbook,which arouses students’ in-depth thinking.By sorting out,summarizing and summarizing the above-mentioned research process and research results,this article puts forward the following suggestions on textbook compilation and teaching practice:(1)Clarify the knowledge structure system and build a curriculum framework with distinct levels;(2)Enrich the content of chapter introduction,grasp the main line and value of knowledge;(3)Reasonably arrange example exercises to increase the depth and flexibility of the teaching materials;(4)Set the type of legend reasonably,and give full play to the guiding role of the legend in the textbook.