A Comparative Study Of Trigonomitric Functions In New Adition Of High School Textbooks ——Take PEP,SEP,BNUP As An Example

Various versions of new mathematics textbooks have been published after High School Mathematics Curriculum Standards(2017 Edition)was officially issued.The national curriculum design and corresponding textbooks play very important roles in every student's growth.The research chose PEP mathematics textbooks 1 and 2(2019edition)? SEP mathematics textbook 2(2020 edition)and BNUP mathematics textbook 2(2020 edition)as research objects,in which Trigonometric function is the main research content.The research adopted literature analysis and comparative method that includes qualitative analysis and quantitative analysis to compare the structural design and the content arrangement of each textbook.The structural design mainly focuses on the course framework,teaching links and knowledge structure of the textbooks so as to find the similarities and differences in structural design and the shining points of textbooks.The content arrangement covers the chapter introduction,opening situations,examples and exercises,mathematical culture,information and communication technology,chapter summary.Through this research,the following conclusions are obtained.(1)In terms of structural design,the differences are reflected in curriculum framework.The curriculums in PEP textbook are in spiral mode,in which knowledges are logically connected.The SEP curriculums separate calculation from function so that its' content is distinctly showed step by step,which makes it easy for both teachers and students to find the important parts of the task.BNUP textbook emphasizes on the relationship between the trigonometric functions and plane vectors.So the trigonometric transformation is set in a separate chapter after finishing Plane Vectors and Trigonometric Functions.Therefore,the internal connectivity of the curriculums in BNUP is not as close as those in PEP and SEP,but the relationship between trigonometric functions and the factors in other mathematics principle line is more clearly showed in BNUP.The similarity of course design within three editions is that trigonometric functions are arranged after the Concept and Properties of functions.It's convenient for students to use the studying methods of functions they have learned,when it's time to learn trigonometric functions.As for teaching links and knowledge structure,there is no obvious difference between three textbooks.Their overall arrangement is similar,whose schema is "Introduction of course--Opening of concept,principle introduction –definition of concept and principle--examples--exercises--content summary--review exercises".According to the quantitative comparison,the parameters of knowledge structure in three editions(breadth,depth,complexity,interconnectedness)are similar with each other.(2)In the prospective of content layout,the commonness of three textbooks are that they all answer “Why to study”,“How to study”,and “What to study” in their chapter introduction.There are still some differences in detail;In terms of opening situation,they are all lack of the connection between mathematics and real life,mathematics and other subjects;In the settings of examples and exercises,three textbooks pay more attention to the pure mathematics problems which examine the understanding of basic concepts and principles,when the proportion of the exercises relevant with daily use and science technology is very small.Besides,the proportion of different kinds of exercises is not balanced;In the aspect of mathematical culture,the contents of the three textbooks mainly focus on mathematics and real life.However,the content about the history of mathematics,mathematics and science technology,mathematics and humanity arts are very weak;The penetration of Information and communications technology(ICT)in three editions is not deep enough.SEP textbook has no obvious content related with ICT.Compared with BNUP,there are more contents about ICT in PEP textbook.In chapter summary,SEP is relatively simple,when PEP chapter summary is the most abundant one by contrast.There are both knowledge structure diagram and review with reflection content,as well as the association diagram between the theme of this chapter and other contents in mathematics or other disciplinary factors.Especially,there are extended questions proposed at the end of the summary paragraph,which are thought-provoking.After this comparative study,the following suggestions are put forward:For textbook compilation:(1)Pay attention to the overall structure and build an organic connection within the content;(2)Advocate and emphasize the diversity of background materials;(3)Pay attention to promoting the applied value,scientific value,aesthetic value and spiritual value of mathematics;(4)Pay attention to the effective integration of ICT and curriculum to improve teaching efficiency.For curriculum teaching:(1)Grasp the essence of mathematics content and pay attention to the intrinsic quality of teaching;(2)Make effective use of teaching resources and arrange various kinds of materials reasonably;(3)Examine own mathematical literacy and insist on lifelong learning.