The Comparative Research On The Content Of Function In High School Mathematics Textbooks Between China And America

With the conduct of the curriculum reform, international comparation oncurriculum standards and textbooks have been the central issue of education research.The education of the United States specializes in the cultivation of students’innovative consciousness and application capabilities, our country’s situation is justthe opposite. To make up for our education,it is necessary to study mathematicseducation in the United States deeply.This paper aiming at the core content of mathematics—function, select theSenior Middle School mathematics textbooks (A version) publiced by PEP Press andCore Plus Mathematics materials publiced by McGraw-Hill Companies, AmericanPress (hereinafter referred to as the United States CPM textbook) as the researchobject. Study differences and similarities of the function content,presentation and thedifficulty of function.In order to show differences in macro and micro level offunction content,the way and idea in textbook comprehensive organization,the meansto cultivate applications and innovative abilities. On this basis, the thesis will providevaluable and meaningful proposals for textbook organization and new ideas for thecultivativation of application and innovative abilities.The study found:First,the differences of the function content between two countries are obvious;on a macro level, function contents in the Chinese material are catered, valuing thetheory and system of the knowledge, on the contrary,functions in American textbookare easy,valuing the application of function model; on a micro level, Chinesetextbooks summarize function conceptwith the linear variation, guiding conceptualunderstanding of the function relatively one-sided; American textbook study a varietyof specific changes mode, making for a comprehensive and accurate understanding ofthe concept of function.Second, the external structure of function is that Chinese textbook published byPEP are formally mixed materials, but essentially different from required1tomandatory5, more likely Polyclinic materials;American CPM required materialsfunction-based,together with probability and geometry, followed by four main from,shallow to deep,among mainlines function mainly interspersed mosaic, or evengo hand in hand layout,layout features vary due to volume;the internal structure is thatit is parallel relationship for function model and symmetric relations between twotypes of basic elementary functions,the order in American materials is "function→function and equation→inverse function”.Third,the way of the presentation in the chapter is obviously different, Chinesetextbook adopts inspired approach as the explaination and strengthening of theknowledge points the center, American textbook makes knowledge points intoproblems solution using exploring ways.The application of material in PEP Press Aversion is not as good as American textbooks, in which,the background of exercisesand pictures are extremely rich, fully demonstrating the American’s culture, customs;technology is compulsory content.Fourth,the function’s difficulty in American CPM textbook is higher than PEPPress A version, the Sino-US "function",the statistical value of which is4.87and5.64,America is larger0.77than China. Statistics found that the knowledge breadth, depthand comprehensive exercises difficulties of the function in American textbook aremore difficult than Chinese,the differences of the comparable breadth and comparabledepth is not obvious,Amercia is large0.8than China, while the difference ofcomparable exercises difficulty is a little lager, Amercia is large5than China,so theexercises difficulty is the main factors leading to the difficulty of function;thefactors of the nature and content of knowledge affecting exercises difficulty inAmerican are all higher0.2than Chinnese, backgrounds of exercises in American is0.4than in Chinnese,so exercises background is the main factor leading to thedifferences in exercise difficulty.According to the conclusion above, the paper summarizes several suggestion:(1)Function concept should build on relationships in a variety of specific changes inorder to be more comprehensive and accurate understanding of the function.(2)Thematerials’ arrangement should focus on connection among contents;(3)value the useof information technology of computer software, calculator;(4)exercises backgroundscan be set to competitive sports, entertainment, adventure, ecological environment.