【摘要】：數(shù)學(xué)教材的國際比較研究是教育研究比較的熱點.本文希望能夠通過中美兩國教材比較找出美國在教育上對于學(xué)生在創(chuàng)新上的培養(yǎng),能夠?qū)ξ覈慕滩木帉懱峁┙ㄗh.研究選取中國的“人教版(A版)”(PEP教材)、“北師版”(BNU教材)和美國的芝加哥大學(xué)數(shù)學(xué)項目(THE UNIVERSITY OF CHICAGO SCHOOL MATHEMATICS PROJECT)研發(fā),麥格勞-希爾教育(McGraw-Hill Education)出版的高中數(shù)學(xué)教材INTEGRATED MATHEMATICS (UCSMP教材)作為教材研究對象,研究的內(nèi)容為微積分.通過靜態(tài)的比較研究,發(fā)現(xiàn)三版教材中的差異和特色,以期對我國教材在微積分內(nèi)容的編寫提供有用的建議.通過研究發(fā)現(xiàn)：(1)美國教材中關(guān)于微積分內(nèi)容的知識點數(shù)量比我國教材中多,美國教材在知識點中呈現(xiàn)出“寬”的特點,而中國教材則呈現(xiàn)出“窄”的特點；另外,美國教材的核心知識點是“導(dǎo)數(shù)”和“積分”,而中國教材的核心知識點是“極限”和“導(dǎo)數(shù)”(2)在微積分內(nèi)容的外部呈現(xiàn)方式上,美國教材分布在不連續(xù)的章節(jié)中,而中國教材則分布在一個章節(jié)中或者連續(xù)的章節(jié)中；在微積分的內(nèi)部結(jié)構(gòu)呈現(xiàn)中,美國教材與中國教材的差異在于：美國教材先講了導(dǎo)數(shù)的意義再講導(dǎo)數(shù)的概念,而中美教材則是先給出了導(dǎo)數(shù)的概念再講了導(dǎo)數(shù)的意義；美國教材中有使用“差商”、“黎曼和”專業(yè)術(shù)語,中美教材中給出了其含義但是沒有專業(yè)術(shù)語的使用.(3)中美兩國高中數(shù)學(xué)教材有各自特色的欄目設(shè)置,但是最大的差別在于美國教材將“信息技術(shù)應(yīng)用”融入到數(shù)學(xué)學(xué)習(xí)以及考試中,而中國教材中“信息技術(shù)應(yīng)用”并沒有完全貫穿在課堂中.(4)中美兩國高中數(shù)學(xué)教材在微積分習(xí)題難度的設(shè)置中,中美教材在運算水平和知識含量水平的習(xí)題難度要高于美國教材；在探究性水平的習(xí)題設(shè)置中,兩國教材都是以應(yīng)用性和探究性的習(xí)題為主,但是美國教材中探究性的習(xí)題所占的百分比高于中國教材.基于以上比較的差異,建議中國教材合理增加定積分內(nèi)容的知識點和專業(yè)術(shù)語的使用；注重內(nèi)容與信息技術(shù)的結(jié)合；合理增加背景性習(xí)題和探究性習(xí)題的數(shù)量.
[Abstract]:The international comparative study of mathematics textbooks is a hot spot in educational research. This paper hopes to find out the cultivation of students' innovation in education in the United States through the comparison between Chinese and American textbooks, and to provide suggestions for the compilation of textbooks in our country. In this study, we selected the Chinese version of PEP (version A), the version of Bei Shi (BNU textbook) and the research and development of (THE UNIVERSITY OF CHICAGO SCHOOL MATHEMATICS PROJECT), a mathematics project of the University of Chicago, USA. McGraw-Hill Education (McGraw-Hill Education) (INTEGRATED MATHEMATICS (UCSMP textbook of Senior High School Mathematics) is the research object of high school mathematics, and the content of the study is calculus. Based on the static comparative study, the differences and characteristics of the three editions of textbooks are found in order to provide useful suggestions for the compilation of the content of calculus in Chinese textbooks. It is found that: (1) the number of knowledge points in American textbooks about calculus is more than that in Chinese textbooks. The American textbooks have the characteristics of "width" in the knowledge points, while the Chinese textbooks have the characteristics of "narrow"; In addition, the core knowledge of American textbooks is "derivative" and "integral", while the core knowledge of Chinese textbooks is "limit" and "derivative" (2) in the external presentation of the content of calculus. American textbooks are distributed in discontinuous chapters, while Chinese textbooks are distributed in one chapter or successive chapters. In the presentation of the internal structure of calculus, the difference between American textbooks and Chinese textbooks lies in the fact that the American textbooks first talk about the meaning of derivative then the concept of derivative, while the Chinese and American textbooks first give the concept of derivative and then talk about the meaning of derivative; The use of "difference quotient", "Riemann" and "Riemann" in American textbooks has its meaning but no use of technical terms. (3) Chinese and American high school mathematics textbooks have their own special column settings. But the biggest difference is that American textbooks incorporate "IT applications" into math studies and exams. However, the "application of information technology" in Chinese textbooks has not completely penetrated the classroom. (4) the difficulty of calculus exercises in Chinese and American senior high school mathematics textbooks is set up. The exercise difficulty of Chinese and American textbooks in the level of operation and knowledge content is higher than that in American textbooks. In the setting of inquiry-based exercises, both textbooks are mainly applied and inquiring exercises, but the percentage of inquiring exercises in American textbooks is higher than that in Chinese textbooks. Based on the above differences, it is suggested that Chinese textbooks should reasonably increase the use of knowledge points and technical terms of definite integral content, pay attention to the combination of content and information technology, and reasonably increase the number of background exercises and inquiring exercises.
【學(xué)位授予單位】：華中師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：G633.6

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