中美两国高中数学教材中微积分内容的比较研究
发布时间：2018-10-31 09:07
【摘要】：数学教材的国际比较研究是教育研究比较的热点.本文希望能够通过中美两国教材比较找出美国在教育上对于学生在创新上的培养,能够对我国的教材编写提供建议.研究选取中国的“人教版(A版)”(PEP教材)、“北师版”(BNU教材)和美国的芝加哥大学数学项目(THE UNIVERSITY OF CHICAGO SCHOOL MATHEMATICS PROJECT)研发,麦格劳-希尔教育(McGraw-Hill Education)出版的高中数学教材INTEGRATED MATHEMATICS (UCSMP教材)作为教材研究对象,研究的内容为微积分.通过静态的比较研究,发现三版教材中的差异和特色,以期对我国教材在微积分内容的编写提供有用的建议.通过研究发现：(1)美国教材中关于微积分内容的知识点数量比我国教材中多,美国教材在知识点中呈现出“宽”的特点,而中国教材则呈现出“窄”的特点；另外,美国教材的核心知识点是“导数”和“积分”,而中国教材的核心知识点是“极限”和“导数”(2)在微积分内容的外部呈现方式上,美国教材分布在不连续的章节中,而中国教材则分布在一个章节中或者连续的章节中；在微积分的内部结构呈现中,美国教材与中国教材的差异在于：美国教材先讲了导数的意义再讲导数的概念,而中美教材则是先给出了导数的概念再讲了导数的意义；美国教材中有使用“差商”、“黎曼和”专业术语,中美教材中给出了其含义但是没有专业术语的使用.(3)中美两国高中数学教材有各自特色的栏目设置,但是最大的差别在于美国教材将“信息技术应用”融入到数学学习以及考试中,而中国教材中“信息技术应用”并没有完全贯穿在课堂中.(4)中美两国高中数学教材在微积分习题难度的设置中,中美教材在运算水平和知识含量水平的习题难度要高于美国教材；在探究性水平的习题设置中,两国教材都是以应用性和探究性的习题为主,但是美国教材中探究性的习题所占的百分比高于中国教材.基于以上比较的差异,建议中国教材合理增加定积分内容的知识点和专业术语的使用；注重内容与信息技术的结合；合理增加背景性习题和探究性习题的数量.
[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.
【学位授予单位】：华中师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：G633.6
本文编号：2301606
[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.
【学位授予单位】：华中师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：G633.6
【参考文献】
相关期刊论文 前3条
1 王建磐;章建跃;;高中数学教材核心数学内容的国际比较[J];课程.教材.教法;2014年10期
2 吴志坚;肖滢;吴兴玲;;中美微积分教材比较研究[J];高等数学研究;2010年03期
3 郭民;史宁中;;中英两国高中数学教材函数部分课程难度的比较研究[J];外国中小学教育;2013年07期
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