中美大学微积分极限与导数内容的教材比较研究
发布时间：2019-02-22 16:49
【摘要】：伴随着高等教育的逐步普及,微积分课程的改革与发展已成为国际数学教育家们关注的焦点。如何正确地认识和改进现行教材成为了当今数学教育界的一大问题,本研究旨在通过中美数学教材的比较,深入了解和认识中美微积分教材的现状。本研究选取高等教育出版社朱来义主编的《微积分》和美国John WileySons,Inc 出版,Deborah Hughes-Hallett,Andrew M Gleason,William G McCallum 等人编著的《Calculus》为研究对象;从宏观和微观两个角度对两版教材的极限与导数部分的内容进行了比较研究,最后还结合了柴俊等人关于中美大学微积分的实证研究进行了分析。本研究希望回答三个问题:在宏观上两版教材有何异同?在微观上两版教材有何异同?中美微积分教材的差异对中美大学生在微积分部分的测试结果有何影响?经过仔细对比和数据分析得出以下结论:(1)宏观上,在编排顺序方面,中版《微积分》教材主要采用直线式编排;美版《Calculus》教材则采用螺旋式的组织结构进行编排;课程广度上,中版《微积分》的编排表现出“宽而紧”的特点,而美版《Calculus》则是“繁而专”;课程深度上,美版教材则在内容深度上来说明显低于我国;课程时间上,中美微积分课程的课程时间是几乎没有差别的;数学问题的难度方面,中版《微积分》教材的中的问题(包括例题和习题)的综合难度指标高于美版微积分教材。从具体的难度因素来看,中国教材对“认知”、“推理”和“知识含量”要求较高;而美版教材的“背景”水平比中国略高。(2)微观上,中版教材逻辑严密,相关数学问题的难度较大,对学生的认知水平要求较高,概念导入以直接导入为主,图表的使用和信息技术的使用较少;美版《Calculus》则更加注重概念的记忆与领会,注重培养学生的数学直观和基础理解,相关数学问题的难度较小,形式多样,图表和信息技术的使用比较丰富。(3)通过对比教材差异与测试结果发现,学生对教材正文中给出的性质或定理比例题中得出的结论要掌握的更好;学生对教材中自成一节,篇幅较长的内容掌握得更好;学生对之前接触过的内容,再次学习时进步很快。
[Abstract]:With the gradual popularization of higher education, the reform and development of calculus curriculum has become the focus of international mathematics educators. How to correctly understand and improve the current teaching materials has become a major problem in the field of mathematics education. The purpose of this study is to deeply understand and understand the current situation of Chinese and American calculus textbooks through the comparison of Chinese and American mathematics textbooks. In this study, "Calculus", edited by Zhu Laiyi, a higher education publishing house, and "Calculus" by Deborah Hughes-Hallett,Andrew M Gleason,William G McCallum, published by John WileySons,Inc in the United States, are selected as the research objects. This paper makes a comparative study on the content of the limit and derivative parts of the two editions from the macro and micro perspectives, and finally analyzes the empirical research on the calculus of Chinese and American universities by Chai Jun and others. This study wishes to answer three questions: what are the similarities and differences between the two textbooks in the macro view? What are the similarities and differences between the two editions on the micro level? How does the difference between Chinese and American Calculus textbooks affect the test results of Chinese and American college students in the Calculus part? After careful comparison and data analysis, the following conclusions are drawn: (1) in macroscopic view, the Chinese version of Calculus is mainly arranged in a straight line, while the American version of < Calculus > is arranged with a spiral organizational structure. In terms of curriculum breadth, the arrangement of Chinese version of Calculus shows the feature of "wide and tight", while the American version of < Calculus > is "complex and specialized", and the American version of textbooks is obviously lower in depth than in our country. In the course time, the curriculum time of Chinese and American calculus course is almost no difference, and the comprehensive difficulty index of the Chinese version of Calculus textbook (including examples and exercises) is higher than that of the American version Calculus textbook. From the point of view of the specific difficulty factors, Chinese textbooks have higher requirements for "cognition", "reasoning" and "knowledge content"; However, the "background" level of American edition textbooks is slightly higher than that of China. (2) microscopically, the Chinese edition textbooks have strict logic, the difficulty of related mathematical problems is relatively high, the students' cognitive level is higher, and the introduction of concepts is based on direct introduction. Less use of charts and information technology; The American version of "Calculus" pays more attention to the memory and understanding of concepts, and to the cultivation of students' mathematical intuition and basic understanding. The related mathematical problems are less difficult and have various forms. The use of charts and information technology is relatively rich. (3) by comparing the differences between the textbooks and the test results, it is found that the students have a better grasp of the nature given in the text of the textbook or the conclusions reached in the theorem scale; Students form a section on their own in the textbook, better grasp of the longer content; students have come into contact with the content before, learning progress quickly.
【学位授予单位】：华东师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O172-4;G642.3
本文编号：2428412
[Abstract]:With the gradual popularization of higher education, the reform and development of calculus curriculum has become the focus of international mathematics educators. How to correctly understand and improve the current teaching materials has become a major problem in the field of mathematics education. The purpose of this study is to deeply understand and understand the current situation of Chinese and American calculus textbooks through the comparison of Chinese and American mathematics textbooks. In this study, "Calculus", edited by Zhu Laiyi, a higher education publishing house, and "Calculus" by Deborah Hughes-Hallett,Andrew M Gleason,William G McCallum, published by John WileySons,Inc in the United States, are selected as the research objects. This paper makes a comparative study on the content of the limit and derivative parts of the two editions from the macro and micro perspectives, and finally analyzes the empirical research on the calculus of Chinese and American universities by Chai Jun and others. This study wishes to answer three questions: what are the similarities and differences between the two textbooks in the macro view? What are the similarities and differences between the two editions on the micro level? How does the difference between Chinese and American Calculus textbooks affect the test results of Chinese and American college students in the Calculus part? After careful comparison and data analysis, the following conclusions are drawn: (1) in macroscopic view, the Chinese version of Calculus is mainly arranged in a straight line, while the American version of < Calculus > is arranged with a spiral organizational structure. In terms of curriculum breadth, the arrangement of Chinese version of Calculus shows the feature of "wide and tight", while the American version of < Calculus > is "complex and specialized", and the American version of textbooks is obviously lower in depth than in our country. In the course time, the curriculum time of Chinese and American calculus course is almost no difference, and the comprehensive difficulty index of the Chinese version of Calculus textbook (including examples and exercises) is higher than that of the American version Calculus textbook. From the point of view of the specific difficulty factors, Chinese textbooks have higher requirements for "cognition", "reasoning" and "knowledge content"; However, the "background" level of American edition textbooks is slightly higher than that of China. (2) microscopically, the Chinese edition textbooks have strict logic, the difficulty of related mathematical problems is relatively high, the students' cognitive level is higher, and the introduction of concepts is based on direct introduction. Less use of charts and information technology; The American version of "Calculus" pays more attention to the memory and understanding of concepts, and to the cultivation of students' mathematical intuition and basic understanding. The related mathematical problems are less difficult and have various forms. The use of charts and information technology is relatively rich. (3) by comparing the differences between the textbooks and the test results, it is found that the students have a better grasp of the nature given in the text of the textbook or the conclusions reached in the theorem scale; Students form a section on their own in the textbook, better grasp of the longer content; students have come into contact with the content before, learning progress quickly.
【学位授予单位】：华东师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O172-4;G642.3
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