中美大學(xué)微積分極限與導(dǎo)數(shù)內(nèi)容的教材比較研究
發(fā)布時(shí)間：2019-02-22 16:49
【摘要】：伴隨著高等教育的逐步普及,微積分課程的改革與發(fā)展已成為國(guó)際數(shù)學(xué)教育家們關(guān)注的焦點(diǎn)。如何正確地認(rèn)識(shí)和改進(jìn)現(xiàn)行教材成為了當(dāng)今數(shù)學(xué)教育界的一大問題,本研究旨在通過中美數(shù)學(xué)教材的比較,深入了解和認(rèn)識(shí)中美微積分教材的現(xiàn)狀。本研究選取高等教育出版社朱來義主編的《微積分》和美國(guó)John WileySons,Inc 出版,Deborah Hughes-Hallett,Andrew M Gleason,William G McCallum 等人編著的《Calculus》為研究對(duì)象;從宏觀和微觀兩個(gè)角度對(duì)兩版教材的極限與導(dǎo)數(shù)部分的內(nèi)容進(jìn)行了比較研究,最后還結(jié)合了柴俊等人關(guān)于中美大學(xué)微積分的實(shí)證研究進(jìn)行了分析。本研究希望回答三個(gè)問題:在宏觀上兩版教材有何異同?在微觀上兩版教材有何異同?中美微積分教材的差異對(duì)中美大學(xué)生在微積分部分的測(cè)試結(jié)果有何影響?經(jīng)過仔細(xì)對(duì)比和數(shù)據(jù)分析得出以下結(jié)論:(1)宏觀上,在編排順序方面,中版《微積分》教材主要采用直線式編排;美版《Calculus》教材則采用螺旋式的組織結(jié)構(gòu)進(jìn)行編排;課程廣度上,中版《微積分》的編排表現(xiàn)出“寬而緊”的特點(diǎn),而美版《Calculus》則是“繁而專”;課程深度上,美版教材則在內(nèi)容深度上來說明顯低于我國(guó);課程時(shí)間上,中美微積分課程的課程時(shí)間是幾乎沒有差別的;數(shù)學(xué)問題的難度方面,中版《微積分》教材的中的問題(包括例題和習(xí)題)的綜合難度指標(biāo)高于美版微積分教材。從具體的難度因素來看,中國(guó)教材對(duì)“認(rèn)知”、“推理”和“知識(shí)含量”要求較高;而美版教材的“背景”水平比中國(guó)略高。(2)微觀上,中版教材邏輯嚴(yán)密,相關(guān)數(shù)學(xué)問題的難度較大,對(duì)學(xué)生的認(rèn)知水平要求較高,概念導(dǎo)入以直接導(dǎo)入為主,圖表的使用和信息技術(shù)的使用較少;美版《Calculus》則更加注重概念的記憶與領(lǐng)會(huì),注重培養(yǎng)學(xué)生的數(shù)學(xué)直觀和基礎(chǔ)理解,相關(guān)數(shù)學(xué)問題的難度較小,形式多樣,圖表和信息技術(shù)的使用比較豐富。(3)通過對(duì)比教材差異與測(cè)試結(jié)果發(fā)現(xiàn),學(xué)生對(duì)教材正文中給出的性質(zhì)或定理比例題中得出的結(jié)論要掌握的更好;學(xué)生對(duì)教材中自成一節(jié),篇幅較長(zhǎng)的內(nèi)容掌握得更好;學(xué)生對(duì)之前接觸過的內(nèi)容,再次學(xué)習(xí)時(shí)進(jìn)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.
【學(xué)位授予單位】：華東師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O172-4;G642.3
本文編號(hào)：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.
【學(xué)位授予單位】：華東師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O172-4;G642.3
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，本文編號(hào)：2428412
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