【作者】 刘盛利；

【导师】 代钦；

【作者基本信息】 内蒙古师范大学 ， 科学技术史， 2012， 博士

【摘要】 清政府于1904年颁布并实施《癸卯学制》后,揭开中国教育的新篇章,高等数学教育亦进入新的时代。作为高等数学基础知识的微积分教科书建设是亟需解决的问题。在新型教育体制下,微积分教科书的编写、出版内容体系的变迁等情况如何?以此为切入点,以文献研究法为主,以比较法、图表法、个案分析法为辅,对中国在1904～～1949年间中文版微积分教科书进行梳理,呈现该时期微积分教科书之发展经纬。首先,论述了选题目的与意义、国内外研究现状、研究思路和拟创新之处。目前,中国关于微积分教科书发展史的研究尚显薄弱,在已有的研究成果中,有的主题比较宽泛,针对性不强；有的从宏观上综述各门教科书的发展情况,而没有详细论述某一门学科教科书的发展过程。本文从宏观上爬梳1904～1949年间中国微积分教科书之沿革,再从微观上分析其内容变化与编写特点。其次,将1904～1949年划分为四个阶段,分别阐述每个时间段中国微积分教科书之发展概况及其编写特点。其中1904～1911年以潘慎文(Alvin Pierson Parker,1850～1924)与谢洪赉(1872～1916)合译的《最新微积学教科书》为案例,1912～1922年以匡文涛翻译、根津千治著的《微积分学讲义》为案例,1923～1934年以熊庆来的《高等算学分析》为案例,1935～1949年以李俨的《微积分学初步》为案例,详细分析研究其编排形式、内容特点、名词术语的采用等。最后,以微分与导数、积分、微分中值定理为对象,横向分析研究其在1904～1949年微积分教科书中的发展历程,厘清其在不同时期不同称谓的演变情况。拟创新之处如下：第一,基于第一手资料之研究,以数学史和数学教育史为视角,从宏观上梳理中国1904～1949年间微积分教科书之发展历程,从微观上分析研究每个时间段中国微积分教科书之编写特点。第二,探究中国微积分教科书编写的宗旨、指导思想及其制约因素。厘清中国微积分教科书所蕴含的文化变革与思想方法之完善历程。第三,在纵向梳理微积分教科书之基础上,以微分与导数、微分中值定理及积分为切入点,横向研究其在教科书中之沿革情形,说明这些知识点在叙述上更加严密,在逻辑推理上更加科学。更多还原

【Abstract】 After the Guimao School System promulgated by the late Qing government in1904, it opened a new page in Chinese education as well as mathematics teaching of university. At that time, the compiling of calculus teaching material which was rudimentary knowledge of university mathematics, became a problem to be solved. Under the new education system, how would calculus textbooks be compiled and published? How would the content system in calculus textbooks be transformed? In the paper, the above questions will be taken as the starting point for the study. The document research method is the main method, and the methods of comparison, graphology as well as the case analysis are supplemented to study the history of calculus textbooks development from1904to1949in China. During the period, there were many Chinese calculus textbooks which are studied in the paper.Firstly, the purpose, significance, research status at home and abroad, research thought and innovation about the selected topic are chiefly related and analyzed. At present, the study on the development history of the calculus textbooks was still weak and insufficient. For instance, some subjects are wide and not clear; though the development of the textbooks was summarized in a macroscopic view, the textbooks on the course were not discussed in detail. So the development of calculus textbooks in China will be sorted out between1904and1949in the paper in a macroscopic view, then contents changing and editing features will be analyzed in a microscopic view.Secondly, the period between1904to1949is divided into four stages,1904～1911,1912～1922,1923～1934,1935～1949. The Chinese calculus textbooks’development situation and their writing characteristics are summarized during each stage. Take the following textbooks as examples respectively. The Chinese translation of the Elements of Differential and Integral Calculus (translated by Alvin Pierson Parker and Xie-Honglai), the calculus teaching material(written by Netusenji and translated by Kuang-Wentao), the Advanced Mathematics Analysis(written by Xiong-Qinglai), Calculus preliminary(written by Li-Yan), their editing features and version forms as well as vocabulary terms are expounded in different stage.Finaly, the development process of differential and integral, differential mean value theorem in the calculus textbooks are analysed and clarified their different appellations in different stage as a whole.The innovations of this study are follows:First, in a macroscopic view, on the basis of studying a plenty of detailed first-hand informations, the compiling process of calculus textbooks from1904to1949is systematically analysed from the perspective of the mathematics history and education. In a microscopic view, the writing characteristics of calculus textbooks are analysed in different stage.Second, the compilation purpose, guiding ideology as well as restrictive factors of the calculus textbooks are explored. The cultural reform and the course of thinking methods improvement in the calculus textbooks are embodied clearly.Third, on the basis of vertically analysing calculus textbooks, taking the differential and derivative, the mean law and integral as the starting point of the study, their developments in calculus textbooks are stated in cross sectional research method. Then we can draw the following conditions:they are more precisely narrated and more logically reasoninged with the development of society.更多还原