A Study On Calculus Textbooks In China(1904—1949)

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.