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The Education of Abacus Addition in China and Japan Prior to the Early 20th Century

  • Yifu ChenEmail author
Chapter
Part of the Mathematics Education in the Digital Era book series (MEDE, volume 11)

Abstract

Despite the voluminous prior research on the history of the abacus before the 20th century in East Asia, little has been studied on the educational ideas contained in the descriptions of manipulation of this counting device to perform elementary operations. The aim of this chapter is to explore the educational ideas related to the execution of the most elementary operation—addition—on abacus presented in the documents from the middle 15th century to early 20th century in China and Japan. The analysis focuses on different aspects related to the manipulation of this counting device in order to unveil their educational ideas. The results of this study show that the education of abacus addition experienced a historical change around the Meiji Restoration (1868), from an era of the use of verses to an era of the elaboration of “techniques of fingers,” dealing with positions of fingers on instruments, and their movement. This study may be of importance in providing an understanding of the education of abacus addition in China and Japan before the early 20th century, as well as in proposing a method of analysis for exploring the educational ideas of other elementary operations performed on the abacus or other counting devices in the history of mathematical education.

Keywords

Chinese abacus (suanpanJapanese abacus (sorobanCounting instruments Computing devices Abacus education Mathematics education 

References

  1. Bréard, Andrea. 2014. On the transmission of mathematical knowledge in versified form in China. In: Scientific Sources and Teaching Contexts Throughout History: Problems and Perspectives, Boston Studies in the Philosophy and History of Science 301, ed. A. Bernard and C. Proust, 155–185. New York etc.: Springer.Google Scholar
  2. Chen Yifu. 2013. L’étude des Différents Modes de Déplacement des Boules du Boulier et de l’invention de la Méthode de Multiplication Kongpan Qianchengfa et son Lien avec le Calcul Mental. PhD dissertation. Paris: Université Paris Diderot-Paris 7.Google Scholar
  3. Endō Toshisada 遠藤利貞. 1878. Sankajutsu jugyōsho 算顆術授業書 [Textbook of the Art of Counting beads]. Tokyo: Tokyo shihangakkō 東京師範学校. National Diet Library Digitized Contents Database, http://dl.ndl.go.jp/info:ndljp/pid/829098.
  4. Horiuchi, Annick. 1994. Les mathématiques japonaises à l’époque d’Edo. Paris: Librairie Philosophique J. Vrin. [For an English version of this work see Horiuchi 2000].Google Scholar
  5. Horiuchi, Annick. 2000. Japanese Mathematics in the Edo Period (1600–1868). A Study of the works of Seki Takakazu (?–1708) and Takebe Katahiro (1664–1739). Basel: Springer. Google Scholar
  6. Hua Yinchun 華印椿 (ed.). 1987. Zhongguo zhusuan shigao 中國珠算史稿 [Sketch of a history of computation with beads in China]. Beijing: Zhongguo caizheng jingji chubanshe 中國財政經濟出版社.Google Scholar
  7. Jami, Catherine. 1998. Abacus (Eastern). In Instrument of science: an historical encyclopedia, ed. R. Bud, and D. Warner, 3–5. New York/London: Garland.Google Scholar
  8. Kawamoto Koji 川本亨二. 1968. Gakuseiki no shuzan kyōiku ni kansuru ichikōsatsu 学制期の珠算教育に関する一考察 [Survey on the Abacus Education in the Period from 1872 to 1879]. Kyōikugaku zasshi 教育学雑誌 [Journal of Educational Research] 2: 23–35.Google Scholar
  9. Ke Shangqian 柯尚遷. 1578. Shuxue Tonggui 數學通軌 [Avenue to Mathematics]. Reprinted in Guo Shuchun 郭書春 ed. 1993. Zhongguo kexue zhishu dianji tonghui 中國科學技術典籍通彙. Shuxue juan 數學卷 vol. 2, 1167–1212. Zhengzhou: Henan jiaoyu chubanshe 河南教育出版社.Google Scholar
  10. Li Gong 李塨. 1705. Xiaoxue Jiye 小學稽業 [Course of Minor Learning]. Beijing: Zhonghua shuju 中華書局, 1985. Reprint.Google Scholar
  11. Suzuki Hisao 鈴木久男 and Toya Seiichi 戶谷清一 (ed.). 1960. Soroban no rekishi そろばんの歴史 [History of the Soroban]. Tokyo: Morikita Publishing Co., Ltd. 森北出版株式会社.Google Scholar
  12. Tamaoki Tetsuji 玉置哲二 and Ishibashi Umekichi 石橋梅吉. 1913. Shuzan seigi 珠算精義 [Essential of Computation with the Beads]. Tokyo: Buneikan 文永館. National Diet Library Digitized Contents Database. Available at http://dl.ndl.go.jp/info:ndljp/pid/952188.
  13. Uegaki Wataru 上垣渉. 1998. Gakuseiki ni okeru sanjutsu kyōkasho no taiyō 学制期における算術教科書の態様 [On a Phase of Textbooks for Arithmetic in the Period from 1872 to 1879]. Nihon sūgaku kyōiku gakkaishi Sūgakukyōiku 日本数学教育学会誌 数学教育 [Journal of Japan Society of Mathematical Education, Mathematical Education] 80(6): 89–96.Google Scholar
  14. Uegaki Wataru上垣渉. 2000. Meiji chūki ni okeru shuzan no fukkōundō ni kansuru ichikōshō 明治中期における珠算の復興運動に関する一考証 [A study on the Reconstructional Movement of the Calculation with Abacus (Soroban) in the Meiji Middle Period]. Miedaigaku kyōikugakubu kenkyūkiyō Kyōiku kagaku 三重大学教育学部研究紀要 教育科学 [Bulletin of the Faculty of Education, Mie University, Educational Science] 51: 1–20.Google Scholar
  15. Uegaki Wataru 上垣渉. 2001. Shogaku sanjutsusho no tanehon ni kansuru saikôshô 小學算術書の種本に関する再考証 [Re-study on the Source Book of Shogaku sanjutsu-sho: Elementary text of arithmetic]. Nihon sūgaku kyōiku gakkaishi 日本数学教育学会誌 [Journal of Japan Society of Mathematical Education] 76: 3–16.Google Scholar
  16. Volkov, Alexeï. 2001. L’abaco (Abacus). In Storia Della Scienza (Encyclopedia on History of science, in Italian), vol. 2 (Cina, India, Americhe), gen. ed. S. Petruccioli, volume eds. K. Chemla, F. Bray, D. Fu et al., 481–485. Rome: Istituto della Enciclopedia Italiana.Google Scholar
  17. Wang Wensu 王文素. 1524. Xinji tongzheng gujin suanxue baojian 新集通証古今算學寶鑒 [Precious Mirror of Mathematicsm newly collected and provedly]. Reprinted in Guo Shuchun 郭書春 (ed.). 1993. Zhongguo kexue zhishu dianji tonghui 中國科學技術典籍通彙. Shuxue juan 數學卷 vol. 2, 337–971. Zhengzhou: Henan jiaoyu chubanshe 河南教育出版社.Google Scholar
  18. Wu Jing 吳敬. 1450. Jiuzhang Suanfa Bilei Daquan 九章算法比類大全 [Great Compendium of the Comparison and Classification in Nine Chapters of Mathematical Methods]. Reprinted in Guo Shuchun 郭書春 (ed.). 1993. Zhongguo kexue zhishu dianji tonghui 中國科學技術典籍通彙. Shuxue juan 數學卷 vol. 2, 1–333. Zhengzhou: Henan jiaoyu chubanshe 河南教育出版社.Google Scholar
  19. Xu Xinlu 徐心魯 (ed.). 1573. Panzhu Suanfa 盤珠算法 [Computational Methods with the Beads in a Tray]. Reprinted in Guo Shuchun 郭書春 (ed.). 1993. Zhongguo kexue zhishu dianji tonghui 中國科學技術典籍通彙. Shuxue juan 數學卷 vol. 2, 1143–1158. Zhengzhou: Henan jiaoyu chubanshe 河南教育出版社.Google Scholar
  20. Zenkoku shuzan kyōiku renmei 全国珠算教育連盟 [League for Soroban Education of Japan]. 1971. Nihon shuzanshi 日本珠算史 [History of computation with beads in Japan]. Tokyo: Akatsushi shuppan Co., Ltd. 暁出版株式会社.Google Scholar

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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Independent ScholarKaohsiungTaiwan

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