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The Revolution in Mathematics Education During the Meiji Era (1868–1912): A Study of the Textbooks Used to Teach Computation, Geometry and Algebra

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Researching the History of Mathematics Education

Part of the book series: ICME-13 Monographs ((ICME13Mo))

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Abstract

During the Edo period, Japan was relatively closed, although there was an important intensification of cultural and scientific activities. In 1853, Commodore Perry and his black ships landed on Edo bay to force Japan to open its trade road: authorities had to soften the border control and to face the realities of a new international configuration. As a consequence, the Meiji period (1868–1912) witnessed a nationwide modernization program in Japan, including sweeping reforms in the education system. This paper offers a general view of the reform of mathematics curricula by presenting several case studies: in elementary schools, where traditional teachings based on the manipulation of computation devices (abacus or counting rods) were abandoned; in middle schools, where Euclidean geometry and its argumentative language were introduced; and in higher level education, where traditional tenzan 点竄 algebra was replaced with Western algebra.

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Notes

  1. 1.

    For example, we know that the Suanjing shishu 算経十書 (Ten Classics of Calculation), a compilation of textbooks gathered in China during the Tang dynasty, was adopted in mathematical education intended for the imperial administration after the Taika reform (645). See Horiuchi (2010, p. 6) and Keller and Volkov (2014, pp. 64–65).

  2. 2.

    Horiuchi’s body of work gives a general view of how wasan developed. For the period until the first half of the 18th century, see Horiuchi (2010) and for an overview of the later period, see Mikami and Smith (1914, pp. 163–253), and Horiuchi (1998).

  3. 3.

    For general analysis of mathematics education during the Meiji era, see Ogura (1974) and Matsubara (1987). In English, Ueno (2012) gives a good overview of the situation and the reader can also refer to the report on mathematical education given by Kikuchi (1909, see paragraph 2.2) at the University of London.

  4. 4.

    The kanji 漢字 are Chinese ideograms that have several pronunciations in Japanese, and there are two types of phonetic characters, the syllabary hiragana ひらがな (used for Japanese terms), and the syllabary katakana カタカナ (used for foreign terms).

  5. 5.

    See the “Teaching directives for elementary schools” (Shōgaku kyōsoku 小学教則) of 1872 reproduced in Ogura (1974, pp. 231–232).

  6. 6.

    “Brush computation”, as opposed to computation with devices, was a term used to name the computation methods imported from the West, executed on paper with a brush.

  7. 7.

    Horiuchi described the research associated to the tenzan method as a “notational algebra” based on the “positional algebra” developed by Chinese mathematicians (tianyuan method).

  8. 8.

    Regarding the debates about the translation of “algebra”, see Horiuchi (2003, pp. 247–248), Ōya (1966, pp. 294–298) and the reports on these debates in issue 43 of Tōkyō sūgaku kaisha zasshi 東京数学会社雑誌 [Journal of Tokyo Mathematical Society], TSK (1882).

  9. 9.

    Regarding the textbooks printed traditionally (fukuro toji 袋綴じ method), as pagination was done using the folio system (where folded leafs are counted, not pages), the first page of leaf n is labeled na and its second page is labeled nb.

  10. 10.

    In China already, the repetitive aspect of Euclidean geometry had been criticized. See Martzloff (2006, pp. 112–118).

  11. 11.

    The formatting (especially the use of bold lettering) is the one of the original text.

  12. 12.

    Here, it seems that Nakamura made a mistake. He should have translated “parallel to each other”.

  13. 13.

    The katakana (see Footnote 4) used to name the figures are transcribed with a phonetic transcription and with a capital letter at the beginning of each katakana transcription.

  14. 14.

    See Footnote 12.

  15. 15.

    On Tanaka and his textbooks, see Cousin (2013, pp. 116–117 and pp. 276–311).

  16. 16.

    The –eba form (conditional form) is used at the end of the setting-out.

  17. 17.

    Nari is the conjunctive form of the verb naru (be, become).

  18. 18.

    For an analysis of Kikuchi’s language in his geometry textbooks, see Cousin (2013, pp. 539–570).

  19. 19.

    In Nakamura (1873), Latin letters were transcribed using the katakana syllabary (see Nakamura’s text studied above) and in Endō (1883), they were replaced by special kanji (see Footnote 9).

  20. 20.

    On the apparition of horizontal writing in Japanese mathematics books, see Ogura (1974, pp. 251–253) and Cousin (2013, pp. 456–459).

  21. 21.

    Concerning the curricula of these institutions and the establishment of the University of Tokyo (especially its mathematics curriculum), see Cousin (2013, pp. 381–389).

  22. 22.

    William E. Parson (1845–1905), American, and Stéphane Mangeot (?–?), French.

  23. 23.

    On the emergence of a “Research tradition of Western mathematics” in Tokyo University, see Sasaki (1994, pp. 181–184).

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  1. Lyons Institute of East Asian Studies (ENS Lyon), Lyon, France

    Marion Cousin

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  1. Marion Cousin
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  1. DIMA—Dipartimento di Matematica, Genoa University, Genoa, Italy

    Fulvia Furinghetti

  2. Teachers College, Columbia University, New York, New York, USA

    Alexander Karp

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Cousin, M. (2018). The Revolution in Mathematics Education During the Meiji Era (1868–1912): A Study of the Textbooks Used to Teach Computation, Geometry and Algebra. In: Furinghetti, F., Karp, A. (eds) Researching the History of Mathematics Education. ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-319-68294-5_3

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