The Process of Adapting a German Pedagogy for Modern Mathematics Teaching in Japan

Abstract

Modern geometry teaching in schools in Japan was modeled on the pedagogies of western countries. However, the core ideas of these pedagogies were often radically changed in the process of adaptation, resulting in teaching differing fundamentally from the original models. This paper discusses the radical changes the pedagogy of a German mathematics educator, P. Treutlein (1845–1912), underwent when adopted by a Japanese mathematics teacher, T. Kunimoto (1895–1985), during the modernization of geometry teaching in the 1930s in Japan.

Notes

¹ The authors would like to thank Prof. G. Schubring for his review and attention to detail.

² Fujita, T. “The Reform of School Geometry in the Early 20th Century in England and Japan: The Design and Influences of the Textbooks by Godfrey and Siddons.” Ph.D. thesis, University of Southampton, 2002.

³ Treutlein, P. Der geometrische Anschauungsunterricht als Unterstufe eines zweistufigen goemetrischen Unterrichtes an unseren höheren Schulen. Paderborn: F. Schoeningh, 1985; original: Leipzig, Berlin: Teubner, 1911.

⁴ Kunimoto, T. Theory and Practice of Intuitive Geometrical Instruction (in Japanese). Tokyo: Baihukan, 1925.

⁵ For an extended description of this section, see the Appendix to this paper.

⁶ Sato, E. “The History of Mathematics Teaching in Secondary Schools in Modern Japan” (in Japanese). Ph.D. thesis, Tokyo University, 2003.

⁷ Yamamoto, S. Study of the Teaching of Geometry in Secondary Schools in the Early 20th Century: The Influences of Treutlein’s Geometrical Intuitive Instruction, Research Report of the Scientific Research and Development Expenditure (in Japanese). Kumamoto, Japan, 1999.

⁸ Behm, H. W. “Peter Treutlein.” Zeitschrift für mathematischen und naturwissenschaftlichen Unterricht 43 (1912): 521–30; Coleman, R. Jr. The Development of Informal Geometry. New York: AMS Press: 1942; Fladt, K. “Los von Eukild oder hin zu Euklid?, Tradition und Forschritt im Geometrieunterricht der Unter‐ und Mittelstufe der höheren Schule.” Der Mathematikunterricht no. 1 (1955): 5–10; Schönbeck, J. “Peter Treutlein (1845–1912) und die Entwicklung der geometrischen Propädeutik.” In Der geometrische Anschauungsunterricht, by P. Treutlin. Paderborn: F. Schoeningh: 1985: E5–E15.

⁹ Die Gessellschaft Deutscher Naturforscher und Arzte. “Reformvorschläge für den mathematischen und naturwissenschaftlichen Unterricht.” Zeitschrift für mathematischen und naturwissenschaftlichen Unterricht 36 (1905): 533–80.

¹⁰ Wittmann, E. Ch. “Themenkreismethode und lokales Ordnen.” Der Mathematikunterricht 20, no. 1 (1974): 5–18.

¹¹ Treutlein, Der geometrische Anschauungsunterricht, 150, 154, 161.

¹² “Diese Ubung bezweckt die entwickelnde Einfuehrung der neuen Formen und eine moglichste Anregung der Raumphantasie bei den Schulern.” Ibid., 111.

¹³ “Da dieser sie sozusagen selbst geschaffen und danach gezeichnet hat, sind sie sein gewiss unverlierbares Eigentum geworden.” Ibid., 119.

¹⁴ Ibid., 113.

¹⁵ Ibid., 248.

¹⁶ Ibid., 198.

¹⁷ Herbart, J. F. “Pestalozzis Idee eines ABC der Anschauung untersucht und wissenschaftlich aus geführt.” In Joh. Fr. Herbart, Pädagogische Schriften, 1. Bd, edited by W. Asmus. Düsseldorf–München: H. Kupper, 1964: 174. I also referred to the translation by Eckoff in 1896: ‘That great science (mathematics) gives to the imagination (die Einbildungskraft) at least as much occupation as to the faculty for drawing conclusions (das Schlussvermögen). Before the latter can commence to demonstrate, the former must have sketched the figures, it must have pierced the bodies by manifold lines and intersected them by planes, it must have stretched out the infinite series, it must have interwoven them with other series. All the plenitude of combinatory presentations pertains to the imagination’ (Herbart, 1802, translated by Eckoff in 1896, 161). Herbart, J. F. Herbart’s ABC of Sense‐perception, translated by W. J. Eckoff. New York: AstroLogos Book, 2004 (original: New York: Appleton Press, 1896).

¹⁸ See also Aso, Makoto, and Ikuo Amano. Education and Japan’s Modernization. Tokyo: Japan Times, 1983.

¹⁹ For example, from 1924 to 1936 in Kumamoto Prefecture, Japan, there were 28,561 students who graduated from primary schools in this area. Of these students, 62.2% of boys and 41.1% of girls advanced to upper primary schools, 9.9% of boys to secondary schools, and 11.9% of girls to higher girls’ schools.

²⁰ With regard to the history of ‘Wasan’, see Smith, David Eugene, and Yoshio Mikami. A History of Japanese Mathematics. New York: Dover Publications, 2004.

²¹ Koyama, N. Japanese Students at Cambridge University in the Meiji Era, 1868–1912. London: Lightning Source, 2004.

²² Kikuchi, D. Plane Geometry (in Japanese). Tokyo: Monbusyo, 1888. This textbook is based on the syllabus by the Association for the Improvement of Geometrical Teaching (AIGT, founded in 1871) in England. Kikuhi was particularly influenced by I. Todhunter (1820–1884), a Cambridge textbook author in the nineteenth century. See also Barrow‐Green, June. “‘The advantage of proceeding from an author of some scientific reputation’: Isaac Todhunter and his mathematics textbooks.” In History of the University of Cambridge Texts and Studies, IV, edited by J. Smith and C. Stray. Cambridge: Cambridge University Library, 2001: 177–203.

²³ Perry, J., ed. Discussion on the Teaching of Mathematics. London: Macmillan, 1901.

²⁴ Price, Michael. “The Perry Movement in School Mathematics.” In The Development of the Secondary Curriculum, edited by M. Price. London: Croom Helm, 1986: 103–43.

²⁵ Fujita, T. “The Reform of School Geometry in the early 20th Century in England and Japan: The Design and Influences of the Textbooks by Godfrey and Siddons.” Ph.D. thesis, University of Southampton, 2002.

²⁶ Behrendsen, D., and E. Götting. Lehrbuch der Mathematik nach modernen Grundsätzen. Leipzig–Berlin: Teubner, 1911.

²⁷ Treutlein, P. Der geometrische Anschauungsunterricht, 1985/1911.

²⁸ Kuroda, M. Plane Geometry (in Japanese). Tokyo: Baihukan, 1916.

²⁹ Yamamoto, S. A Study of the Teaching of Geometry in Secondary Schools in the Early 20th Century: The Influences of Treutlein’s Geometrical Intuitive Instruction, Research Report of the Scientific Research and Development Expenditure (in Japanese). Kumamoto, Japan, 1999.

³⁰ Ogura, K. A History of Mathematics Education (in Japanese). Tokyo: Iwanami Shoten, 1932.

³¹ Kunimoto, T. Theory and Practice of Intuitive Geometrical Instruction (in Japanese). Tokyo: Baihukan, 1925.

³² Ueda, A. “A History of Mathematics Education in Japan before World War II.” Journal of Japan Society of Mathematics Education LXXXII, nos 7 & 8 (2000): 107–9.

³³ An English edition was published by the Japanese Society of Mathematics Education, Japanese Society of Mathematics Education, Mathematics Programme in Japan. Tokyo: JSME, 2000.

³⁴ See Hazama, S. “Geometry, Mathematics Education in Japan during the Fifty‐five Years since the War: Looking towards the 21st Century” (in Japanese). Journal of Japan Society of Mathematics Education LXXXII, nos 7 & 8 (2000): 167–72. For the current design of Japanese textbooks, see Fujita, Taro, and Keith Jones. “Interpretations of national curricula: the case of geometry in Japan and the UK.” British Educational Research Association Annual Conference 2003, Heriot‐Watt University, Edinburgh (11–13 September 2003).

³⁵ Kunimune, S. “A Change in Understanding with Demonstration in Geometry” (in Japanese). Journal of Japan Society of Mathematics Education 82, no. 3 (2000): 66–76.