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Teachers College, Columbia University
Teachers College
Columbia University
International Journal for the History of Mathematics Education

Algebra
From Pierre de la Ramée, Algebra 1560

International Bibliography

Japan

  • Annick Horiuchi, " Sur la recomposition du paysage mathématique japonais au début de l'époque Meiji ". eds. C. Goldstein et al., L'Europe mathématique (Paris: Editions de la Maison des sciences de l'homme, 1996), p. 221-248.
  • Annick Horiuchi, "Entre science et art, les écoles de mathématiques japonaises (wasan) au XIXe siècle", eds. J.P. Berthon et J. Kyburz, Japon pluriel 2, Actes du deuxième colloque de la Société française des études japonaises (Paris: Ph. Picquier, 1998), pp. 247-256.
  • Annick Horiuchi, "Kikuchi Dairoku, un mathématicien à l'époque de la modernisation", Daruma, Revue d'études japonaises, n° 12/13, Automne 2002 / Printemps 2003.
  • Annick Horiuchi,  "Langues mathématiques de Meiji: à la recherche du consensus?", eds.  Pascal Crozet et A. Horiuchi, Traduire, transposer, naturaliser: la formation d'une langue scientifique moderne hors des frontières de l'Europe au XIXe siècle (Paris : L'Harmattan, 2004) (forthcoming).
  • Yasuo Iijima, "Trends of arithmetic education in the Taisyo period, from the view of living arithmetic movement". (Japanese; English)  Mathematics education in Japan 1996. Philosophies of mathematics education in the twentieth century. JSME yearbook. Vol. 2. Japan Society of Mathematical Education (JSME), (Tokyo: Japan Society of Mathematical Education, 1997), p. 65-76.
    • Mathematics education in Japan in the Taisyo period did not undergo a great change, as a whole, from that of the Meiji period. However, during the Taisyo period, a great reform of arithmetic education in the next period -- the great revision of national textbook -- was prepared. Under the influence of Perry's Movement in mathematics education, the advancement of psychology and thoughts of liberal education, new arithmetic movement and living arithmetic movement appeared. Several leading advocates were: Takeshi Sato, Seijo elementary school; Yoshinori Katori, elementary school attached to Chiba normal school (later, Seikei elementary school); Jingo Shimizu, elementary school attached to Nara women's higher normal school; Yoshie Iwashita, elementary school attached to Tokyo women's higher normal school; Kyoichi Nakano, elementary school attached to Hiroshima higher normal school; and others. In this article, an approach is made by taking the view of their theories and practices.
  • Osamu Kota, "A history of calculus education in Japan". (English) Proceedings of the HPM 2000 conference - History in mathematics education: challenges for a new millennium. Vol. 1. Editor(s): Wann-Sheng Horng; Fou-Lai Lin (Taiwan, Dept. of Mathematics 2000), p. 54-62
    • In former times, calculus was a branch of higher mathematics and was taught only in post-secondary level. The idea of differential and integral calculus was introduced into school mathematics in Japan by a drastic change of the curriculum in 1942. However, this curriculum was not carried out completely due to the World War II. After the War, elements of calculus were introduced into upper secondary mathematics systematically, and, as a result of the spread of upper secondary education, 'popularization of the calculus' has been made. However, there remain problems concerning calculus education, so calculus education should be improved. (Author's abstract)
  • Naomichi Makinae, "The brief sketch of mathematics education for immediately follow the World War II in Japan". (English) Proceedings of the HPM 2000 conference - History in mathematics education: challenges for a new millennium. Vol. 1., eds. Wann-Sheng Horng; Fou-Lai Lin (Taiwan, Dept. of Mathematics 2000), p. 63-70 .
    • The purpose of this paper is to outline and state the feature of mathematics education immediately followed World War II in Japan. A historical survey of GHQ/SCAP Records were conducted, which resulted in the following three observations. 1. Japanese mathematics education immediately followed the war age was established while there were two comparing positions: accepting American progressive education and keeping Japanese pre-war education. 2. Under the leadership of C.I.E., Japanese ministry officers were forced to lower the level of mathematics teaching and develop experimental units for subject matter. 3. Japanese ministry officers tried to make sure that mathematical significance was not lost in these experimental units. (Author's abstract)
  • Kawajiri Nobuo, "Mathematics education in the Meiji period: a change from traditional Japanese mathematics to European mathematics". (Japanese; English), Mathematics education in Japan 1996. Philosophies of mathematics education in the twentieth century. JSME yearbook. Vol. 2. Japan Society of Mathematical Education (JSME), (Tokyo: Japan Society of Mathematical Education, 1997), p. 3-15.
    • The status of mathematics education during the Meiji Period has been well studied especially from a factual point of view. However, there are some facets that have received little attention. One such facet is the relationship between the mathematics education in the Meiji Period and the characteristics of the mathematics that was introduced from Europe. The author throws some light on the topic by looking at the characteristics of Wasan (traditional Japanese mathematics) and historical changes in the concepts of European mathematics.
  • Atsumi Ueda, "A history of mathematics education in Japan before World War II." (English) Nihon Sugaku Kyoiku Gakkaishi, 2000, 82(7-8): p. 107-108. Special Issue: Mathematics education in Japan during the 54 years since the war. Looking towards the 21st century.
    • With the Meiji restoration, Western mathematics was introduced in Japan. We needed about 30 years to standardize the curriculum of mathematics in primary and secondary schools. But it went the contrary to the so-called Perry-movement. To innovate it, we had to wait for the advent of Green Cover in primary school and the outcome of the reconstruction movement in secondary school. 

The following categorization is given by Yasuhiro Sekiguchi just for convenience.

Educational Reform

  • Wataru Uegaki, "On Japanese adaptation of international reformation movement in mathematical education". (Japanese)  Bulletin of the Faculty of Education, Mie University, Educational science, 1998, 49: 49-72.
  • Eiji Sato, [Traces of industrialism in "mathematics education reform movement"]. "'Sugaku kyoiku kaizo undo' ni okeru sangyo shugi no keifu". (Japanese)  Kyoshoku Kenkyu, 2001, no. 11: 11-19.

Educational theories

  • Tsutomu Okano, [Some problems on the criticism of "the mental discipline" in the history of arithmetic teaching]. "Sanjutsu kyoikushi ni okeru 'keishiki toya' hihan no monndai". (Japanese)  Bulletin of the Faculty of Education, Hokkaido University, 1991, no.56: 115-141.
  • Eiji Sato, [Reexamination of Fujisawa Rikitaro's theory of mathematics education: On the relation between "arithmetic" and "algebra". "Fujisawa rikitaro no sugaku kyoiku riron no saikento: 'Sanjutsu' to 'daisu' no kanren ni chumoku shite". (Japanese)  Japanese Journal of Educational Research, 1995, 62(4): 20-29.
  • Eiji Sato, [The controversy on "sansugaku" (arithmetic mathematics) and "sanjutsu" (arithmetic) at Tokyo Sugakugaisha Yakugo Kai]. "Tokyo sugakugaisha Yakugo Kai ni okeru 'sansugaku' to 'sanjutsu' wo meguru ronso". (Japanese)  Bulletin of the Graduate School of Education, the University of Tokyo, 1995, 35: 295-303.
  • Eiji Sato, The continuation of "riron-ryugi-sanjutsu" (theoretical arithmetic) and its historical context. (Japanese)  Journal of Japan Society of Mathematical Education, 1997, 79(no. 3): 24-31.
  • Eiji Sato, [Intuition and logic in mathematics education of Ogura Kinnosuke]. "Ogura Kinnosuke no sugaku kyoiku ni okeru chokkan to ronri". (Japanese)  Bulletin of the Graduate School of Education, the University of Tokyo, 1997, 37: 231-239.

Education System

  • Wataru Uegaki, [Historical investigation on the adoption process of the Western mathematics in the "Educational System" of the Meiji 5th]. "Meiji 5 nen ni okeru yosan saiyo katei ni kansuru jidai kousho". (Japanese)  Shuzan Sunju, 1998, no. 82: 2-13.
  • Wataru Uegaki, [From the arithmetic education at the dawn]. "Reimeiki no sanjutsu kyoiku kara". (Japanese)  Shuzan Sunju, 1998, no. 82: 14-20.
  • Wataru Uegaki, [A new investigation into the process of change from Wasan (traditional Japanese mathematics) to the Western mathematics]. "Wasan kara yosan e no tenkan katei ni kansuru aratanaru kousho". (Japanese)  Aich University of Education, Ipusiron, 1998, no. 40: 87-103.
  • Wataru Uegaki, [A historical investigation into the meanings of "Wasan" (traditional Japanese mathematics) and "Yousan" (the Western mathematics)]. "'Wasan' to 'Yosan' no gogi ni kansuru siteki kousho". (Japanese)  Bulletin of the Faculty of Education, Mie University, Educational science, 1999, 50: 13-29.
  • Wataru Uegaki, [The establishing process of school subjects during the post-war chaos and reconstruction: On arithmetic and mathematics]. Shusen chokugo no konran to saiken no jiki ni miru kyouka no seiritsu katei: Sansu-sugaku no baai (Report of Research Project, Grant-in-aid for Scientific Research, 2001). (Japanese)
  • Shinya Yamamoto, "The Entering Rate to Secondary Schools in Kumamoto Prefecture from 1924 to 1936". Journal for Historical Studies in Mathematics Education, 2001, 1, 28-34. (In Japanese)

Course of Study

  • Naomichi Makinae, "A Study on the ‘Abilities Chart' in Mathematics Education Immediately after World War II: Through Comparing with Virginia State Course of Stud". Journal for Historical Studies in Mathematics Education, 2001, 1, 3-14. (In Japanese)

Mathematics Teachers

  • Eiji Sato, [The teaching certification examination problems of "mathematics" and their analysis]. "'Sugaku' no shiken mondai to sono bunseki". (Japanese)  In "Bunkenn" Kenkyukai (ed.), "Bunken" shiken mondai no kenkyu: Senzen chuto kyoin ni kitai sareta senmon·kyoshoku kyoyo to gakushu (Gakubunsha, 2003 p. 73-107).

Curricula of Arithmetic

  • Tsutomu Okano,: [The formation process of "surishiso" as a goal of arithmetic teaching]. "Sanjutsu kyoiku no mokuteki to shiteno 'surishiso' no keisei katei: kyoiku naiyo ron tono kanrende". (Japanese)  Bulletin of the Faculty of Education, Hokkaido University, 1990, no.54: 127-154.
  • Watari Uegaki, "On the Arithmetic Curriculum in Mie Prefecture in Gakusei Period". Journal for Historical Studies in Mathematics Education, 2001, 1, 15-20. (In Japanese)
  • Wataru Uegaki,: [A study on arithmetic education during Gakusei period]. "'Gakusei' ki ni okeru sanjutsu kyoiku no kenkyu" (Report of Research Project, Grant-in-aid for Scientific Research, 2003). (Japanese)

Textbooks of Arithmetic

  • Tsutomu Okano, [An analysis of arithmetic textbook: On the first grade "Shogaku sanjutsu"]. "Sansu kyokasho bunseki no kokoromi: 'Shogaku sanjutu' dai ichi gakunen wo taisho to shite". (Japanese)  Kyojugaku no Tankyu, 1987, no.5: 117-157.
  • Tsutomu Okano, [The introduction process of multiplication of natural numbers in "Shogaku sanjutu"]. "'Shogaku sanjutsu' ni okeru shizensu no joho no donyu katei". Niigata University, Faculty of Education, Kyoiku Jissen Kenkyu Shido Center Kenkyu Kiyo, 1992, no.11: 75-86.
  • Tsutomu Okano, [The logic of teaching multiplication of natural numbers in "Shogaku sanjutsu" (1): On the treatment of distribution law]. "'Shogaku sanjutsu' ni okeru shizensu no joho shido no ronri (1): Bunpai hosoku no atsukai wo chushin ni". (Japanese)  Memoirs of the Faculty of Education, Niigata University, natural sciences, 1992, 34 (no. 1): 1-8.
  • Tsutomu Okano, [The logic of teaching multiplication of natural numbers in "Shogaku sanjutsu"(2): On the treatment of commutative and associative laws]. "'Shogaku sanjutsu' ni okeru shizensu no joho shido no ronri (2): Kokan hosoku - ketsugo hosoku no atsukai wo chushin ni". (Japanese)  Memoirs of the Faculty of Education, Niigata University, natural sciences, 1993, 34(no. 2): 75-80.
  • Wataru Uegarki,:On a phase of textbooks for arithmetic in the period from 1872 to 1879.  (Japanese)  Journal of Japan Society of Mathematical Education, 1998,. 80(no. 6): 9-16.
  • Wataru Uegaki,: Re-study on the source book of Shogaku Sanjutsu-sho (Elementary text of arithmetic). (Japanese)  Journal of Japan Society of Mathematical Education, 2001, 76 (supplementary issue): 3-16.
  • Tsutomu Okano, [The process of change in the construction principles of instructional contents at the arithmetic textbooks in Meiji kenteiki period: On the properties of fraction, comparison of sizes, the addition and subtraction at the second half of the first stage and the second stage]. "Meiji kenteiki sanjutsu kyokasho ni okeru kyoiku naiyo kosei kosei genri no henyo katei: Dai I ki  kouki oyobi dai II ki ni okeru, bunsu no seishitsu, daisho kankei, kaho·genpo wo taisho toshite". (Japanese)  Japanese Journal of Curriculum Studies, 2002, 11: 29-44.
  • Wataru Uegaki & Makoto Murakami, "On the compilation of the arithmetic text for higher primary school". (Japanese)  Bulletin of the Faculty of Education, Mie University, Educational science, 2002, 53: 1-7.
  • Katsuhiko Suda, [Fundamentals and basics of science education in textbooks: During the formation of public school system in Japan]. Kyokasho ni miru kagaku kyoiku no kiso · kihon: Nihon no koukyoiku seiritsu · keiseiki ni gentei shite (Report of Research Project, Grant-in-aid for Scientific Research (C)(2), 2003). (Japanese)
  • H. Matsumoto, "A Study of the Arithmetic Textbook Reform Conference at the Ministry of Education in Japan: Focusing on Jingo Shimuzu's Report at the Teachers' Meeting of Attached Primary School of Nara Female Higher Normal School". Journal for Historical Studies in Mathematics Education, 2002, 2, 31-36. (In Japanese)

Fraction

  • Tsutomu Okano, [The logic of instruction contents and material construction of fraction in "Shogaku sanjutsu": From its introduction to the teaching of its addition and subtraction]. "'Shogaku sanjutsu' ni okeru bunsu no kyoiku naiyo - kyozai kosei no ronri: Donyu kara kaho - genpo no shido made." (Japanese)  Memoirs of the Faculty of Education, Niigata University, natural sciences (1994) v. 35 (no. 2) p. 95-127.
  • Wataru Uegaki, [A historical study on the origin of fraction]. "Bunsu no kigen ni kansuru shiteki kosatsu". (Japanese)  Bulletin of the Faculty of Education, Mie University, Natural science (1996) v. 47 p. 1-17.
  • Tsutomu Okano, [The introduction processes of fraction in the arithmetic textbooks in Meiji kenteiki period: On the ways of meaning formation and explanation]. "Meiji kenteiki sanjutsu kyokasho ni okeru bunsu no donyu katei: Imizuke - setsmei no hoho ni chakumoku shite". (Japanese)  Research Journal of Educational Methods (1999)v. 25 p. 79-87.
  • Tsutomu Okano, [The construction of instructional contents of fraction in the arithmetic textbooks in Meiji kenteiki period: From the definition to the addition and subtraction at the first half of the first stage]. "Meiji kenteiki sanjutsu kyokasho ni okeru bunsu no kyoiku naiyo kousei: Dai I ki · zenki ni okeru teigi kara kaho · genpo made wo taisho to shite". (Japanese)  Japanese Journal of Curriculum Studies (2001) v. 10 p. 1-17.
  • Tsutomu Okano, "The construction of the contents of multiplication of fractions in the arithmetical textbooks from 1886 to 1894". (Japanese)  Journal for Historical Studies in Mathematics Education (2002) (no. 2) p. 1-11.
  • Tsutomu Okano, „The Construction of the Contents of Multiplication of Fractions in the Arithmetical Textbooks from 1886 to 1894". Journal for Historical Studies in Mathematics Education, 2002, 2, 1-11. (In Japanese)
  • Tsutomu Okano, [Fractions in the history of mathematics education: Historical position of the textbook "Atarashii su: Bunsu (kaiteiban)"]. "Sugaku kyoikushi no naka no bunsu: Jugyosho 'Atarashii su: Bunsu (kaiteiban)' no rekishiteki ichizuke". (Japanese)  Kyojugaku no Tankyu (2003) (n. 20) p. 73-83.

Abacus

  • Wataru Uegaki, [The origin and change of the term "Shuzan" (calculation on the abacus) in Japan]. "Nihon ni okeru yogo 'shuzan' no kigen to sono suii". (Japanese)  Shuzan Shunju (1999) (no. 83) p. 2-16.
  • Wataru Uegaki, "A study on the reconstructional movement of the calculation with abacus (soroban) in the Meiji middle period". (Japanese)  Bulletin of the Faculty of Education, Mie University, Educational science (2000) v. 51 p. 1-20.

Textbooks of Secondary School Mathematics

  • Eiji Sato, [Mathematics education during the war: Comparison of approved textbooks for junior high school first and fifth classes]. "Senjiki no sugaku kyoiku: Chugakko yo isshu kentei kyokasho to goshu kentei kyokasho no hikaku" wo chushin to shite". (Japanese)  The Japanese Journal of Curriculum Studies (2001) (no. 10) p. 17-29.
  • Kunio Ota, "On the Stop Gap Textbooks for Secondary Schools in 1946". Journal for Historical Studies in Mathematics Education, 2002, 2, 12-21. (In Japanese)

Teaching of Secondary School Mathematics

  • Eiji Sato, [Formation and spread of "school mathematics" in secondary education]. "Chuto kyoiku ni okeru 'gakko sugaku' no keisei to hukyu". (Japanese)  Journal of Japanese History of Education (1999) (no. 18) p. 1-26.
  • Eiji Sato, [The emergence and its change of mathematics for girls' high schools: Comparison with textbooks for junior high schools]. "Koto jogakko yo no sugaku no shutsugen to sono henka: Chugakko yo kyokasho to no hikaku kento". (Japanese)  Bulletin of the Graduate School of Education, the University of Tokyo (1999) v. 39 p. 393-401.
  • Eiji Sato, [Historical development of mathematics education at secondary schools in modern Japan]. Kindai nihon no chuto gakko ni okeru sugaku kyoiku no shiteki tenkai (Doctoral dissertation, University of Tokyo, 2002).
  • K. Kataoka, "Mathematics Lessons Based on the 1942-43 Mathematics Syllabi around the End of World War II". Journal for Historical Studies in Mathematics Education, 2002, 2, 22-30. (In Japanese)

Teaching of Function

  • Masahura Nakanishi, "On Ryoichiro SATO's Teaching of Functions". Journal for Historical Studies in Mathematics Education, 2001, 1, 21-27. (In Japanese)

Teaching of Secondary Geometry

  • Wataru Uegaki & Yuko Yamamoto,: "A historical study on the definition of similar figures". (Japanese)  Bulletin of the Faculty of Education, Mie University, Educational science (1995) v. 46 p. 63-77.
  • Wataru Uegaki, & Yuko Yamamoto, "A study on the evolution of the definition of similar figures". (Japanese)  Bulletin of the Faculty of Education, Mie University, Educational science (1996) v. 47 p. 1-45.
  • Wataru Uegaki & Yuko Yamamoto, [A historical study on the similitude ratio and its representation]. "Sojihi to sono hyogen ni kansuru shiteki kosatsu". Bulletin of the Center for Educational Research and Training, Mie University (1996) (no. 16) p. 15-27.
  • Shinya Yamamoto, "On the reform of the teaching of geometry in secondary schools in the 1920s." (Japanese)  Memoirs of the Faculty of Education, Kumamoto University, Humanistic science (1996) (no. 45) p. 13-31.
  • Shinya Yamamoto, ["Constructions of new figures" in Treutlein's "die geometrische Anschauungsunterricht"] "Treutlein no 'kikagakuteki chokkan kyoju' ni okeru 'shin zukei no kousei'". (Japanese)  Kyushu Sugaku Kyoiku Gakkai Shi (1998) (no. 5) p. 57-65.
  • Eiji Sato, [The formation and acceptance of Kikuchi Tairoku's ideas on geometry teaching]. "Kikuchi Tairoku no kikagaku kyoiku shiso no keisei to juyo". (Japanese)  Journal of History of Science, Japan (1999) (no. 209) p. 27-35.
  • Shinya Yamamoto, The influence of "Meran Vorschläg" (1905) on Japanese mathematics education: Teaching of the concept of function in M. Kuroda's geometry textbook (1916). (Japanese)  Journal of JASME: Research in Mathematics Education (2000) v. 6 p. 25-33.
  • Shinya Yamamoto, [Epistemological backgrounds of Treutlein's "die geometrische Anschauungsunterricht"] "Treutlein no kikagakuteki chokkan kyoju no ninshikironteki haikei". (Japanese)  Memoirs of the Faculty of Education, Kumamoto University, Humanistic science (2000) (no. 49) p. 201-213.
  • Shinya Yamamoto, The meaning of spatial imagination in geometrical intuitive instruction of P. Treutlein. (Japanese)  Journal of JASME: Research in Mathematics Education (2001) v. 7 p. 105-116.
  • Taro Fujita, "The Study of Elementary Geometry (1903) by Godfrey and Siddons: The Role of Experimental Tasks in the Teaching of Geometry". Hiroshima Journal of Mathematics Education, 2001, 9, 11-19.
  • Taro Fujita, 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. Unpublished Ph.D. Thesis, Research and Graduate School of Education, University of Southampton, UK 2002.
  • Taro Fujita, and K. Jones, "The Bridge between Practical and Deductive Geometry: developing the "geometrical eye"." In A. D.Cockburn & E. Nardi (Eds), Proceedings of the 26th Conference of the International Group for the Psychology of Mathematics Education, Vol 2 (pp. 384-391). (Norwich, UK: University of East Anglia, 2002).
  • Taro Fujita, and K. Jones, "The design of geometry textbooks for secondary schools : The place of experimental tasks". In Pope, S. and McNamara, O. (Eds.), Research in Mathematics Education, Volume 5. London: British Society for Research into Learning Mathematics. (in press).
  • S. Yamamoto, Taisho Showa shoki no chugakko kika kyoujushi kenkyu: P. Treutlein no "kikagakuteki chokkan kyoju" no juyo to teichaku [A study on history of teaching of geometry at junior high schools during Taisho and early Showa periods: Acceptance and establishment of "die geometrische Anschauungsunterricht" of P. Treutlein]. Report of Research Project, Grant-in-aid for Scientific Research (C)(2), 1999. (No. 09680279). (In Japanese)

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