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Challenges, Hopes, Actions, and Tensions in the Early Years of the International Commission on the Teaching of Mathematics

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Abstract

The International Commission on the Teaching of Mathematics can be considered the parent of the International Commission on Mathematical Instruction (ICMI). This chapter describes the activities and major ideas of this Commission from its foundation in 1908 through the First World War. A brief account of the events in the community of mathematicians that formed the background of this foundation is presented as well. The chapter also outlines the steps that first brought the dissolution of the Commission and, later, its reconstitution in 1928 during the International Congress of Mathematicians in Bologna.

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Notes

  1. 1.

    See the website Furinghetti and Giacardi (2008) ) for information and documents on the first hundred years of ICMI and its ancestors. Information about the characters mentioned in this chapter who had been members of the Commission can be found in the “Portrait gallery” of this website.

  2. 2.

    For many decades English, French, German, and Italian were the official languages of the International Congresses of Mathematicians and of the Commission.

  3. 3.

    This is the way the meeting is mentioned in the official website of the International Mathematical Union (IMU).

  4. 4.

    The Deutsche Mathematiker-Vereinigung was founded in 1890, the New York Mathematical Society (becoming the American Mathematical Society in 1894) in 1888.

  5. 5.

    Auvinet (2013) reported from Brigaglia (1984, p. 46) that since 1891, Laisant had already been the author of a “projet d’association universelle internationale des mathématiciens” (project of an international universal association of the mathematicians).

  6. 6.

    Lemoine was the author of a paper read at the Chicago Congress .

  7. 7.

    The representative from Ann Arbor was Alexander Ziwet, who participated in Chicago Conference of 1893 and reported on Klein’s Lectures on mathematics: delivered from Aug. 28 to Sept. 9, 1893 (New York: Macmillan, 1894).

  8. 8.

    All translations in this paper are by the author.

  9. 9.

    J’avoue que j’ai été déçu par la nature des travaux présentés à la Section d’Enseignement au Congrès de Heidelberg. Il ne m’a pas semblé que les sujets traités étaient envisagés dans leur véritable sens pédagogique. Il s’agissait le plus souvent de certains détails mathématiques, et non pas d’études approfondies des problèmes généraux de l’éducation mathématique. (La Rédaction 1905, p. 471)

  10. 10.

    These papers were first presented during the conference celebrating the centenary of ICMI in Rome (see Menghini, Furinghetti, Giacardi, and Arzarello 2008, pp. 205–211 and 113–130, respectively).

  11. 11.

    Il Congresso, avendo riconosciuto la importanza di un esame accurato dei programmi e dei metodi d’insegnamento delle matematiche nelle scuole secondarie delle varie nazioni, confida ai Professori KLEIN, GREENHILL e FEHR l’incarico di costituire un Comitato internazionale che studii la questione e ne riferisca al prossimo Congresso. (Castelnuovo 1909 , Vol. 1, p. 33)

  12. 12.

    In the document of the period, it was usually indicated as Comité Central. The French language, which was the most used language in L’Enseignement Mathématique, was the usual language for circulars and reports of the Commission.

  13. 13.

    O’Connor and Robertson (1997) write that “He spoke French rather well, and read German easily.”

  14. 14.

    Donoghue (2008) reports the quoted passages from: Smith, D. E. (n.d.). ICTM: Memoranda, notes, etc. David Eugene Smith Professional Papers, Rare Book and Manuscript Library. New York: Columbia University.

  15. 15.

    In the report of the activities of the Commission at the International Congress of Mathematicians in Cambridge, Fehr (1912, p. 456) mentions the following meetings of the Central Committee: Cologne in September 1908, Karlsruhe beginning of April 1909, Basel end of December 1909, Brussels August 1910, Milan September 1911, Hahnenklee (Harz mountains) July 1912. Fehr (1910, p. 371) also mentions a meeting in Gottingen in April, 1910. Of course, there were also informal contacts. The most relevant issues resulting from these meetings are reported in Circular no. 1 signed by Klein and Fehr (1909) for the meeting in Carlsruhe (April 5–6, 1909) and Circular no. 2 signed by Klein and Fehr (1910) for the meeting in Basel (December 28, 1909).

  16. 16.

    In Circulaire no. 4 (1911. L’Enseignement Mathématique, 13, 122–137) the mistake involving Japan was noticed later, and it was listed among the participant countries.

  17. 17.

    In this chapter the spelling of the surnames of people is reported as found in the cited documents.

  18. 18.

    Faire une enquête et publier un rapport général sur les tendances actuelles de l’enseignement mathématique dans les divers pays. (Klein, Greenhill and Fehr 1908 , p. 450)

  19. 19.

    Etat actuel de l’organisation et des méthodes de l’instruction mathématique.

  20. 20.

    Les tendances modernes de l’enseignement mathématique.

  21. 21.

    Some lexical changes reveal the different approaches of the first part concerning the status quo and the second part which projected into the future. In the first part, it is recommended to consider the “écoles des jeunes filles” (girls schools) (p. 453), and in the second, the recommendation becomes to consider “la question de la coéducation des deux sexes” (the question of the coeducation of the two sexes) (p. 454).

  22. 22.

    A. Dans quelle mesure peut-on tenir compte dans les écoles moyennes ( lycées , collèges, gymnases, écoles réales, etc.) de l’exposé systématique des mathématiques? – La question de la fusion des différentes branches mathématiques dans l’enseignement moyen.

    B. L’enseignement mathématique, théorique et pratique, destine aux étudiants en sciences physiques et naturelles. (Fehr 1911, p. 122)

  23. 23.

    The portrait by Schubring in Furinghetti and Giacardi (2008) mentions Lietzmann’s interest in the problem of rigor as well as the studies he carried out about the Italian approach to this issue.

  24. 24.

    As Godfrey (1912) pointed out in his report on Milan Conference, in Italy the concept of rigor had changed since the times of the first textbook based on Euclid and published in 1867–1868. According to him for the Italians rigor did not mean Euclid, but Peano and Hilbert, while in Germany intuition was widely used and rigor was confined to the university.

  25. 25.

    This manual was written together with Anselmo Bassani.

  26. 26.

    In the Congress there were four sections. In the fourth section, entitled Philosophy, history, didactics (Hobson and Love 1913 , Vol. 2, pp. 447–653), there were 29 contributions split into the following subsections: a and b (Philosophy, history, didactics , ibid., Vol. 2, pp. 447–458), a (Philosophy, history, ibid., Vol. 2, pp. 459–541), and b (Didactics, ibid., Vol. 2, pp. 543–653).

  27. 27.

    A) L’intuition et l’expérience dans l’enseignement mathématique de Ecoles moyennes.

    B) Les mathématiques en physique. Connaissances mathématiques utiles aux physiciens et réclamées par ceux-ci. (L’Enseignement Mathématique, 1912, 14, p. 39).

    These themes essentially treated variations of the themes discussed in Milan.

  28. 28.

    A. Les résultats obtenus dans l’introduction du Calcul différentiel et intégral dans les classes supérieures de l’enseignement moyen.

    B. La place et le rôle des mathématiques dans l’enseignement technique supérieur. (L’Enseignement Mathématique, 1913, 15, pp. 394–395)

    The translations into German, English, and Italian of the questions were published in L’Enseignement Mathématique (1913, 15, pp. 394–412).

  29. 29.

    He could not accomplish the task because died in August 12 (L’Enseignement Mathématique, 1914, 16, p. 54)

  30. 30.

    “La Science est la grande pacificatrice” (Les directeurs 1894, p. VIII).

  31. 31.

    Des crimes sans nom vont laisser dans l’histoire des nations coupables une tache, que des signatures au bas d’un traité de paix ne sauraient laver. (Villat 1921 , p. xxxi)

  32. 32.

    All information about correspondence among the members of the central Committee is taken from the article Schubring (2008) .

  33. 33.

    The answer from Greenhill is missing.

  34. 34.

    This table was firstly published in Fehr’s report on the activities of the Commission (Fehr 1920–1921, p. 339). In the version of 1929, the mistake in the sum of the number of papers is amended (in 1920–1921 it was 310 instead of 300).

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Authors and Affiliations

  1. Dipartimento di Matematica. Università di Genova, Genoa, Italy

    Fulvia Furinghetti

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  1. Fulvia Furinghetti
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Correspondence to Fulvia Furinghetti .

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Editors and Affiliations

  1. Teachers College, Columbia University, New York, NY, USA

    Alexander Karp

Appendices

Appendix 1

Central Committees of CIEM/IMUK (Commission Internationale de L’Enseignement Mathématique/Internationale Mathematische Unterrichtskommission).

1908–1912

 

President

Felix KLEIN (Germany)

Vice-President

George GREENHILL (UK)

Secretary-General

Henri FEHR (Switzerland)

1912–1920

 

President

Felix KLEIN (Germany)

Vice-Presidents

George GREENHILL (UK), David Eugene SMITH (USA)

Secretary-General

Henri FEHR (Switzerland)

Members (co-opted in 1913)

Guido CASTELNUOVO (Italy), Emanuel CZUBER (Austria), Jacques HADAMARD (France)

1928–1932

 

President

David Eugene SMITH (USA)

Vice-Presidents

Guido CASTELNUOVO (Italy), Jacques HADAMARD (France)

Secretary-General

Henri FEHR (Switzerland)

Member

Walter LIETZMANN (Germany)

1932–1936, 1936–

 

President

Jacques HADAMARD (France)

Vice-Presidents

Poul HEEGAARD (Norway), Walter LIETZMANN (Germany), Gaetano SCORZA (Italy)

Secretary-General

Henri FEHR (Switzerland)

Member (co-opted in 1932)

Eric Harold NEVILLE (UK)

Appendix 2

Table 1.1 Publications of the Commission (Atti del Congresso 1929, Vol. I pp. 109–110)Footnote

This table was firstly published in Fehr’s report on the activities of the Commission (Fehr 1920–1921, p. 339). In the version of 1929, the mistake in the sum of the number of papers is amended (in 1920–1921 it was 310 instead of 300).

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Furinghetti, F. (2019). Challenges, Hopes, Actions, and Tensions in the Early Years of the International Commission on the Teaching of Mathematics. In: Karp, A. (eds) National Subcommissions of ICMI and their Role in the Reform of Mathematics Education. International Studies in the History of Mathematics and its Teaching. Springer, Cham. https://doi.org/10.1007/978-3-030-14865-2_1

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