1960-1966


30 May - 2 June 1960, Aarhus (Denmark) - Symposium on The teaching of Geometry in Secondary School, sponsored by ICMI and the Mathematics Institute of Aarhus University

Among the lectures are the following: H. Behnke, Felix Klein und die heutige Mathematik; G. Choquet, Recherches d'une axiomatique commode pour le premier enseignement de la géométrie élémentaire; J. Dieudonné, The introduction of angles in geometry; H. Freudenthal Logik als Gegenstand und als Methode (Internationale Mathematische Nachrichten, 66, 1961, p. 1).


21 August - 19 September 1960, Zagabria - Dubrovnik (Yugoslavia)
book

At the initiative of the OEEC, a seminar is held in order to prepare a program for secondary schools that can be used as the basis for the preparation of manuals and experimental courses. (cf. Un programme moderne de mathématique pour l'enseignement secondaire, OEEC, 1961, and Bollettino della Unione Matematica Italiana, s.III, XVII, 1960, p. 204)


19-24 September 1960, Belgrade (Yugoslavia) - Symposium on The Co-ordination of the Teaching of Mathematics and Physics, sponsored by the ICMI and the Yugoslav Association of Mathematicians and Physicists
Among others, talks are given by G. Choquet, R. Courant, D. Kurepa, P. Libois, A. Revuz, M.H. Stone, G. Walusinski (Cf. Internationale Mathematische Nachrichten, 66, 1961, 4-5 and EM II s., VI, 1960 p. 140-141)





26-29 June 1961, Lausanne - Seminar on the teaching of analysis and relative manuals, sponsored by the ICMI and the Swiss Mathematical Society (EM II s., VI, 1960, 311 ).
Presentations by H. Behnke, Ch. Blanc, P. Buchner, G. Choquet, W.H. Cockcroft, A. Delessert, O. Frostman, and M.A. Ory are printed in EM II s., VIII, 1962, 93-178 . In particular, the lecture by Choquet, L'analyse et Bourbaki, addressed the following points: the axiomatic method (characteristics and pitfalls); instruments of the axiomatic method; methods of discovery related to the axiomatic system; characteristics of the work of Bourbaki in analysis; modern analysis in the world; conclusions for teaching; the place of analysis in teaching; global mathematical activity (pp. 109-135). Concerning teaching he invites teachers to
Choquet
Gustave Choquet
Rendre apparentes les grandes idées simplificatrices, leur apprendre à débrouiller des situations complexes, en leur enseignant des théories qui unifient, qui jettent des ponts entre diverses disciplines. (p. 131)
Moreover, Choquet says :
Les bases de l'Analyse, même dans l'enseignement secondaire, sont l'algèbre (algèbre des ensembles, étude du corps R, algèbre linéaire, groupes) et la topologie. Or la même base algébrique est nécessaire à l'étude de la géométrie (qui au niveau secondaire se réduit à l'étude d'un espace vectoriel à deux ou trois dimensions muni d'un produit scalaire). Il devient donc essentiel de concevoir un enseignement dont les grandes fibres soient les structures fondamentales. (p. 134)



4-8 October 1961, Bologna (Italy) - Seminar on A discussion of the Aarhus and Dubrovnik reports on the teaching of geometry at the secondary level is held, sponsored by ICMI and by the Italian national commission on mathematical instruction.

Conference papers are published in L'Enseignement Mathématique
Bologna
Bologna, Palazzo dell'Archiginnasio
(EM II s., IX, 1963, 1-104) E. Artin, H. Freudenthal, P. Libois, L. Lombardo Radice and T. Viola express doubts on the educational validity of introducing the axiomatic system into the teaching of geometry at the secondary level. Artin maintains that, "Mon point de vue est donc de limiter l'axiomatique à l'algèbre où elle est féconde" (p. 4).

Freudenthal
In his talk, Enseignement des mathématiques modernes ou Enseignement moderne des mathématiques? , Freudenthal insists on the importance of "recherches franchement didactiques" and observes that one of the cause of the failure of mathematics teaching is the "l'inversion didactique des niveaux": "on descend des niveaux supérieurs aux inférieurs au lieu de monter de bas en haut", and further, "cette inversion anti-didactique est poussé à l'extrême dans les programmes récents de géométrie axiomatique" (pp. 29, 34, 41).


4-9 December 1961, Bogotá (Colombia) - Inter American Conference on Mathematical Education , organised by ICMI with the co-operation of UNESCO and other local organisations.
Among others, talks are given by E. G. Begle, G. Choquet, M.H. Stone (Cf. Internationale Mathematische Nachrichten, 70, 1962, 9).


10 August 1962 - Meeting of the ICMI in Saltsjöbaden, near Stockholm (EM II s., IX, 1963, 112-114 )


In his Report for the period 1959-1962 (EM II s., IX, 1963, 105-112) ICMI president M. Stone points out first of all the various seminars and symposia organised by the ICMI in collaboration with other associations and the contacts made with the OEEC, UNESCO and other international organisations. In particular, he expresses his hope that in the future there will be a profitable collaboration with the SCOTS (Special Committee on the Teaching of Science), created by the Executive Committee of the IMU in order to collaborate with UNESCO in the broader field of science education. However, he laments the fact that the SCOTS is not a subcommittee of the ICMI: Frostman, Behnke and Kurepa point out the risk that the SCOTS would take over the study of the teaching of mathematics at the university level, leaving only that of the secondary level to the ICMI.

Above all, Stone dwelles upon the Commission's problem of finances : a small annual subvention arrives from the IMU, other funds are provided by the ICSU (International Council of Scientific Unions, founded in 1931), and still others by way of voluntary contributions from some member countries, but the financial means are inadequate:
Thus it would be entirely reasonable for I.C.M.I. to envisage an annual budget of approximately $ 9,000. World interest in the field of mathematical instruction is becoming intense, and I.C.M.I. can hardly play its proper role in relation to the resulting movements for experimentation and reform unless it is able to maintain this rather modest level of activity (pp. 108-109).
Stone also presents some guidelines for the future Executive Committee:
  • that the general program of I.C.M.I. provide for not less than three scientific meetings during each calendar year, at least one of which should be outside Europe, with an annual budget of $ 9,000;
  • that I.C.M.I. study methods and means for satisfying the growing demand for an international bibliographical informational service in the field of education …
  • that I.C.M.I. extend its activity to new areas, such as Africa… (p. 111)
15-22 August 1962 - The XIV International Congress of Mathematicians takes place in Stockholm under the presidency of Rolf Nevanlinna

The Opening Ceremony takes place at the Concert Hall in Stockholm
The Opening Ceremony takes place
at the Concert Hall in Stockholm
Nevanlinna combines the roles of the President of IMU and the President of the Congress: at the IV General Assembly which is held in Saltsjöbaden, near Stockholm (11-13 August 1962), the new role of the IMU in the ICMs had been established concerning the assignation of the Fields Medal, decisions regarding the scientific programs, and the congress venue (cf. LEHTO 1998, 153-155).

2107 ordinary members participate at the congress.

Section VIII is expressly dedicated to Education : in the proceedings of the congress there are 20 short communications listed, but no invited lecture is dedicated to education. Within Section VIII the ICMI organises three meetings on the following topics:
  1. Which subjects in modern mathematics and which applications of modern mathematics can find a place in programmes of secondary school instruction? (Reported by J. G. Kemeny)
  2. Connections between arithmetic and algebra in the mathematical instruction of children up to the age of 15 (Reported by S. Straszewicz)
  3. Education of the teachers for the various levels of mathematical instruction (Reported by K. Piene) (Cf. Proceedings of the International Congress of Mathematicians, 15-22 August 1962, Djursholm, Sweden, Institut Mittag-Leffler, 1963, p. XXXVI).

The reports by J. G. Kemeny and S. Straszewicz are published in L'Enseignement mathématique. Kemeny, after having presented the national reform movements in various countries (France, Germany, Italy, Israel, Poland, Scandinavian countries, the United States), observes that the majority of the 21 reports submitted recommend 4 areas of modern mathematics - elementary set theory, an introduction to logic, some topics from modern algebra, and an introduction to probability and statistics - while there is no agreement on how far the axiomatic system should be applied to mathematics, and in particular to geometry. He further observes that the most frequent motivation for teaching modern mathematics "is to prepare the student for his university experience" and that the greatest difficulties are "the shortage of qualified teachers, and the lack of suitable text materials" (EM II s., X, 1964, 152-176).

Straszewicz examines the 11 reports that were submitted, giving particular attention to some of the topics addressed: algebraic notation, equations, sets, functions and relationships, and the concept of number. He notes that the general tendency, even though with different shades of meaning, is that of "rapprocher l'enseignement scolaire des mathématiques - même dans les classes inférieures - de la science contemporaine et des nouvelles applications en faisant introduire progressivement le langage mathématique moderne. On propose, par exemple, d'introduire assez tôt les plus simples notions de l'algèbre des ensembles et de la logique propositionnelle, de faire mieux ressortir les propriétés structurales des différents systèmes de nombres considérés… " (EM II s., X, 1964, 271-293).
Fréderique Papy
Fréderique Papy


Beginning in the 1960s numerous editorial projects and initiatives flourish:

1961
the School Mathematics Project is founded in Great Britain; it is aimed at secondary school students 11 years old and up


Nuffield Project
1963
the first volume of Mathématique moderne by George et Fréderique Papy appears
Nuffield Project



1964
the English Nuffield Project starts under the direction of Geoffrey Matthews: it is aimed at primary and lower secondary schools and is based on the so-called active and discovery methods, with influences from Piaget.








14-15 February 1964 - Meeting of the ICMI in Paris
The ICMI, in agreement with the President of the IMU, decides to "reconnaitre le statut de sous-commission nationale propre … à des commissions nationales représentatives de pays non membres de L'Union Mathématique Internationale" (EM II s., XII, 1966, 134). This decision is immediately put into effect in the case of Luxemburg, and successively in that of Senegal.
It is decided to propose to the Organising Committee of the next International Congress of Mathematicians in Moscow a plenary lecture held by a Russian mathematician on the teaching of numerical analysis at the university, and to present reports on the following topics:
  • Programme for the university formation of future physicists; whether particular courses are necessary or not;
  • The use of the axiomatic system in the teaching at the secondary level;
  • The development of students' mathematical activities; the role of problems in this development.
The Executive Committee decides to adhere to two important initiatives of UNESCO:
  • The creation of a centre for documentation and information about mathematics teaching;
  • The preparation of a source book (a list of manuals, periodicals, anthologies of articles, etc.
(EM II s., X, 1964, 294-296)

The Executive Committee of ICMI and Members at large from January 1963 to December 1966, are:
André Lichnérowicz
André Lichnérowicz

President: A. Lichnerowicz
Vice-Presidents: S. Straszewicz, E. Moise
Secretary: A. Delessert
Members: Y. Akizuki, H. Behnke, H. Freudenthal
Ex officio: G. de Rham (President of IMU)
Members at large: S. Bundgaard, G. Choquet, O. Frostman, R.L. Jeffery, J. Karamata.
(EM II s., X, 1964, 297)



A very rich period of noteworthy activity begins for the ICMI thanks to the collaboration with UNESCO and other organisations.


1964-65 - Numerous international congresses are held:

Frascati (Italy), 8-10 October 1964:
27 members from 5 European countries and from Argentina
General Theme: Mathematics at the coming to university. Real situation and desirable situation
Lectures by: J. Lelong, J. Desforge, H.G. Steiner, G. Papy, G. Walusinski, Kirsch, A. Revuz, B. de Finetti, H. Behnke, Deheuvels, Manara, G. Pickert, Bass, Kiellberg

Utrecht (Holland), 19-23 December, 1964 (Cf. Internationale Mathematische Nachrichten, 80, 1965, 3):
28 members from 9 European countries and from the United States and Canada
General Theme: International colloquium on modern trends in the teaching of mathematics in secondary schools.
Lectures by: A. Wittenberg, H. Freudenthal, H. Troelstra, L.R.J. Westermann, S. Straszewicz, M. Beberman, M. Thwaites, W.O. Storer, Th. Korthagen, J. van Lint, W. Servais, J. Dzewas, W.G. Steiner, A.Z. Krigowska, L. Felix, E. Castelnuovo (EM XII, 1966, 195-199), A. Delessert.
The lecture by A. Wittenberg, Priorities and responsibilities in the reform of mathematical education: an essay in educational meta-theory, is published in EM II s., XI, 1965, 287-308.
Wittenberg underlines the following points: the importance of addressing the meta-questions in education, "so as to establish at least a framework of coherent and responsible discussion of the many issues involved" (p. 288); the necessity of creating university chairs for mathematical education; the urgency of founding an international journal specifically dedicated to mathematics teaching so that diverse approaches can be compared.

Dakar (Senegal), 14-22 January 1965:
84 members from 9 African countries, 4 American countries, 5 Asian countries, 9 European countries. They included specialists in Astronomy, Biology, Geology, Economics, Mathematics, Physics, etc.
General Theme: Congress on science teaching and economic progress
The ICMI was represented by its president, A. Lichnérowicz, and by the secretary, A. Delessert.
Exchange of views were based on document prepared in advance by: H. Heller, T.N. George, Ch. Pisot, H.W. Fehr, Y. Bernard, J. G. Baer.
Lectures by: H. Stone, A. Bouc, W. Jacobson.
The lecture by A. Delessert, Qu'attend de l'Université le maitre enseignant les mathématiques à l'école secondaire? is expanded and published in EM II s., XI, 1965, 309-320. The author underlines the importance of in service teachers continuous training and proposes the creation of university courses for future teachers on questions of elementary mathematics from an advanced standpoint, mathematics courses for physicists, chemists, engineers, etc., and seminars for teachers who are already working.

Echternach (Luxemburg), 30 May - 4 June 1965
92 members from 8 European countries
General Theme: The repercussions of mathematics research and teaching
Lectures by: H. Behnke, C. Bréard, H.G. Steiner, A. Kirsch, W. Servais, A. Revuz, Ch. Pisot, G. Papy, J. Dieudonné, G. Pickert, A. Delessert, P. Debbaut, G. Choquet, J. de Siebenthal, L. N.H. Bunt, A. Engel.
Echternach (Luxemburg)
There is a meeting of the Executive Committee of the ICMI in which representatives of UNESCO also participate. It is decided that the reports on the three topics previously chosen for the ICM in Moscow will be presented respectively by Ch. Pisot (the university education of future physicists), H.G. Steiner (the axiomatic method in secondary teaching), Z. Krygowska (development of students' mathematical activities and the role of problems).
With the support of UNESCO, the publication of a series of volumes entitled New trends in mathematics teaching is planned, and Anna Zofia Krygowska is entrusted with the task of overseeing the publication (Cf. Internationale Mathematische Nachrichten, 83, 1966, 3)

Other meetings are noted in the volume prepared by ICMI and published by UNESCO, New trends in mathematics teaching, I, 1966 ( Unesco, Paris 1967) , where articles dedicated to this topic are collected (EM II s., XII, 1966, 132-133 , 135-136).








20 May 1966
The out-going Executive Committee of the ICMI, given the remarkable broadening of the Commission's activities, requests the creation of a permanent Secretariat for the ICMI (EM II s., XII, 1966, 138), which will be refused (ICMI Archives 14B 1967-1974, 146).


ICMI stamp
16-26 August 1966 - The XV International Congress of Mathematicians takes place in Moscow under the chairmanship of Ivan G. Petrovsky
Abstracts
4282 mathematicians participate and this constitutes an important occasion for mathematicians from the West and the East to meet.

The work of the Congress is divided into 15 sections. The fifteenth, History and Pedagogical Questions, numbers 73 communications (45 in Russian), of which 35 are dedicated to education (Cf. Abstracts of Brief Scientific Communications, ICM Moscow 1966).

In the session dedicated to the ICMI are presented the following reports:
  1. Ch. Pisot, Rapport sur l'Enseignement des mathématiques pour les physiciens (EM II s., XII, 1966, 201-216);
  2. Z. Krygowska, Développement de l'activité mathématique des élèves et rôle des problèmes dans ce développement (EM II s., XII, 1966, 293-322).
In his long and detailed presentation,
Anna Zofia Krigowska
Anna Zofia Krigowska
Krygowska, given the heterogeneity of the reports submitted by the subcommittees, limits himself to the following three questions: various ways of conceiving students' mathematical activities; favourable and unfavourable factors for the development of such activities; the problems in the context of modern mathematics programmes. In conclusion he invites mathematicians, educators and pedagogists to collaborate in the resolution of the problem in question, identifying the following objectives:
  1. développement de la recherche fondamentale concernant la méthodologie de l'enseignement de la résolution des problèmes ;
  2. construction de collections de problèmes adaptés aux programmes et à l'esprit nouveaux ;
  3. élaboration des moyens et des formes de la préparation consciente des futurs maîtres à l' "enseignement par les problèmes " au cours de leurs études ;
  4. recherche et expériences relatives à l'évaluation des progrès faits par les élèves en vue d'éliminer l'influence nocive de l'enseignement " pour les examens " paralysant la véritable activation de la pensée mathématique. (p. 320)
George Polya
George Polya

Among those who contribute to the report is George Polya (Cf. L'enseignement par les problèmes, EM II s., XIII, 1967, 233-241).


Livia Giacardi
March 2008