2 July 1955 - H. Behnke convokes in Geneva the new Executive Committee of the ICMI

Heinrich Behnke
Heinrich Behnke

It is constituted as follows:
President: H. Behnke
Vice-Presidents: D. Kurepa, M.H. Stone
Secretary: J. Desforge
Members: Ram Behari, E.A. Maxwell, K. Piene
Ex officio: H. Hopf (President of the IMU)

The election of the Indian mathematician Ram Behari to the Executive Committee shows that the ICMI is beginning to be a truly international commission.

Of the 29 countries that are part of the IMU, at this time only 15 have designated their two delegates to the ICMI:
Germany: W. Suss; E. Kamke
England: R. P. Gillespie; A. P. Rollett
Canada: P. A. Petrie; A. Gauthier
Denmark: S. Bundgaard; M. Pihl
Finland: K. Väisälä; I. Simola
France: A. Chatelet; J. Desforge
Greece: K. Papaioannou; Michalopoulos
Israel: A. Fraenkel; N. Elyoseph
Italy: L. Brusotti; M. Villa
Japan: S. Iyanaga; M. Hukuhara
The Netherlands: H. Freudenthal; J. H. Wansink
Sweden: O. Frostman; L. Sandgren
Switzerland: G. De Rham; E. Trost
USA: E. H. C. Hildebrandt; Syer
Yugoslavia: I. Bandic; L. Gabrovsek ( EM II s., 1, 1955, pp. 195-198 )

Shortly after would be added:
The Republic of Argentina: A. Sagastume; J. Babini
Australia: T. G. Room; Chong.
Belgium: W. Servais
Luxemburg: A. Gloden
Norway: K. Piene
Portugal: S. Silva; V. Gronçalves; G. Calado; P. Da Silva (EM II s., I, 1955, p. 202)

During the meeting a plan of work is established for the period 1955-1958. The following three themes are proposed for study: the continuation of the inquiry on the role of mathematics and mathematician at present time; the teaching of mathematics to students up to the age of fifteen years thus completing the studies undertaken for the Amsterdam Congress; the scientific basis of mathematics teaching in secondary schools and teachers training.
There follows an animated discussion, during which Hans Freudenthal makes this important contribution: il "estime que le sujets d'enquête proposés ont un caractère trop général, et qu'ils risquent de donner lieu ... à des rapports qui feront intervenir des questions d'organisation et d'administration plus que des questions proprement scientifiques; or, la CIEM doit plutôt susciter des recherches et des études dans l'ordre scientifique".
He therefore suggests these more limited and precise themes:
  • The need for an intuitive approach at the first lessons in geometry;
  • The aid that psychology can provide in the first phases of mathematics teaching;
  • The importance of the teaching of geometry
  • Logic and the teaching of mathematics.
As much interest as the discourse of Freudenthal arouses, it leads only to the substitution of the first theme initially proposed, so that the work plan of the ICMI turns out to be composed of three study projects:

  • mathematical instruction up to the age of fifteen years;
  • the scientific basis of mathematics in secondary school teaching;
  • a comparative study of the methods used in the initiation to geometry (EM II s., I, 1955, pp. 198-201 and EM II s., I, 1955, p. 268).

The journal L'Enseignement Mathématique is confirmed as the official organ of the ICMI.
Its second series begins in 1955.
Einsegnement mathematique
"This second series will be devoted to the reform and development of mathematical instruction; it will publish articles focusing on and explaining modern theories in a manner comprehensible to non-specialised mathematicians; deal with the arrangement and organisation of teaching; study the psychological formation of mathematical ideas; and publish accounts of the work done and surveys carried out by the ICMI" (EM II s., I, 1955, 270-271)
On the occasion of the Geneva meeting a symposium is organised to commemorate the important work undertaken by H. Fehr for the ICMI (1908-1954) and in directing L'Enseignement mathématique.

22-28 February 1956 - The Conference on Mathematical Instruction in South Asia is held in Bombay at the Tata Institute of Fundamental Research.

ICMI is represented by its Vice-president, M. Stone, who gives one of the invited talks, together with G. Choquet, H. Freudenthal, A.D. Alexandrov, and others. (Cf. Report of a Conference on Mathematical Education in South Asia, The Mathematics Student, 24, 1956, 1-183) This conference "was the first of this kind and it is hoped that may serve as a model for similar events in the future" (Cf. Internationale Mathematische Nachrichten, 47/48, 1956, p. 9).

27 May 1956 - Meeting in Münster-Westfalen

During this meeting the Executive Committee of the ICMI (EM II s., II, 1956, pp. 317-323 ) disposes a series of a total thirty quarter-hour periods for all the talks which will be given at the upcoming International Congress of Mathematicians in Edinburgh, and designates the speakers for the three inquiries: H. F. Fehr for the first theme (mathematical instruction up to the age of fifteen years), H. Behnke for the second (the scientific basis of mathematics in secondary school teaching) and H. Freudenthal for the third (a comparative study of the methods used in the initiation to geometry), and it is decided to ask J. Piaget to present a general report.

K. Piene is designated treasurer of the ICMI, even though the Commission does not have its own budget but receives funding from the IMU solely for travel on the occasions of its meetings. Behnke points out that since the expenses of a secretary and for translations are not paid for the IMU, the German government has assumed responsibility for those expenses for the period from 1 January 1955 to 31 December 1958.

There is an effort to establish greater connections between the Subcommittees and the Executive Committee, so that the ICMI can "play a still better part as an international body".

December 1956
H. Hopf, president of IMU, invites the ICMI to undertake a study on "the difficulties that arise in recruiting professors of mathematics and professors of natural sciences - difficulties which are mostly due to the industrial development which necessitates a greater number of engineers". (EM II s., III, 1957, 79)

Gilbert Walusinski
Gilbert Walusinski

1956 - 1957, Paris - At the Institut Poincaré, some lectures on modern mathematics

They are organised by the Société Mathematique de France (SMF) and the Association des Professeurs de Mathématiques de l'Enseignement Public (APMEP) at the initiative of Gustave Choquet and Gilbert Walusinski, president of the APMEP. (cf. Monographie 7 de L'Enseignement Mathématique, Structures algébriques et structures topologiques, 1958).

These talks are aimed at mathematics professors in all secondary schools and contribute to a change in mentality that is reflected in the curricula and in the methods of teaching.

3 Juillet 1957, ICMI Meeting in Bruxelles

Among the other themes, the Executive Committee discusses about the Regulations of the ICMI:
"L'organisation actuelle de la CIEM est assez complexe et certaines difficultés surgissent parfois, en particulier en ce qui concerne l'envoi de circulaires et de documents aux différents pays. Il serait nécessaire de procéder à une révision des statuts, ou moins de préciser certains points concernant, entre autres, les relations entre le Comité Executif et les Sous-Commissions nationales. M. Hopf, Président de l'UMI a fait connaître a M. Behnke qu'une petite commission pour la révision des statuts de la CIEM avait été constitué; elle comprend MM. le Professeurs Koksma (Amsterdam), Hopf, Behnke et Stone et un autre représentant de la CIEM qui doit être choisi par le Comité; sur la proposition de M. Behnke, M. Desforge est désigné pour faire partie de cette commission" (ICMI Archives 14A 1955-1957, 33)

4 October 1957 - The Soviet launch of Sputnik stimulates debate in the USA and in Europe about the need for major reforms in scientific and mathematical education.

Edward Begle
Edward Begle
1958 Edward Begle is appointed director of the School Mathematics Study Group (SMSG),

it was the largest and most influential of the so-called new math curriculum projects in the U.S.A.
SMSG published and distributed extensive collections of books and films for teachers as well as a series of monographs for students, the New Mathematical Library.

28 May 1958 - Meeting in Münster-Westfalen

In this meeting the Executive Committee of the ICMI (EM II s., IV, 1958, pp. 213-219 ) organises its participation at the Edinburgh Congress. President Behnke presents a project for the reform of the ICMI (pp. 216-217) in which, among other things, he expresses his hope for the formation of national subcommittees for mathematics teaching that could join to form more ample "regional groups".

D. Van Dantzig, H.F. Fehr, D. Kurepa and W. Servais are assigned to the preparation of a questionnaire regarding the inquiry proposed by Hopf concerning the difficulty of recruiting mathematics teachers (EM II s., IV, 1958, pp. 220-223 )

Piene proposes the following three work themes for the period 1959-1952:
  • A study of the different types of examinations and especially of the exams that permit entrance to upper level teaching;
  • A study of what themes and applications of 'modern mathematics' might find a place in the teaching programs of secondary schools;
  • A comparative study of the teaching methods used to in the passage from arithmetic to algebra.

11-13 August 1958

The General Assembly of the IMU, held in St. Andrews (Scotland), welcomes as IMU members the socialist countries of Europe, including the USSR, and Alexandrov is elected a member at large of the ICMI.
M.H. Stone is elected as president of the ICMI. The General Assembly expresses interest in the activities of the European group of the ICMI, and agrees on the necessity to make certain changes in the regulations of the ICMI in such a way that the Commission is made up of:
  • 10 members at large elected by the General Assembly of the IMU upon nomination by its President;
  • 1 representative of each national subcommittee (EM II s., IV, 1958, pp. 227-228).
The General Assembly takes also in consideration ICMI's recommendation that membership in the ICMI is not to be restricted to the members of the IMU and resolves that "new terms of reference for ICMI be prepared by the Executive Committee of IMU in cooperation with the Executive Committee of ICMI and submitted to the members of the Union for approval"(Internationale Mathematische Nachrichten, 68/69, 1961, 26, 29).
New Terms of Reference will be adopted in 1960.

Summer 1958 - The first edition of the World Directory of Mathematicians is released

14-21 August 1958 - The XIII International Congress of Mathematicians is held in Edinburgh under the presidency of William V.D. Hodge

McEwan Hall; University of Edinburgh
McEwan Hall;
University of Edinburgh
1658 full members participate, with 582 appointed delegates representing 308 organisations.

In his inaugural address, Hodge underlines the importance of good mathematics teaching:

"It is part of our duty to see that our pupils ... understand that mathematics is an integral part of world culture; not only a pillar of the technological civilization of today, but an essential item in the intellectual equipment of the good citizen" ( Proceedings of the International Congress of Mathematicians, 14-21 August 1958, edited by J.A. Todd, Cambridge, Cambridge University Press, 1960, pp. lii).

Among the half-hour addresses by invitation of the Organizing Committee, one is dedicated to education: D. Kurepa, Some principles of mathematical education (pp. 567-572).
Kurepa's contribution comprises the following points: Functional point of view, Definition of a function, Functional principle, Active interpenetration principle, Practical consequence for mathematical education, Shifting principle, Ecological principles, Impact of logic. Kurepa particularly emphasises the importance of connecting the teaching of algebra to the teaching of geometry, of using various methods in teaching, and of involving all of the senses in the teaching process:
"an active interpenetration of methods, domains, topics, is of great importance and usefulness... In the teaching process, the hands are to be active (writing, showing), the tongue, ears, brain, i.e. all organs are more or less in active interdependence and co-operation. Let us remember that for a long time, even in instruction of geometry, and still more in arithmetic, the factors action and perception were either eliminated or at least neglected" (p. 570)
In section VIII, dedicated to History and Education, ample space is reserved to the ICMI.
In the Proceedings are listed 14 talks dedicated to education, and the following 3 reports:

I.C.M.I. First Topic. Mathematical instruction up to the age of fifteen years , reported by Professor H. F. Fehr, Columbia University, New York;
I.C.M.I. Second Topic. The scientific bases of mathematics in secondary education , reported by Professor H. Behnke, Münster;
I.C.M.I. Third Topic. Comparative study of methods of initiation into geometry, reported by Professor H. Freudenthal, Utrecht;

The reports presented by H. Fehr and H. Freudenthal, are also published in L'Enseignement mathématique (EM II s., V, 1959, 61- 78, EM II s., V, 1959, 119-145).

Outing to the Firth of Clyde. In the center are Italian mathematicians E. Marchionna and A. Terracini
Outing to the Firth of Clyde.
In the center are Italian mathematicians
E. Marchionna and A. Terracini
After having noted the fact that some national delegates had misinterpreted the questionnaire and had sent an account of their programmes of geometry, and that "comparative studies in education have to account for a large diversity of educational systems", Freudenthal goes on to a rich and profound examination of the teaching subjects and the teaching methods. He notes that there is a general agreement that the first phase of teaching geometry must be concrete and intuitive and that recourse to real problems can considerably improve the conditions of transfer of training and can also be a powerful means of motivation. In the final part of the report, he addresses the theme of the impact that psychological and pedagogical research may have on geometrical instruction in the initiating phase and states:
"All will admit that Piaget's research is highly interesting. But it is quite another thing to apply his results to teaching mathematics, firstly because Piaget's mathematical background has been rather weak, but mainly because Piaget's approach hardly reflects the teaching situation in the classroom, but the rather unusual laboratory situation of the psychologist. Mathematical teaching theory can be furthered by mathematical teachers who are able mathematicians and able educators" (EM II s., V, 1960, p. 139)
At the initiative of the ICMI is presented an exhibit of books, journals, and documents (some 2000 works from 17 countries) relative to the teaching of mathematics at the secondary level. The organisation and layout of the exhibit is directed by Inspector Dolmazon of the Institut Pédagogique National in Paris (EM II s., IV, 1958, pp. 223-228).

1959 - The first International Mathematical Olympiad (IMO) is held in Romania.

7 countries participate

Executive Committee of ICMI and Members at large for the period 1 January 1959 - 31 December 1962

President: M. H. Stone
Vice-Presidents: H. Behnke, D. Kurepa
Secretary: G. Walusinski
Members: Y. Akizuki, D. Alexandrov, O. Frostman
Ex officio: R. Nevanlinna (President of IMU)
Members at large: Y. Akizuki, D. Alexandrov, H. Behnke, P. Buzano, G. Choquet, H. Fehr, H. Freudenthal, D. Kurepa, E. A. Maxwell.
(EM II s., V, 1959, pp. 151-152)
Successively J. Karamata will be co-opted, as the editor of L'Enseignement mathématique (EM II s., V, 1959, pp. 290-292)

September 1959 - Woods Hole on Cape Cod (USA)
A conference is held with the aim of improving science education in primary and secondary schools, bringing together scientists, mathematicians, educators, biologists, psychologists and other professionals. J. S. Bruner, who published a report on it, places the accent on learning through structures and learning through discovery (J. S. Bruner, The Process of Education , Cambridge, Harvard University Press, 1960).

23 November - 4 December 1959 - At the initiative of the OEEC, a seminar is held at the Centre Culturel de Royaumont, Asnière-sur-Oise (France) on the following topics: new thinking in mathematics, new thinking in mathematical education, and implementation of reform.

Chairman of the seminar is the president of the ICMI, Marshall Stone, who makes the introductory address. Three delegates from every country are invited to participate: an outstanding mathematician; a mathematics educator or person in charge of mathematics in the ministry of education; an outstanding secondary school teacher of mathematics. The seminar was preceded by the distribution of a questionnaire, "Survey of current practices and trends in school mathematics" (cf. Appendix B in New Thinking in School Mathematics, OEEC, 1961, pp. 221-237).

In his introductory address, Stone formulates a veritable "program of research in the teaching of mathematics" (study and experimentation), expressing his hopes for the creation of ad hoc institutes for research and the insertion in the universities of research projects regarding the teaching of mathematics (p. 28-29).

The most influential talk is that of Jean Dieudonné, whose proposals for the reform of the teaching of mathematics are explicitly inspired by the Bourbaki school:

"If the whole program I have in mind had to be summarised in one slogan it would be: Euclid must go! ... If we had a curriculum at last freed from the dead-weigh of "pure geometry", what would we put in its place?... I would list the following ones:
  1. Matrices and determinants of order 2 and 3.
  2. Elementary calculus (functions of one variable).
  3. Construction of the graph of a function and of a curve given in parametric form (using derivatives)
  4. Elementary properties of complex numbers.
  5. Polar co-ordinates" . (Cf. New Thinking in School Mathematics, op. cit., pp. 35, 38)

7-8 December 1959, Paris - Meeting of some ICMI members

In attendance are president M. Stone, vice-president Behnke, IMU president R. Nevanlinna, H. Freudenthal, H. Fehr, G. Choquet, G. Walusinski, S. Bundgaard, O. Frostman, A. Gloden, J. Karamata, T. Viola. J. Gass, head of division of the OEEC, is in attendance as an observer. Stone gives an account of the work done at Royaumont and of the decisions made. He presents the themes chosen for the next ICM and their relative presenters:

  • What are the questions of modern mathematics and what are their applications that can be inserted into secondary teaching programmes (J.G. Kemeny);
  • Training of the teachers for the various levels of mathematical instruction (K. Piene);
  • The relationships between arithmetic and algebra in the teaching of mathematics to students up to 15 years old (S. Straszewics).

Choquet proposes that the ICMI form one or two work groups for writing new textbooks for the teaching of mathematics (EM II s., V, 1959, pp. 284-287).
It is decided to send a questionnaire to the national subcommittees in order to create a catalogue of the associations of mathematics professors, of periodicals, textbooks, and didactic materials in general (EM II s., V, 1959, pp. 289-290).

Livia Giacardi
March 2008