The International Commission on Mathematical Instruction (ICMI) was established at the beginning of the 20th century, essentially under the impulsion of a group of mathematicians of different nationalities initially interested in identifying direct ways of analysing the similarities and differences in the teaching of mathematics among various countries of the occidental world. Naturally in the background of this analysis stood the intention of improving the learning of mathematics in all countries.
The question I want to examine briefly here is the following: as we have witnessed, especially in the last part of the 20th century, the emergence of so many other international organisations dealing with great efficiency with the issues which interested ICMI at its inception, what would be nowadays the main tasks in which ICMI could be involved in a natural way?
Substantial studies concerning particular aspects of mathematics education have been undertaken in a systematic way by a few working groups of great importance. The International Group for the Psychology of Mathematics Education (PME) organises on a regular basis its meetings which gather a large number of experts in mathematics education. There is also the International Study Group on the Relations between the History and the Pedagogy of Mathematics (HPM), and another group interested in the issues raised by the full integration of women in mathematics research and mathematics education (IOWME, the International Organization of Women and Mathematics Education). International competitions, in the form of olympiads or similar activities, are basically the responsibility of the World Federation of National Mathematics Competitions (WFNMC). These four organisations are formally constituted as so-called "Affiliated Study Groups" of ICMI. Consequently one can ask with which problems does, or should, the International Commission deal directly in this day and age.
On the other hand there are the ever more influential ICMI Studies. For almost two decades every few years, in recent times almost every year, ICMI, after a very careful preparation, launches by invitation an international meeting of more than fifty experts in order to analyse one of the most important issues of the moment in mathematics education. From it, after more or less one year, an ICMI Study book is published in which the main results and proposals for the solutions of the related problems are included. The ever expanding collection constitutes a very important reference for all in the field of mathematics education. For instance, the most recent ICMI Studies dealt respectively with geometry, history in mathematics education and the teaching and learning of university mathematics.
Now clearly the "star activity" of ICMI is the International Congress on Mathematical Education (ICME), taking place every four year under the direct responsibility of the Commission which devotes much care, in the early organisation, in the formation of various committees, especially the International Programme Committee, in charge of its multiple activities. Since about a decade a doubt has been expressed as to whether such gigantic congresses (with around 4000 participants) still have the meaning and the impact they should have. One should keep in mind here the extraordinary quantity of energy which needs to be mobilised, as well as the amounts of money necessary both for the organisers and the participants. Some have discussed the opportunity of holding an international congress basically located in one city, but with various meetings taking place simultaneously in other parts of the world and interconnected for many of their activities. This would allow much opportunities for an adaptation to local interests of communities of mathematicians in many countries, without special expenses for them.
There are however two problems which appear to me much more important nowadays and which concern both ICMI and the International Mathematical Union (IMU), the mother organisation of which ICMI is a commission. These two problems should be at the centre of the regular activities of both bodies.
In my opinion, the main problem with which ICMI should be concerned, as an organism responsible for the health of mathematics education at a global level, as well as IMU, as an organism which has to attend to the good state of the mathematical activity, is the huge gap in many places around the world between those members of the mathematical community whose main activities are related to education, and those whose main occupation is the furtherance of mathematical research, be it oriented towards its more theoretical or its more applied aspects.
This situation is currently happening intensively and openly in the United States, where direct confrontations are having serious repercussions on the educational policy not only of various states in the country, but also in a subtle way in other countries as well. Including for instance my own country, Spain.
For a number of years, a traditional standpoint adopted by the community of those involved in mathematical research (especially university faculty) towards theoretical and practical pedagogical issues, which are of deep concern to another important segment of the mathematical community - such as mathematicians interested by the processes of mathematical learning or those interested in their daily tasks in identifying ways to facilitate this learning at any level -, has been to look at those issues with contempt. Maybe they disregard pedagogical studies and occupations on the basis that they constitute a field of second or third category, where it is very easy to decide at any time what are the appropriate options and where one who has taught for a few years has as much authority as anyone to express a valid opinion.
The danger of such an attitude is clear. A deep gap in the mathematical community benefits to no one, neither to those interested in the progress of mathematical knowledge of one type or another nor to those concerned by its transmission at any level. And even less, clearly, to a sound understanding of what mathematicians do and what is mathematics education. But above all such an attitude would be probably most detrimental to the younger generations, because of the resulting confusion regarding the panorama of mathematical activity.
And the possibility, dangerous in my opinion, that ICMI could split into an organisation without special links to IMU, is not negligible. For many years before IMU existed, ICMI had a relatively vigorous life, in spite of the events of the World Wars and other obstacles.
What could ICMI and IMU do? They should deal with things as they currently are in reality through the consensus for which a certain moment in the history of both organisms is heading. Let each of those bodies help the other accomplish its duty in a true spirit of assistance, collaboration and understanding. ICMI is the education commission of IMU and it would be most reasonable that such a situation be fully recognised, for instance in the International Congresses of Mathematicians (ICMs), the international congresses of IMU, or in other occasions where activities having to do with mathematics education are being organised.
Clearly ICMI should strive to encourage the participation in the ICMs of members of the mathematical community more closely linked to education, so that quite a number of mathematicians of this type could be seen at these congresses. But still more clearly IMU should strive to stimulate the presence in the ICMEs, the congresses on mathematical education, of those mathematicians interested in educational issues at any level and especially at the tertiary level, those mathematicians combining their research duty with their teaching duty. I believe that it is many ICMEs ago that a President of the IMU has for the last time attended one of these congresses, a fact which I see as quite significant.
The second problem which, in my mind, should constitute a permanent preoccupation on the agenda of both ICMI and IMU is the solidarity between countries on matters pertaining to mathematics education. The manifesto which marked the beginning of the organisation of the World Mathematical Year 2000 (WMY2000) pointed out quite rightly that mathematics education is these days one the indicators of the possibilities of progress of countries. Being responsible for the health of mathematics education at the global level, ICMI should consequently make as an aim of its activity that the mathematical communities of all countries should help one another intensively, for example by trying to foster in the more developed countries, on mathematics education matters, an attitude of exchange and assistance with those countries which could benefit from such collaborations and which would eagerly desire them.
The launching of the Solidarity project of ICMI, during the Québec ICME congress in 1992, was only a timid beginning of what needs to be done. It is true that a few countries, through their ICMI National Sub-commission, have responded with enthusiasm and generosity. Such is the case for instance in France, especially in connection with its contacts with various African countries. Also in Spain there has been in recent years a rather strong and well-organised trend towards a cooperation in matters of mathematical education with several Spanish speaking countries.
But I firmly believe that what we are doing is for the moment very insufficient. I think that ICMI should take the initiative in such an important and necessary task at all levels. This is, to my mind, one of the most appropriate goals for ICMI to work now and in the future.
Miguel de Guzmán
Past ICMI President (1991-98)
Facultad de Ciencias Matemáticas
28040 Madrid SPAIN email@example.com