On 1st January 1999 the members of the new Executive Committee of ICMI, elected in Berlin last August by the General Assembly of the IMU, will start their term. For all the members of the outgoing Executive Committee is an honour to be succeded by persons as eminent as the members of this new team. For us, in particular, it is a pleasure to be substituted in our respective positions by collegues as qualified in the fields of mathematics and of mathematics education as Hyman Bass and Bernard Hodgson, the new President and the new Secretary, respectively. We are certain that they will be able to perform, with great efficiency, the tasks of which the international mathematical community has appointed them to be in charge.
We would like to use this opportunity first of all to thank, in our own name and on behalf of the International Mathematical Union, - and thus on behalf of the whole international mathematical community - for the magnificent work of collaboration done by all the members of the two successive Executive Committees with which we have had the pleasure to work during the past eight years. The constant spirit of understanding and collaboration has made the task of all of us very pleasant and, we hope, also reasonably fruitful.
We further wish to recall with thanks the continued and enthusiastic collaboration of the groups affiliated to ICMI, of the National Representatives which whom we have been in contact, of the different national subcommissions of ICMI, and of the many people who have served on the numerous committees that have been working so efficiently to organize the many congresses and meetings of all types which have been held under ICMI auspices, such as the ICMEs, the ICMI Study Conferences, regional meetings, and so forth. We also would like to thank the many national mathematical societies, of different kinds, which have offered their continuous help in the organization of a multitude of events contributing to the ever expanding activities concerning mathematical education. The list of individuals and organizations that have contributed to ICMI related activities during the past eight years would be very long indeed. To all of them we here extend our sincere thanks.
We wish to use this occasion to briefly present our reflections with particular regard to some of the main activities in which ICMI has been engaged during the two terms of our offices. We think this may be useful in order to explore possible further developments of ICMI in the future.
During this period ICMI has experienced a considerable expansion in many different respects. The number of Member States has increased from 59 to 72 and is still increasing. But, even more importantly, the organization in different countries of the ICMI Subcommissions has proven to be a very efficient instrument for strengthening the ties of the different countries with ICMI. In our opinion, this might well, in the future, serve as the ordinary structure of connection between each of the Member States with ICMI, more operative and reliable than the single person delegations which has been the tradition for a long time. The experiences with the organization of the national ICMI Subcommissions in some countries could serve as models or sources of inspiration for other countries where the old way of representation is still in use.
It has been our constant intention throughout our terms to try and make of ICMI a truly international organization, in which the traditional influence and dominance of specific cultures in the field of mathematical education could be balanced with a healthy development of initiatives and activities in countries which, until recently, had only limited opportunities to establish this field as an important focus of attention. The last two Executive Committees have made a serious effort to look for new places and new countries in which different activities related to mathematical education could be set up, as well as for new people to serve on the different bodies charged with the organization of such activities. We think that this policy has been and will continue to be rather fruitful for the future of mathematical education in the entire world, even if the pursuit of it might, from time to time, run the risk of not achieving all the ideal goals if viewed from the perspective of some established quarters. We have tried to achieve the goal of broadening the scope and platforms of ICMI related activities through a careful choice of the venues of congresses and meetings organized under ICMI's auspices, and through a balanced selection in all regards (to the extent this was within reach of the ICMI EC) of the persons involved in the organization of such meetings and events.
During our terms a considerable amount of efforts has been invested in continuing the lines of action initiated during the 80's by the previous ECs, under the leadership of Jean-Pierre Kahane and Geoffrey Howson, concerning the ICMI Studies. These studies, each of which includes a correponding ICMI Study Conference, have become essential instruments for ICMI to influence the trends in mathematical education. The foci of attention of these studies have been greatly expanded, now ranging from studies with a socio-educational component, such as "Towards Gender Equity in Mathematics Education", to content-oriented ones, such as the "Perspectives on the Teaching of Geometry in the 21st Century", and including studies related to research in mathematics education, such as "Mathematics Education as a Research Domain: A search for Identity", to mention only the most recent completed studies. A remarkable expansion of the action of ICMI is represented by the two ongoing studies on 'The Role of the History of Mathematics on the Teaching and Learning of Mathematics", and on "Teaching and Learning of Mathematics at University Level". One can rightly say that the ICMI Studies have become a place of reference for the whole mathematical community.
The field of influence of ICMI has become manifest also through the continuously increasing number of participants in the quadriennial International Congresses on Mathematical Education (the ICMEs), one of the most important activities of ICMI. At ICME-6 (Budapest, 1988) there were about 2500 participants, at ICME-7 (Québec, 1992) about 3300, and at ICME-8 (Sevilla, 1996) their number was close to 4000. But even more important and satisfactory than the number of participants is, in our opinion, the fact that the number of participants from many countries which until recently were not represented at all in events like the ICMEs, has increased considerably increased. This was, for instance, a very remarkable feature of ICME-8.
One reason why this has been made possible is the impact of the Solidarity Program and Fund for Mathematical Education set up by the EC at the time of the ICME-7 (Québec, 1992). The response of many individuals and of numerous mathematical societies and other organizations from different countries has been a model of a true spirit of international solidarity. We believe that this line of development may be one of the main tasks of ICMI to pursue for the future. Although some activities have already taken place under the umbrella of the Solidarity Fund, it seems to us that the Solidarity Program has far from reached its ceiling, and it will be necessary and worthwhile to look for imaginative ways to develop its field potential. In this respect, the incoming EC has an important task to face.
There is a particular point with which the outgoing EC feels rather satisfied. It is fairly obvious that the work done by ICMI, in cooperation with the organizations that has collaborated with it, has enjoyed increasing acknowledgement within the mathematical community at large during the last decades, particularly so by people working in mathematical education. A testimony of this recognition is the increasing number of requests by a variety of mathematical organizations to obtain some kind - mostly just moral - support from ICMI. To be related to ICMI some way or another has become a sort of seal of guarantee of solidity and quality in mathematical education.
Of course we would not want to claim that there has been no problems and difficulties during our terms. In fact there has - of course - been several minor and also a few major problems. But there is one particularly serious problem that we would like to comment on in some detail. It probably has to do with the degree of complexity that mathematical education and the mathematical community have now reached, and we feel that, in spite of the efforts of the present and the past ECs, we have not been able to cope with the problem in a satisfactory way.
The mathematical community is now a rather heterogeneous world. Within it, several different subcommunities and subcultures co-exist whose views on mathematical education sometimes do not agree, sometimes even strongly disagree. So, their relationships are not always as smooth as one would have wished them to be. First of all there is the immensely numerous group of teachers and professors at all levels who are directly responsible for tasks connected with the teaching of those aspects of mathematics which are currently considered the most appropriate ones to be learned. Then there is the large group of mathematicians engaged in the development and application of mathematics as a scientific discipline, either at universities or at other centers, institutions, organisations and companies. In recent times the very complexity of mathematics education has given rise to the emergence of a large group of people who devote themselves to the scientific and scholarly investigation of problems in mathematical education. Of course one could distinguish other groups of people engaged in different tasks within the mathematical community. Such distinctions do not exclude an individual from being members of several different groups at the same time. Many of us are.
Especially at times of transition, reform and lack of clear definitions regarding the best ways to bring about mathematical education, many different points of view related to the diverse situations and problems that mathematical education is confronting do arise, and have to arise. To these differences in view correspond, in a natural way, tensions not only between individuals but also between the different mathematical subcommunities. The life of ICMI, as a commission for mathematics education within the IMU, has been affected in significant ways and extents in the past by such conflicts and tensions, and may continue to be so in the future, unless we are all able to take appropriate measures to counteract them. We are convinced that it will be very important for the future of mathematical education in the whole world that mutual respect and a deep sense of collaboration amongst the different individuals, quarters and subcommunities of mathematics be reached. This should lead to an appropriate and effective balance of influence in the process of taking important decisions. In our view we have not yet reached an ideal state in this respect, and we sincerely hope that the incoming Executive Committee will be able to lead the mathematical community dealing with the problems of education closer to such a state.
As a final and personal remark we, the outgoing President and Secretary, would like to emphasize that for both of us this eight year period of intensive work and dedication has been extremely pleasant and rewarding thanks to, among other things, the high degree of communication and mutual understanding between the two of us. Through our deep and continuous cooperation we have been able to confront many problems and periods of heavy work that could have been too strenuous in other circumstances. We wish for our successors that they will succeed in developing a similarly profund, rewarding and pleasant working community and friendship.
We leave full of confidence that the leadership of ICMI will be in very competent and skillful hands in the next term(s), and we have no doubt that ICMI's course in the future will be extremely fruitful for the whole mathematical community and its subcmmunities.
Miguel de Guzmán, President Mogens Niss, Secretary