From time to time, ICMI officials are asked by people inside or outside of the ICMI community what ICMI is, what it does, and how it operates. Presumably, the majority of the readers of this Bulletin already have this information, at least in outlines. However, as the readership is changing, and in fact also growing, it might be worth giving a brief account of the basic aspects of these questions.
The International Commission on Mathematical Instruction, ICMI, was first established at the International Congress of Mathematicians held in Rome, Italy, in 1908. The first President was Felix Klein while the first Secretary-General was Henri Fehr. From the very beginning, L'Enseignement mathematique, founded by Fehr in 1899, was adopted as the official organ of ICMI, which it still is, in conjunction with this Bulletin. When the international mathematical community was reorganised after the Second World War, ICMI was reconstituted (in 1952) as an official commission of the International Mathematical Union, IMU. This is still the state of affairs. Thus, the Terms of Reference of ICMI are established by the General Assembly of the IMU which is also responsible for the election of the Commission's Executive Committee. Moreover, the far majority of the funding of ICMI comes from IMU. The fact that IMU is a member organization of the International Council of Scientific Unions, ICSU, implies that IMU, and hence ICMI, are to abide to the ICSU statutes, one of which establishes the principle of non-discrimination. According to this principle, scientists involved in activities under ICSU auspices have the right and freedom to associate in international scientific activity regardless of citizenship, religion, political opinion, ethnic origin, sex, and so forth. Apart from observing general IMU and ICSU rules and principles, ICMI works with a large degree of autonomy.
The members of ICMI are not individuals but countries. Member states are of two categories.
All those countries which are members of the IMU are automatically members of ICMI as well. The membership of IMU for a given country is monitored and controlled by a so-called Adhering organization, AO, (typically, the national academy of science, the national mathematical society, or suchlike) which in turn appoints a National Committee for Mathematics to be responsible for the executive aspects of the relations with the IMU.
Besides, ICMI, with the consent of the IMU, may co-opt, as so-called non-IMU members, countries which for some reason or another are unable to join the IMU. Co-option of a country takes place on the basis of an application submitted to ICMI by some body which is chosen to speak on behalf of the major organizations, societies, and associations of mathematics, mathematics teaching, and mathematics education research in that country. If the application is succesful, the applying body will normally act as an equivalent of the AO of that country with respect to ICMI.
ICMI, as a commission, is composed of two components: The Executive Committee, EC, and the National Representatives. The EC is elected by the General Assembly, GA, of the IMU for a four year term. The composition of the present EC can be found in the beginning of this Bulletin. The election of the next EC will take place at the GA of IMU to be held in conjunction with the International Congress of Mathematicians, in Berlin, Germany, in August 1998. The new EC will take office as of 1 January 1999. The National Representatives, both of IMU and non-IMU member states, are appointed by/ or on behalf of the AO or the CM of their respective countries. The EC and the National Representatives together constitute the General Assembly of ICMI which is summoned every four years in conjunction with the quadriennial International Congresses on Mathematical Education. Representatives of the so-called Affiliated Study Groups (see below) are invited to attend the GAs without the right to vote.
In quite a few countries National Sub-Commissions of ICMI have been established. National Sub-Commissions serve the dual purpose of (a) providing an organised forum for exchange of information and for dealing with issues of mathematics education at a national level, and (b) of offering a link between the national and the international mathematics education communities.
Every year ICMI has to file a scientific and a financial report of the activities of that year for the endorsement of the IMU. Both reports are published in the ICMI Bulletin. Qaudriennial reports are presented to the General Assembly of ICMI.
The ICMI EC publishes a semi-formal Bulletin twice a year, in June and December. For the time being it is edited by the Secretary of ICMI.
Since the mid-70's a number of study groups, each focussing on a specific field of interest and study, have obtained affiliation to ICMI as a so-called Affiliated Study Group. These are:
The Affiliated Study Groups are neither appointed by ICMI nor operating on behalf of or under the control of ICMI. In other words, they work independently, also in terms of finances, but produce quadriennial reports to be presented to the ICMI GAs. In addition to meeting in connection with the International Congresses on Mathematical Education, the Affiliated Study Groups hold separate meetings on a more or less regular basis.
Probably the most important of the activities undertaken by/on behalf of ICMI are the International Congresses on Mathematical Education, ICME, which are held every four years under ICMI auspices. So far 8 Congresses have been held since ICME-1 in 1969 (a 'irregular' year in the sequence). ICME-9, to be held in Makuhari near Tokyo, Japan, in 2000 is under planning. The scientific programme is planned by an International Programme Committee, IPC, which is appointed by but in principle working independently of the ICMI EC. However, in order to ensure continuity and conformity with general ICMI principles the ICMI EC normally has 1-3 representatives on the IPC. The practical and financial organization of the ICMEs are the independent responsibility of the Local (or National) Organising Committee, again under the observation of general ICMI principles. In other words, it is not ICMI as such which is organising an ICME, neither in terms of the scientific nor of the practical aspects of the Congress. In spite of that, all ICMEs are held under ICMI auspices.
Since the mid-80's ICMI has invested a considerable and increasing effort in mounting the so-called ICMI Studies to deal with key issues or topics of particular significance to contemporary mathematics education. An ICMI Study may give emphasis to either analytical or action oriented investigations but some analytical component will always be present.
The typical scheme for an ICMI Study is as follows:
The ICMI Study themes are decided upon by the ICMI EC. Once a theme has been chosen, the EC appoints a fairly small International Programme Committee which on behalf of ICMI is responsible for conducting the Study. Usually a country which is willing to host the corresponding Study Conference has been identified concurrently with the appointment of the IPC.
The first task of the IPC is to produce a Discussion Document in which a general problematique, a number of key issues and sub-themes related to the theme of the Study are identified, presented and described in a preliminary way. The Discussion Document is then published and circulated internationally as widely as possible in journals, newsletters, institutions, etc., including L'Enseignement mathematique and the ICMI Bulletin. Readers are invited to react to the Discussion Document by sending abstracts of papers, proposals, raising issues etc.
On the basis of the submission received and the deliberations of the IPC, the next step is for the IPC to invite a limited number (50-100) of individuals to participate in an invited Study Conference, organised by the IPC. This conference will form a working forum for investigating the theme of the Study. Particular emphasis is given to bringing together both experts in the field and newcomers with interesting ideas or promising work in progress, as well as to gathering representatives with a variety of backgrounds from different regions, traditions, and cultures.
The final outcome of an ICMI Study is a Study Volume, published in the ICMI Study Series (edited by the President and the Secretary of ICMI). An ICMI Study Volume is a carefully structured and edited book, not a conference proceedings. The editors are sub-set of the IPC, normally with the Chair as the editor-in-chief. Sometimes, however, also a conference proceedings is published in addition to the Study Volume.
For further information about recent and forthcoming ICMI Studies, please see elsewhere in this issue.
In 1992 ICMI, on the suggestion of its President, Miguel de Guzman, established a Solidarity Programme to help the furtherance of mathematics education by means of research and development in countries where there is a need for it that justifies international assistance. The first stage in this programme was the creation of a Solidarity Fund based on private contributions from individuals, associations etc. The Fund is to be activated to support concrete initiatives that may foster solidarity in mathematics education between well-defined quarters in developed and less developed places in the world.
In addition to the international activities conducted under direct ICMI involvement, ICMI from time to time sponsors Regional Conferences in different parts of the world. So far the majority of regional conferences have been held in East Asia and Latin America. A regional conference is organised at a regional level and on a regional initiative. On certain conditions the organisers may apply for ICMI sponsorship of their conference. Normally such a sponsorship is of a moral rather than of a financial nature. To the extent ICMI provides financial sponsorship as well (which can only happen with conferences held in non-affluent countries), the funding is merely symbolical.
The above-mentioned activities are of a more or less regular nature. In addition to those, ICMI sometimes involves itself in irregular activities on an ad hoc basis. For instance, ICMI is involved in planning parts of the World Mathematical Year 2000 activities. Also, ICMI is normally involved in planning some of the items on the programme of the International Congresses of Mathematicians, the ICMs.