Members of ICMI are neither individuals nor organizations, but countries. There are two categories of membership the first being countries that are members of IMU and the second being countries specifically co-opted to the Commission.
All member countries of IMU automatically become members of ICMI. The Adhering Organization (AO) of a country (typically the academy of science, the mathematical society or similar institution) monitors the membership of IMU for a given country. The AO appoints a Committee for Mathematics to be responsible for the executive aspects of the relationship with IMU. Relations with ICMI are the responsibility of this Committee, or of the Sub-Commission for ICMI (see below), when it exists.
The second category of ICMI members consists of countries that are not IMU members. With the approval of IMU's Executive Committee, ICMI may, on an individual basis, co-opt countries that are unable to join IMU. When considering an application for membership from a non-IMU country, the ICMI Executive Committee looks for evidence within the country seeking membership of coordinated involvement from major parties in mathematics education, such as organizations of university and research mathematicians, researchers in mathematics education, teachers of mathematics, and so on according to the specific circumstances. If the application is successful, a body (normally the body responsible for the application) will be identified as an equivalent of the country's AO with respect to ICMI.
There are currently more than 90 member countries of ICMI, more than 80 of which are also members or associate members of IMU. Each country, whether an IMU member or not, is invited to appoint a Representative to ICMI, who acts as a liaison between ICMI and the mathematics education community in the country. These representatives elect the ICMI Executive Committee (on a quadrennial basis) during the ICMI General Assembly.
In a number of countries the Sub-Commissions of ICMI have been established with two purposes. The first is to provide an organized local forum for dealing with issues of mathematics education and for the exchange of information related to mathematics education within the country. The second purpose is to offer an interface between the country and the international mathematics education community as represented by ICMI. The Sub-Commission includes among its members the Representative to ICMI, who is often the chairperson.
All members of the International Mathematical Union (IMU), are automatically members of ICMI. But it is also possible for a country not a member of IMU to become a member of ICMI. (Information on this matter can be obtained here or from the Secretary-General of ICMI.)
There are currently 93 member countries of ICMI, 73 of which are also members of IMU and 8 are associate members (am) of IMU. In the following list, (*) indicates one of the 12 members of ICMI that are not members of IMU.
Each member country of ICMI shall appoint a representative to ICMI.
This appointment is the responsibility of the IMU Adhering Organization, for those countries which are Full or Associate Members of IMU, and of the ICMI Adhering Organization and the mathematics education community of the country, for the other countries co-opted under item (8) in the ICMI Terms of reference.
Given the responsibilities of the CR, it is advisable that the IMU Adhering Organizations consult with prominent members of the local mathematics education communities. Representatives for countries with no IMU adhering organizations are appointed by the mathematics education community of the country.
A representative cannot not serve for more than two consecutive four-year terms (Kobe Rule).
Each member country of ICMI shall appoint a representative to ICMI. This appointment is the responsibility of the IMU Adhering Organization, for those countries which are Full or Associate Members of IMU, and of the ICMI Adhering Organization, for the other countries co-opted under item (8) in the ICMI Terms of reference. A representative cannot serve for more than two consecutive four-year terms. (Kobe Rule). For a list of the IMU Adhering Organizations and contact information please go here: http://www.mathunion.org/membership/imu-members
With the aim of extending and consolidating the network of mathematics educators and mathematicians within and between countries, the Executive Committee of ICMI encourages the establishing of Sub-Commissions for ICMI in the member countries. In quite a few countries, such ICMI Sub-Commissions have been established, in some cases many years ago.
According to item 5 of the Terms of Reference for ICMI, the establishing of a Sub-Commission in a country requires acceptance by its Adhering Organisation, which is also to appoint (at least) one member of the Sub-Commission, who serves as the Representative to ICMI for that country and who is often the chairperson. Furthermore, a Sub-Commission should reflect in its membership all educational levels and domains pertinent to mathematics education in the country, including associations of mathematics researchers, university mathematicians, researchers in mathematics education, etc.
Experience shows that Sub-Commissions for ICMI serve to provide an organized local forum for dealing with issues of mathematics education and for exchange of information within the country, while offering an interface between the country and the international mathematics education community as represented by ICMI.
The following 16 countries have currently appointed a Sub-Commission for ICMI.