The members of ICMI are neither individuals nor organizations, agencies, etc., but countries. Member states are of two categories.
All the countries which are member states of 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, CM, to be responsible for the executive aspects of the relations with the IMU.
However, ICMI may, with the approval of the Executive Committee of IMU, co-opt on an individual basis, as so-called non-IMU members, countries which for some reason or another are unable to join the IMU. In considering a non-IMU country?s application for membership in ICMI, the ICMI Executive Committee places emphasis on evidence of coordinated involvement of the major relevant interested parties in mathematics education within the country at issue, such as organizations of university and research mathematicians, of researchers in mathematics education, of mathematics teachers, and so forth, 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 AO of that country with respect to ICMI.
There are currently 72 members states of ICMI. Each member state, whether an IMU country or not, is entitled to appoint a National Representative.
ICMI, as a commission, is defined by two constituent components: the Executive Committee (EC) of ICMI, elected by the General Assembly of IMU for a four-year term, and the ICMI Representatives of the member states, 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 year in conjunction with the quadrennial International Congresses on Mathematical Education (ICMEs). Representatives of the so-called ICMI Affiliated Study Groups are invited to attend the GAs without the right to vote.
In quite a few countries, national Sub-Commissions of ICMI have been established with the dual purpose of providing an organized forum for exchange of information and for dealing with issues of mathematics education at a national level, and of offering an interface between that level and the international mathematics education community as represented by ICMI. In cases when a national Sub-Commission exists, the National Representative to ICMI is one of its members, often the chairperson of the Sub-Commission.