The IREM Network : Mission, Work, Functioning

Regine Douady and Michel Henry

1. Mission

The Research Institutes on Mathematical Education (IREM, Institut de Recherche sur l'Enseignement Mathematique) were created in France, starting in 1969 with the following mission:

There are 26 IREMs in France, including one in Antilles-Guyane.

An IREM has two original features:

The CII gather members of various IREMs interested in the same theme or problematique.

The CS assists the Assembly of the Directors of the IREM (ADIREM) in formulating its scientific policy, in making decisions and in following and assessing the work of the CII.

The activity of the IREMs has evolved significantly since their creation. In order to accompany the reform of the mathematics curricula known as "modern mathematics", research and training were at first guided by the dual necessity of retraining (bringing further mathematical information to high school and elementary school teachers) and innovation. The IREMs turned out to be the places where the serious difficulties to which the reform initiated in 1967 led, were detected and analysed. In that context IREM members from all teaching levels realized that a deep and scientific study of the learning process and the relationship between teaching and learning was urgently needed. In this way the IREMs contributed to the further development of the mathematics curricula in France.

The IREMs are places where teams are formed and meet. The activity of an IREM mainly develops in working groups formed around themes such as the Didactics of Mathematics, the Epistemology and History of Mathematics or the use of New Technologies. The work of these groups leads to the writing of papers or booklets, or provides the material for teacher training courses organised by the IREM. With time, these publications have become an impressive stock pile of multi-faceted work, widely circulated.

In 1984, the ADIREM temporarily created a scientific council in order to assess the work of the IREMs. Its report, published in 1985, is an important document which emphasises the special nature of the research done in the IREMs.

2. Work

2.1 Study and research

The diversity of the work of the 26 IREMs and the 14 Inter-IREM Commissions gives rise to studies which differ strongly in form, content and purpose. These studies lead in particular to

This work by professional researchers together with practising teachers is oriented in three directions:

a) The teaching of mathematics

The form and content of mathematics teaching are constantly developing, sometimes continuously, sometimes with breaks. The traditional practice of mathematics teaching - definition, proof, application - despite its didactical interest (mathematical rigour and economy of time, at least) often conflicts with the need to give meaning to mathematics and with the expectations of the students. The teaching of geometry is an important case: The autonomy of the students and the use of activities are now frequent. This poses specific and complex didactical problems. These problems are analysed by experimentation in secondary schools.

Such work offers mathematics teachers a rich source of documentation. In this way, since 1986, every new high school curriculum has been accompanied by the publication by the IREM network of so called Suivis Scientifiques: Books used by nearly half of all high school teachers.

The resulting studies form the starting point of further research leading to proposals for the adaptation of curricula or teaching methods. Various authorities collect and, directly or indirectly, make use of them.

b) Epistemology and History of Mathematics

The aim of the work in these areas is to determine under which conditions mathematical knowledge was constructed. Such work generates numerous themes for mathematical activities which are very successful with teachers. Epistemology also brings substantial insight into certain difficulties that student have, through studies of the obstacles which occurred in the creation of such and such concept or theory. The publication of several books and handbooks for teachers testifies to the vitality of this section of the work of the IREMs.

c) The Didactics of Mathematics

The study of the processes and phenomena involved in the teaching of mathematics, in the teaching-learning relationship, and in classroom situations have been developing for twenty years or so. These studies could take advantage of the extensive experiments conducted by the IREMs, and of the questions raised by their members or in teacher training. Many PhDs have been carried out in the IREMs.

2.2 The links between research and training

Links between research and training are close. Such links do not emerge spontaneously. The practice known as "recycling", based on the idea that teachers could rely on the mere transmission of skills already mastered by experienced teachers, was a failure. It turned out that the questions for which teachers have concern do not have simple answers: the content of training courses has to be developed constantly, whether from mathematical, didactical or epistemological perspectives.

Nowadays, part of the training consists in developing the teachers' conceptions of what it means to do math, to know math, to teach, or to learn math. This requires that those undergoing training be actively involved in the training project and in the research associated with it. This does not imply that all training necessarily has to start with research, rather that research is an essential element in the training process.

The IREMs attach great importance to this training by research. The position of the IREM working groups enables them to proceed in this dual activity of research and training, each nourishing the other. The link between research and training takes a long time to establish. This is due to the nature of the process and of the work to be done (respect for protocols when an experiment is being carried out, analysis of the results, inquiries...). A little training from time to time does not lead to fundamental and lasting improvement in teaching.

2.3 Training

a) Qualifying initial training

With variations which take the local situations into account, the IREMs contribute to the formulation of the university curricula for the training of mathematics teachers. In some universities, the IREMs take part in the vocational teaching, approaching the problems which arise in the teaching of mathematics, presenting the basics in didactics, history and epistemology of mathematics. They organise observation sessions in high schools math classes for university students. They take part in the preparation of the recruitment competitions and in the training of future teachers of mathematics.

b) In-service training

In-service training is provided in various ways:

The IREM arrangements are directed not only to teachers in secondary schools, but also to the training of elementary school teachers, and sometimes to the young staff in the universities, to mathematics inspectors, and even to administrators of the national educational system.

In all studies or activities referred to, the mathematical content is the backbone and the generator of significance. A narrow and regular collaboration with university mathematicians is needed.

3. The writing and circulation of publications

The IREMs make their work available to teachers by producing publications: regional publications, nationally distributed journals and booklets, books issued by the Inter-IREM Commissions, issues of Reperes-IREM. Among the regional output, let us mention:

Some IREMs publish nationally circulated periodicals, such as Petit x and Grand N in Grenoble, or les cahiers de DIDIREM, documents pour la formation and Mnemosyne (a journal on the history of mathematics in relation to the classroom) in Paris 7, or Annales de Didactique des Sciences Cognitives in Strasbourg. Other journals are published in collaboration with the Association of Mathematics Teachers (APMEP), such as l ouvert in Strasbourg, Plot in Orleans and the EVAPM collection in Besancon.

The publications of the CII have gradually gained more and more importance. They include new texts and selections of local publications. Their connection Bulletins are turned into books distributed nationally by the IREMs or sold commercially, like Mathematiques au fil des ages or histoire de problemes or histoires d'algorithmes.

In order to provide the Inter-IREM publications with some homogeneity and a standard of scientific quality, the ADIREM has established certain terms of reference: there has to be an editorial board, the work has to be supervised by a scientific committee, and the deadlines have to be planned. The proceedings of the Inter-IREM meetings fit into this category. Let us mention L'histoire de la demonstration, La Geometrie, L'enseignement de la statistique en classe de techniciens superieurs.

The journal Reperes-IREM is distributed to more than 2000 subscribers and the IREMs sale separate issues. The ADIREM has set up a permanent editorial committee of 12 people who carry out a demanding review of every paper. The balance between the themes dealt with, the dimensions and the richness of the papers, and their lists of references, make the collection of Reperes-IREM an outstanding tool for the pre- or in-service training of teachers as well as for the development of research in mathematics education.

4. Influence of the IREMs and assistance to development

The IREMs produce exhibitions, organise or are involved in mathematical competitions and rallys, take part in creating or developing teaching software, whether graphic or not, publish documents to assist teaching, sometimes with the use of new technology. So, consultation or decision authorities, such as Ministry Departments, the General Inspection, institutional working groups or commissions, have at their disposal lots of thoughts and ideas stemming from numerous sorts of work.

The meetings of the Inter-IREM Commissions, open to teachers of all levels, are places where researchers and trainers may report on their progress and exhange experiences and views. The reports of the meetings offer an opportunity to follow the current development of work on mathematical education.

The national activities of the IREMs enable this network to be present on the international scene. In this way, the IREMs have established relations with numerous similar institutions in other countries. This cooperation takes various forms, such as joint studies, invitation to courses, lectures in teacher training institutions, construction of curricula, participation in international assessment.

Some IREMs organise or participate in teacher training courses in cooperation with other countries, for instance in Africa. Courses may take place in France or in the partner country. Among international activities, let us mention just a few:

The IREM network is active in international congresses (ICME, PME, HPM,...) on mathematical education, through special publications and presentation of some of its work, and through active participation in working groups.

The IREMs are known outside the circles of French public education, for instance in vocational training. This is reflected in various ways: through the use of IREM documents, requests for training courses, research contracts and so forth.

These national and international dimensions of the activities of the IREMs are made possible by the anchoring of the IREMs in the university community.

5. Functioning

From an instituational point of view, an IREM is a unit in a university, in connection with the department of mathematics of this university. It also maintains relations with the various ministry services which deal with primary, secondary or university education.

The activities of the IREMs are coordinated by the ADIREM (the assembly of the directors of the IREMs) assisted by the CS (the scientific committee). Every IREM is directed by a member of staff in the university to which it is attached. It is governed by a board composed of members of the institute, and representatives of the various institutions with which the IREM cooperates.

Concerning the IREM members, the non-university ones are mathematics teachers of all levels. Colleagues in other disciplines occasionally collaborate as well. A member employed in a school is usually exempted from or compensated for a few hours per week for his/her work in the IREM, with funds provided directly or indirectly by the Ministry of Education. For the university members, the resources in terms of working time come from university positions created especially for the IREM or put at its disposal.

Administrative or technical positions, in particular librarian ones, have been created in the universities and been made available to the IREMs. As far as funds are concerned, these are distributed each year by the directorate of university teaching in the Ministry of Education according to a proposal made by the ADIREM. Within its university, each IREM is fully responsible for the management of its own budget. This financial autonomy allows for quick decision making. Funds are utilised for activities such as publishing, travels to seminars and national meetings, editorial work, renewing computers, printing facilities etc.

Thanks to its university status, every IREM enjoys great autonomy and works according to its own schemes. In particular, researchers are recruited by their peers for research teams, which is an essential feature. The management and the definition of research aims by the staff themselves (within the necessary administrative regulations) form another basic condition for the development of research.

The status of the IREMs as an internal service in the universities accounts very much for the extent of their achievements, as well as for the progress of knowledge on mathematical education in France. This makes France a reference country in the community of this discipline in many countries.

The organisation chart presented below brings to the fore the complexity of the IREM network and of the links it maintains with various partners. (This chart is not included in the electronic version.)

Regine Douady, President of ADIREM,
Director of IREM, Universite de Paris 7,
2, place Jussieu,
75251 Paris cedex 05, FRANCE

Michel Henry, President of CS
Universite de Besancon
16, route de Gray-La-Bouloie
25030 Besancon cedex, FRANCE

Explanation of the abbreviations in the organisation chart:

APMEP: Association des professeurs de mathematiques de l'enseignement public
IUFM: Instituts Universitaires de Formation des Maitres
MAFPEN: Missions Academiques de Formation Continue
Rectorats: Regional representatives of the national Ministry of Education
SFCIEM: Sous-commision francaise d'ICMI
SMF: Societe Mathematique de France