France is way ahead when it comes to maths teaching and the country has a surplus of specialist teachers.
Maths is compulsory at all levels and is the key subject of the scientific baccalaureate which is widely regarded as a prerequisite for selection to the grandes ecoles, the elite higher education institutions.
The aim of the IREM (Instituts de Recherche sur l'Enseignement des Mathematiques (research institutes for mathematics teaching)) is to help pupils understand maths through research into teaching methods. They bring together teachers from schools and universities to collaborate and learn from each other.
The first IREM was established following the student riots of 1968. As a modernised maths curriculum was introduced into schools, institutes were set up in Paris, Lyon and Strasbourg to organise teacher training programmes and produce publications and support materials.
Today there are 28 institutes in France and others in Belgium, Luxemburg, Latin America and Morocco. The IREM is based in university maths departments, has links with education authorities and teacher training institutes and works closely with outside bodies.
The network is headed by ADIREM, the elected assembly of IREM directors. A scientific committee oversees IREM activities such as evaluating publications, monitoring projects and organising debates and conferences.
Fifteen commissions cover the institute's areas of interest. As well as one each for levels of education from primary to university, they include didactics, geometry, epistemology and history of maths, maths and computer science, maths and experimental science, statistics and probability. The Maths in Europe commission conducts comparative studies of maths teaching, while Publimath compiles a data bank. Research areas include integrating new technologies in maths teaching, curriculum changes, introduction of multidisciplinary projects for lycee pupils, analysis of new teaching methods and improving consistency between teaching of maths and other subjects, such as physics.
Each year some 15,000 maths teachers, mostly from secondary schools, follow IREM training courses lasting one to three days. About 1,000 teachers and academics work as IREM organisers.
Marc Legrand, chairman of ADIREM, says: "Essentially, it is training by research. Small groups of secondary and university teachers together think through teaching problems, experiment in the classroom, publish papers or articles and organise courses with other colleagues."
A valuable part of the IREM experience, he says, is removing teachers from the classroom. Teachers discover that instead of dominating a class it is important to hold back, encouraging pupils to take the lead, present their ideas and discover error through debate and experimentation.
Secondary schoolteacher Thomas Lecorre, an organiser at Grenoble IREM for four years, works with fellow organisers every fortnight during the school year. Groups work on different themes, and two weekends a year attend seminars to present their latest research.
He says the IREM "distance approach", helped by collaboration with academics who specialise in didactics, has led to success in classes "where it was thought there was no more hope", by "realising that how pupils perform is the consequence of the teaching methods we choose". Now he lets "pupils take over the situation, ask questions, find the limits of their former interpretations. In this way they can honestly see the need to re-think their old ideas and accept a new way of thinking which is not imposed by the authority of their teacher, but for reasons they have understood".