The ICME organisation has been around for almost 100 years, exchanging current ideas and theory between mathematicians involved in education. Its principles are anti-discriminatory and based on mutual respect for fellow professionals around the world.
There were many similarities of concern within the international perspective at this year's conference: curriculum content; equality of access to appropriate technology; learning that provides openings to future development; cultural and social issues; maths as more than just a tool kit for a specific, limited, working environment.
The atmosphere was one of listening, learning and sharing - international research findings, new perspectives and theoretical understanding. Indeed, accurate and carefully regulated research seemed to be the focus of many participants' interest.
As a teacher at a school for pupils with educational and behavioural difficulties, I was particularly interested by a study group I attended on special needs issues. It dealt with work done with Indian children of "Untouchables" - literally first-generation learners; with different approaches to low achievers in Germany, France and Switzerland; and with strategies for improving teachers' skills with US pupils with learning disabilities.
Among the opportunities to talk with delegates from around the world, I spoke to a Japanese high school teacher who had conducted his own research in both Japanese and Australian schools, which revealed pupils' lack of basic knowledge about each other's countries; his concerns reflected in microcosm those of the conference as a whole. Looking at each country's "performance" in maths as if it were to be graded on some vast international league table is neither constructive nor beneficial to maths education.
We need to share inter-national research, rather than indulge in inward-looking competitiveness. Similarly, politically motivated demands for instant results and mechanistic learning procedures are an obstacle to real understanding; this was reflected in the experiences of speakers, many of whom were up against considerable pressure to "conform".
As I attended the lectures and listened to the various perspectives on "how, what and why", I began to understand the vital role I play as an ordinary classroom teacher. It was echoed throughout the conference: research must focus not on theories and ideologies but on ways of supporting and training individual teachers and improving the quality of interactions in the classroom.
Maths educators, across professional hierarchies, areas of specialisation and national borders, are a cohesive, united body of people. The obstacles we face are divisive: short-sighted political interventions, shallow, quick-fix approaches and any attempts to judge our work by standards other than those of real learning and understanding for all pupils. It is our unity of purpose that creates the quality of the results we achieve.
NICK O'NEIL Nick O'Neil is maths co-ordinator at Falcone EBD school, Hertfordshire SECTION:Features NO PHYSICAL FILEIn the state of California a vigorous "back to basics" movement led by a number of maths professors is forcing a new curriculum on schools. All schemes must be approved by panels of mathematicians from which teachers and teacher educators are excluded. This curriculum has caused such controversy that one teacher is on hunger strike, and others are walking out of compulsory in-service training en masse. Other US states seem to be following suit and the atmosphere among the US delegates at ICME-9 in Tokyo was distinctly edgy.
At the heart of the debate are two schools of thought about maths: the "Platonic" focuses exclusively on the nature of maths and argues that if this is taught directly and clearly then pupils will understand it. Only standard methods of calculation need to be taught, and they just need to be taught well. Even if pupils do not understand at first they will gain understanding through repeated application of the techniques.
The other, "constructivist" view is that pupils construct their understanding of maths as they learn to use it to make sense of their own experience. So its adherents emphasise investigation and believe in a wide exposure to methods of calculation - especially those that build on mental images and mental methods.
Both sides of this argument are appealing to "equity", what we in the UK call inclusion. The particular needs of Hispanics and other minorities are at the heart of the debate. Each side feels that the other is putting such groups at a disadvantage. The back to basics movement has emerged as a sharp reaction to the implementation in 1992 of a curriculum that appeared to endorse the constructivist approach. Some believed that standards were falling. The Platonic view also fits in with the fundamentalist religious right wing views such as creationism The swing from one extreme to another has led to confusion.
We have managed to avoid a similar war in the UK. Some five years ago a group of university mathematicians published concerns through the London Mathematical Society. Dialogue was quickly established largely through the good offices of the Joint Mathematical Council and the Royal Society. A working group (of which I was a member) looked at the key issue of algebra. This had a major impact on Curriculum 2000, leading to greater clarity on the development of manipulative skills. A similar group is working on geometry. In these ways a practical and sensible understanding is being reached. I believe California needs what we have achieved - a fusion of both positions.
Maths is an absolute (as the Platonists assert). But it is precisely this "otherness" that makes sensitive teaching so important. Those who found their school maths easy, as the Californian professors did, may not be best placed to design education for everyone. Equally (if some of the talks at ICME are representative) some constructivists seem only to have a tenuous understanding of maths. The Californian testing regime fits with rote learning better than ours and may well improve. History will judge whether their thinking and learning skills improve in the medium term.
Robert Barbour is county mathematics inspector for Worcestershire