Why are Japanese children so good at maths when they are taught in unstreamed, mixed-ability classes of up to 45? The British invariably attempt to explain this frustrating conundrum by arguing that Japanese teachers use rote-learning techniques, and that their pupils are far more compliant and diligent than children in the West.
But new research into the teaching of maths in Japan's lower secondaries for 12 to 15-year-olds reveals that this is far from being the whole truth.
Julia Whitburn, who watched maths being taught in eight Japanese schools, acknowledges that the country's teachers benefit from a culture that appreciates the importance of education to individuals and the nation. Furthermore, the belief that all children can succeed, provided they work hard, boosts pupils' self-confidence and means that a Japanese child is never heard to say: "I'm no good at maths".
But Ms Whitburn, who has been a maths teacher for 20 years, says that anyone looking for the secrets of Japan's scholastic success has to do more than point to Confucian ideals and count the number of hours that children spend with their maths textbook (which they are allowed to keep). School organisation and teaching techniques are also important contributory factors.
Space and time are used more efficiently than in most British secondary schools. Sometimes this appears to be taken to extremes - swimming pools are invariably built on top of school halls - but this approach often reaps benefits. There is, for example, less disruption when the end-of-lesson bell rings because the teachers, rather than the children, switch classes (the children get frequent breaks in the corridor outside their class).
"Other advantages which result from the use of a 'home room' include the easy identification of absentees, access for pupils to books in lockers if necessary, and the assurance of adequate provision of furniture," Ms Whitburn says. "Teachers in this country will be familiar with the problems of wasted lesson time fetching desks or chairs, sending pupils back to fetch books, or taking a register."
Japanese teachers also save time by asking children to mark their own homework in class while the answers are being worked out on the blackboard. This has the advantage of showing the pupil where and why mistakes have been made - in an unthreatening manner. "This contrasts strongly with the practice in England where teachers spend many hours a week laboriously marking exercise books, knowing full well that their often detailed and helpful comments will pass largely ignored by pupils who take far more interest in the final mark, " Ms Whitburn notes.
The use of standardised "teachers' guides" issued by the Japanese education ministry also means that staff do not have to spend hours preparing their own materials. The maths curriculum is not so tightly regulated that a ministry official can predict what is being taught on any given day - a boast that French bureaucrats could once make - but classes do proceed at a similar rate.
"Midway through the school year most ninth grade classes (14-year-olds), for example, will learn about the solution of quadratic equations," Ms Whitburn says. "The thoroughness with which this topic is taught, both algebraically (formula method, completing the square and factorisation) and graphically, may be contrasted with the more limited approach to the same topic commonly found in English schools."
She was also impressed by the way that new work is introduced. "The teaching progresses at a relatively slow pace, pitched slightly below that of the average pupil: teachers seem content to repeat and elaborate until a particular concept has been understood by the whole class."
This must, however, demand an almost superhuman level of patience in some schools because it is quite common for a single teacher to be asked to teach all the mathematics lessons to a particular year - a task that could involve teaching five classes of 14-year-olds for four lessons a week each. Ms Whitburn points out that this increases "consistency of learning experience", but concedes that this may be unattractive to many teachers. Most British teachers would call that an understatement.
"The teaching of mathematics in Japan: an English perspective", by Julia Whitburn, appears in the current issue of the Oxford Review of Education. The full text of her paper is available, priced Pounds 10, from Carfax Publishing Company, PO Box 25, Abingdon, Oxfordshire OX14 3UE.