Ask a Westerner about Japanese and Korean maths classes and the same mental picture invariably emerges: a large class of ultra-diligent children, proceeding at the same frighteningly high pace and holding back from moving on to the next topic if any of their classmates fall behind.

But that only holds true for primary children. The OECD’s analysis of statistics generated by the Third International Maths and Science Study in 1995 shows that by the age of 13 the top 25 per cent of Korean and Japanese mathematicians are light years ahead of the bottom 25 per cent.

The size of the achievement gap - 130 points in Japan and 142 in Korea - is more than four times the average annual rate of progress (33 points) at this stage of a child’s school career. The only other OECD countries where there was such a gap between the top and bottom quartiles were Australia, Austria, Ireland and the Czech Republic. Even so, it would appear that the Koreans and Japanese have little to worry about. Less than 5 per cent of nine-year-olds in Iceland and Portugal reach the average performance of Korean children. And more than a quarter of Japanese and Korean pupils score higher than nearly all pupils in Greece, Iceland, New Zealand, Norway and Portugal.

Greece can take some comfort from the fact that the gap between the top and bottom 25 per cent did not widen between the ages of 9 and 13. Scotland can claim the same but it has relatively little to celebrate. No only did it perform quite poorly at both ages, there was already a yawningly wide gap between bottom and top quartiles by the age of nine.