One in three English children leaves school unable to do simple sums, a failure which drives them into an underclass of young people who cannot get jobs, according to a paper published today.
Professor Sig Prais, director of the National Institute of Economic Research, says English pupils' poor achievement in maths - especially arithmetic - has become critical. He bases his analysis on comparisons with the achievements of children on the Continent.
He added that the education White Paper, published by the Government last week, failed to address many of the issues that have contributed to the poor performance.
"This larger proportion of low- and under-achievers in England, with particularly great disabilities in basic arithmetic, leads to worries that the English schooling system is in some way malfunctioning, and is contributing to the creation of an economic and social underclass," Professor Prais said. He added that the Government did not appear to be providing enough money to tackle the problem.
He recommended providing suitable textbooks and teaching manuals, guidance on teaching time and giving children more chance to consolidate learning. He said that there should be more work with low- achievers and a review of the use of calculators.
He said: "From the point of view of the employment of school-leavers in an increasingly technical workplace, the problem of this hard-core of under-performers needs to be solved."
His paper is based on data from the Third International Mathematics and Science Study (TIMSS) and compares English pupils' attainment with those in France, Belgium, Austria, the Netherlands and Switzerland.
Professor Prais estimates that a third of English school-leavers cannot subtract 2,369 from 6,000. This simple sum was done correctly by 92 per cent of 13-year-olds in the five Western countries but only by 59 per cent in England. Since the question was multiple choice, the results are actually worse when allowances are made for guesses.
Only 36 per cent of nine-year-olds got the sum right, compared with 86 per cent in the Netherlands and 92 per cent in Austria. After adjusting the figure for guesswork, Professor Prais added that only 15 per cent of English nine-year-olds could be expected to answer correctly compared with about 90 per cent in the Netherlands and Austria.
Professor Prais said the situation is much worse than the picture painted by the broad averages shown in the latest part of TIMSS, published this week by the National Foundation for Educational Research.
He said: "The proportion of secondary pupils with very low scores in England in these mathematics tests was about twice as great as in the Western European countries; for example scores attained by the lowest 10 per cent of Swiss 14-year-olds were attained by the lowest 20 per cent of English pupils. "
He also warned that English pupils' comparatively high attainments in science is of limited significance as scientific application requires arithmetical knowledge.
Dr Wendy Keys, TIMSS national co-ordinator, accused Professor Prais of being selective with the data. She said: "He has ignored the other areas of mathematics, such as geometry and data analysis where English pupils scored well. We must emphasise the successes and then consider what the concerns are."
The Government's national numeracy taskforce intends to spend this summer reviewing the vast literature of mathematics and teaching practice.
Professor David Reynolds, its chair, said he was in no doubt of the seriousness of the situation, particularly in primary school arithmetic. But he did not want to jump to simple conclusions. "This is a very complex situation and that's precisely why the numeracy taskforce is conducting the review. "
He said the TIMSS research showed countries that did well, for example Singapore and Japan, had very different teaching methods.