English teenagers, already thought to be doing badly in international terms, are getting worse, according to leaked accounts of the research, which is set to be the most authoritative of its kind in recent years.

England was 3 per cent above the average performance when the last International Maths and Science Study was undertaken in 1990. Now English 13-year-olds have slipped to 3 per cent below average. They come 19th out of 27 broadly comparable countries in maths, and last in a group of nine industrialised nations in algebra and number work.

In maths English 13-year-olds answered only 53 per cent of the questions correctly. Their peers in Singapore managed to get 79 per cent right, taking them to the top of the international table. Australian pupils are also expected to show strongly.

The results for science are, however, contrastingly good. English pupils are said to be sixth out of 27 countries. Only Singapore, Japan, Korea and the Czech Republic outperformed England, which was 6 per cent better than average. This compared with the previous international study in which England was only 2 per cent above average.

Nearly 14,000 English pupils of all ages took part in the exercise which covered 46 countries and more than 500,000 students in total.

The TIMS findings will be the clearest confirmation to date for those who suspect that British maths teaching lags behind that in other countries - although not all academics accept the validity of international comparisons.

The defenders of the British system maintain that our pupils have a particular strength in problem-solving, which is not always taken into account, and that Britain’s reluctance to hold pupils back for a year or two means that age-related comparisons with other countries are inaccurate. They also maintain that wider cultural differences with, say, the Pacific Rim mean that the educational conclusions can only be tentative.

Professor David Reynolds from Newcastle University is one of the more prominent critics of British teaching methods. Earlier this year he produced a report entitled Worlds Apart for the Office for Standards in Education which appeared to show the countries of the Pacific Rim - Taiwan in particular - far outstripping British schools. He attributed this to the setting of clear targets for the whole class, which was taught as one unit.

The report formed the basis of a much-discussed edition of the BBC’s Panorama programme which featured Her Majesty’s Chief Inspector of Schools, Chris Woodhead, calling for the re-introduction of whole-class teaching methods.

The programme also drew on a research project in the east London borough of Barking and Dagenham where the introduction of Swiss and German teaching styles appears to have improved the teaching of mathematics. These involved “interactive” whole-class teaching (rather than the traditional “lecture”) and the production of centrally approved teaching materials.

This research, funded by the Gatsby charitable trust, was conducted by Professor Sig Prais from the National Institute for Social and Economic Research. Earlier this year, his institute published an analysis of teaching methods and textbooks suggesting that English pupils were two years behind their counterparts in Switzerland and Germany. Many, it said, were doing calculations on their fingers while pupils abroad were able to do sums in their heads.

The Gatsby trust also funded the Kassel study of secondary maths teaching conducted by Professor David Burghes of Exeter University. In March, he concluded that modern teaching methods and “sloppy thinking” had placed British teenagers behind youngsters in a range of countries including Germany, Hungary and Singapore - countries that limited the use of calculators and insisted on whole-class teaching, he said.

Meanwhile, the London Mathematical Society has argued that more rigour is required at mathematics A-level if undergraduates are to cope with university degrees.

The delayed Standards over Time report was commissioned with this sort of concern in mind. This joint analysis, by the School Curriculum and Assessment Authority and the Office for Standards in Education, seeks to establish whether or not standards in A-level maths and science have slipped over the past 30 years.

Publication of this report has been delayed amid disagreement among the quangos about the conclusions it should reach, with OFSTED steering a considerably more traditional line than the SCAA. There seems to be insufficient evidence to draw firm conclusions because the A-level exam has changed in nature over the years.

OFSTED is, however, keen to suggest that these changes, particularly in mathematics, have been damaging.

Controversial as the Standards over Time report will be, it is likely to be overshadowed by the TIMS findings. One of the most impressive aspects of TIMS is the sheer scale and cost of the exercise.

Dr Wendy Keys, the TIMS national research co-ordinator for England and a principal research officer with the National Foundation for Educational Research, said that the size of the operation set it apart from most other international studies.

“There is a problem with international comparisons,” she said. “They must be expensive, time-consuming and difficult if they are going to be reliable. The small-scale studies just can’t, for example, run to the checks on the sampling in every country. The rigour of the sampling and preparation makes TIMS very special.”