The results contradict Government claims, based on national curriculum tests, that maths standards have been rising for the past three years. Last week education minister Estelle Morris hailed further significant improvements from 11-year-olds in maths, English and science.
But researchers from Manchester University say the national maths tests are unreliable, and question the value of the Government's promise that, by the year 2002, three out of four 11-year-olds will be competent in maths.
Two papers by Julie Davies and Ivy Brember conclude that maths standards have been stable for the past eight years.
"The fact that billions of pounds have been spent on the introduction of the national curriculum for no apparent rise in attainment in a key basic skill might be pause for thought," they say.
"However the national curriculum, with its 10 subjects plus RE, caused major changes and disruptions in primary education and made great demands on the time available for the . . . basics such as reading and maths. It could be argued that Year 2 teachers had done well to keep standards stable."
The findings of their companion study on maths standards in Year 6 are almost identical. Each paper examined eight year groups of children, totalling 1,500, from five schools in one local authority.
Their conclusions are vigorously contested by the Government's new curriculum quango, the Qualifications and Curriculum Authority.
A QCA spokeswoman said: "We're very confident that any improvement shown on our test data is real." Evidence taken from just one local authority, she said, could be unreliable.
The debate about standards in maths is fraught with controversy. Pupils in England and Wales do far better according to some measures than others. Last week, for example, The TES revealed that English 13-year-olds are among the world's best at applying maths in real life situations.
Julie Davies believes that the official testing regime is at fault: "Our measure has been the same measure over eight years whereas the national tests have changed. We don't in this country have a proper basis for looking at standards. Relying on such shifting measures it is very difficult to say what's going up and what's going down."
As a result, she said, the Government's literacy and numeracy targets - based on test results - will prove meaningless. "It will be easy to hit the numeracy targets: they will change the tests and change the attainment levels."
Similar views expressed by Peter Robinson of the London School of Economics were dismissed as "claptrap" by Education Secretary David Blunkett.
Davies and Brember conclude, surprisingly, that British pupils do not have a wide spread of attainment, as is often claimed. A "long tail" of under-achievement is frequently blamed for Britain's poor showing in global comparisions.
The latest reports are the second piece of bad news from Manchester University. Last month the same researchers found a notable deterioration in 11-year-old reading standards since 1992.