* A greater proportion of pupils with learning difficulties may have been in special schools in 1976, and would not have taken part in the study.
* Schools catering to more pupils with English as an Additional Language.
* Less willingness now among pupils to take the tests.
* Less incentive for pupils to help low-achieving pupils.
* A greater use now of a curriculum that is targeted at middle-achieving pupils, which could mean that the needs of the brightest and the lowest-achieving pupils are ignored.
The researchers, who will present their findings at the British Educational Research Association (BERA) conference in Manchester today said their 2008 sample was "slightly skewed" towards higher-attaining pupils.
But they added: "Nevertheless, the overwhelming conclusion is that there are far fewer changes in mathematical attainment over a 32-year period than might be expected, or which have been claimed.
"There are greater proportions of pupils with very low attainment in 2008, and either similar or slightly better performance at the higher end. There is no evidence for significant improvement, or significant deterioration, of standards between 1976/7 and 2008.
"Although performance in some areas has improved it looks as if, when all the results are analysed, there will be little evidence for the sort of step-change in mathematical attainment which might be suggested by the claimed improvements in examination results."
Schools Minister Diana Johnson said: "It's time to stop doing down the achievements of our young people. The independent TIMSS 2007 report on mathematics showed pupils in England are making real progress, with only a handful of South East Asian countries doing better.
"Regular rigorous monitoring of standards at GCSE by the independent regulator has shown that standards have been maintained.
"We do not think that research based on tests in a small number of specific topics taken in 11 schools by 11 to 14-year-olds is a good way to judge standards in the maths GCSE - an exam which tests the full breadth of the curriculum and that is taken by older pupils from all schools in the country."