The government-funded study found that the maths tests performance of 7-year olds from all backgrounds was a reliable indicator of their results at the end of primary school in English as well as maths. But it also showed that those from less advantaged families made relatively more progress by the time they reached 11 if they did well in the early tests.

The research was led by Kathryn Duckworth of the Centre for Research on the Wider Benefits of Learning, based at London University’s Institute of Education.

She said: “Maths may not be supported at home in the same way as reading, so the effect of school is greater. This may be more beneficial for those with least help at home.”

An analysis was based on test data from more than 9,000 children taking key stage 2 tests in 2002, 2003 and 2004.

For a child whose parents do not have five good GCSEs, a rise of one level in maths at age 7 leads, on average, to a rise of 9.4 percentage points in their maths mark and 2 percentage points in English at 11.

The effect of rising one level at 7 on a child whose parents have at least two A-levels, is a boost of 8.4 percentage points in maths and 1.2 percentage points in English.

Similarly, children from disadvantaged homes whose maths is weak at age 7 are substantially less likely to do well by 11.

Miss Duckworth said: “There is a lot of continuity so the children who are doing well at 7 are more likely to be doing well later, but ability is not fixed. Tests shouldn’t be taken as casting a child’s level in stone; they should be used to support learning.”

The study found the bottom quarter of children at key stage 1 had a 50-50 chance of staying there, half did better by 11 with 3 per cent making it into the top quarter. Similarly, 63 per cent of children who were in the top quarter at 7 remained there at 11, but 10 per cent had dropped to below average by 11, including 1 per cent in the bottom quarter.

Overall, the study shows that 74 per cent of children made progress by two levels or more in English and 76 per cent in maths.

It reveals the pressure primary schools are under as the target regime is changed. Target-setting guidance for 2009 issued last month said that ministers want to see all children making two levels progress over four years.

The Government has announced a review of primary maths to be led by Sir Peter Williams, chair of the advisory committee on maths education, and will be launching an Every Child Counts programme to help children struggling with maths.

* ‘What role for the 3Rs?’, www.dfes.gov.ukpublications