A programme designed to help children who struggle with maths has helped them perform better but is too expensive to be a realistic option for many schools, a Government-commissioned study has found.

Numbers Count is a one-to-one intervention for the children among the lowest 5 per cent of achievers.

It was part of a wider Every Child Counts programme introduced by the then education secretary Ed Balls, alongside the Every Child a Reader programme.

While the proportion of 11-year-olds reaching the expected level 4 in maths has risen from 59 per cent in 1998 to 80 per cent in 2010, the proportion of those failing to achieve the lower level 3 - expected at age nine - has stayed at around 6 per cent.

Numbers Count is a 12-week programme that targets this problem by working with the lowest-achieving children. They have daily 30-minute sessions either one-to-one or in pairs, with a specially trained Numbers Count teacher. The programme includes a comprehensive assessment of a child’s strengths and weaknesses so it can be tailored to fit the child.

The study, led by academics at York and Durham universities, found that children on the programme made, on average, seven weeks’ more progress than their peers who were not. They also found that there was no difference in achievement between those who had one-to-one tuition or who learnt in pairs.

But the study adds that the impact of the wider Every Child Counts programme on schools was inconclusive.

Funding a Numbers Count teacher working half the week on one-to-one basis, plus the cost of the training course and extra mathematics resources, totals around #163;15,000 a year. This equates to additional costs per child of #163;1,353 if taught one-to-one or #163;902 a year if taught in pairs.

The researchers concluded: “In essence, while we found that Numbers Count is able to improve children’s mathematical skills, the relative cost may preclude it as a realistic option for many schools.”