What are 25 children doing in school on a hot sunny day when their friends are enjoying the long summer vacation?

A casual visitor to Phoenix High School in west London might ask such a question when confronted with the hive of activity that is the numeracy summer school.

From Monday to Friday during a two week period, the 10 and 11-year-olds turn up for lessons at 8.30am and do not leave until after 3pm.

The first part of the summer school day sees intensive coaching in the basics of addition, subtraction, multiplication and division.

Tried and tested methods approved by the government's numeracy task force are used, with the use of calculators kept down to the bare minimum.

Some children are more keen to take part than others

Some children seem keen to take part, while others are more reluctant, perhaps picturing their friends playing in the open air. However, there does appear to be an understanding that the coaching could improve their future at school.

Richard Smith is an enthusiastic paticipant. "It's great," he says.

The rest of the day is less formal, involving a range of practical activities, games and trips - but the focus remains on improving their number skills.

One activity involved a visit to the local Tesco supermarket, with groups of children given a budget for a packed lunch (£3), a picnic for four (£12) and for cleaning the house (£8). The aim was to use mental arithmetic to carry out the three tasks while remaining within budget.

Arithmetic-friendly board games such as chess and monopoly are used during "free" periods.

And even trips to venues such as the National History Museum have a focus on numbers. For example, one exercise saw the children asked to estimate the number of reptiles in a cage.

Four of the school's teachers volunteered for the numeracy scheme: Gary Kynaston, Mack Frederick, Archie Hesse and deputy head Mary Lavery. Their presence ensures a pupil/teacher ration of six to one, allowing each child to receive the individual attention they need.

Mack Frederick: "All of us agreed we needed practical lessons and investigations to keep their interest over the two weeks"

They admit that it is a tiring way to spend a third of their holidays, but are impressed by the results and have found the experience rewarding.

"The students are all showing increased confidence and a greater willingness to try," says Mr Kynaston.

"We have had the time to nurture pupils who are going to join the school in September."

The children taking part in the Phoenix High numeracy scheme will all be attending the school from next term.

They were identified as needing special attention in maths by their primary schools. Letters offering a place were sent out to their parents, with follow-up phone calls made to those not responding to the initial approach.

Some of them have a record of poor classroom behaviour, but Mary Lavery believes the summer school is helping to reduce this problem.

"If we can get the parents with us now, we can keep them with us," she says.

Gary Kynaston: "The most important thing is that the students leave here with the feeling that numbers are fun"

Phoenix High is just one of 51 pilot summer numeracy schemes taking place across England and catering for a total of 1,500 children.

Funded with £500,000 from the Department for Education, they are aimed at children who are about to make the move up to secondary school and are experiencing problems with their maths.

They are running alongside the Department's much expanded summer literacy schemes, which are building on the pilot of last year by catering for 18,000 children across England.

William Atkinson, the inspirational headteacher of Phoenix High who is currently starring in the Teacher Training Agency's recruitment adverts, is in no doubt about the value of summer schools.

"The children involved have shown a high level of enthusiasm for the work, which will give them a head start in this school.

"They have gained not only in terms of their literacy and numeracy, but also in other skills such as following instructions and relating to one another."