But the game they are playing isn’t hopscotch. In fact, it isn’t really a game at all. For these children are in the process of constructing a living brain. “All right,” says Andy Smith, a Year 6 teacher who has postponed his own summer break to supervise the proceedings. “I need two people to act as the mid-brain. You are the long-term memory and the emotions. Can you mime memory? Can you mime emotion? Let’s see you try.”

There’s no exam to pass here. But at the end of each day, teams that perform well in this and other tasks (raft-building is on the agenda if the good weather holds) will be rewarded with a plastic lemonade bottle - one of several mysterious components they will eventually assemble into a launchable rocket. And why do they need such a contraption? Because today and every day this week, these children are stranded on a desert island, and only by launching a rocket can they summon help.

Learning how to think, devise strategies and put them into practice using teamwork might not be on the regular curriculum. But this is a summer school, and increasingly, it’s at summer schools that people are exploring new ways of teaching - ways that would have the life squeezed out of them in the increasingly cramped confines of a normal working day.

This particular summer school is one of a series being run by Norfolk and 14 other LEAs over the next three years in partnership with the University of the First Age (UFA). Funded by lottery money from the New Opportunities Fund, the week-long courses are built around a series of challenges. Groups may be “lost in space”, told they are survivors of an air crash, or responsible for protecting an endangered species - all what the UFA calls “real-world, open-ended problem-solving scenarios”.

One of the aims of these courses is to involve pupils themselves in the running of the programme (three ex-pupils are acting as peer tutors in Thetford this morning), and another is to develop teacher skills in the area of “learning to learn” and the teaching of thinking skills. It’s a lot to take on at the end of an exhausting term, as Andy Smith is discovering. “When we broke up,” he says, “all the other staff were going, ‘Yeah, we’re off!’ But I was in the classroom photocopying student portfolios and so on. There are so many things that have to be organised.”

But he has three classroom assistants to help him, as well as the peer tutors, and it’s clear that his new class of 30 are having the times of their lives. Wyn Manners, who works in Norfolk’s study support unit, is co-ordinating the 10 UFA summer courses catering for 240 children at eight schools in the county. “Everyone is having a great time,” she says, and she has this on excellent authority.

Kim, Emma and Katie, three students from Earlham county high school in Norwich, are operating as a “news team”, reporting on activities at all the summer schools and producing a newspaper complete with digital photos from around the county. “They have phoned, faxed and emailed everyone for me,” says Wyn Manners, “and tomorrow they go out with an Evening Standard reporter. Activities like this give students room to explore. But it does mean time.”

With their emphasis on exploration and expanding horizons, the UFA summer schools reflect the sort of thing that is happening increasingly all over Britain. Last year, the Department for Education and Skills put pound;19million into 1,800 summer schools, and this year it has set aside pound;22million for more than 2,200 projects. And while much of the emphasis, as in term time, is on literacy and numeracy, with many courses specifically targeted at primary school pupils who have failed their level 4 assessment, even these subjects can be handled with flair and imagination in a summer school context.

Take, for example, the 40 or more football clubs that have got together with business to set up literacy and numeracy study centres at or near their grounds as part of the DfES’s Playing for Success project (the three Earlham high news girls will produce their newspaper from an office at the Norwich City FC complex). And look at the number of courses over the summer months that use ICT techniques such as animation or computer gaming as motivational tools, or that combine “fun” activities such as kayaking or abseiling with the development of social skills and co-operative attitudes.

Summer school means tackling old subjects in new ways - coming at them from different angles, and turning the process of learning into a game. Ted Wragg, professor of education at Exeter University, says:

“Children and teachers enjoy the informality - there is no uniform, and everybody is relaxed and friendly. Isn’t this what learning should be like?” That’s certainly the view of Ann Hadfield, an art teacher who in 1993 set up a summer school at Kempston rural lower school in Bedford. She has seen the project expand - by popular demand - to take in the middle school as well. These programmes combine sports and arts activities, partly with a view to improving existing skills, but also to open children up to ideas and activities they might not otherwise have considered. “It’s not the same as in term time,” she says. “Every child starts with a clean sheet. They learn new skills and make new friends. And we teach them how to think.

“The local schools are marvellous, but we can work in smaller groups and give them individual attention. In theatre games, for example, there are six children in each group. And this can help them overcome their self-consciousness. This is particularly true when it comes to boys and music. It gives them the confidence to make choices.”

While the Kempston summer school caters for pupils of all abilities (“We have a mix of extremely bright children and one or two who are good at one or two things,” says Ann Hadfield), the Children’s University, funded by the Bedford Charity, offers summer sessions for 320 children aged between nine and 13 who are particularly able or talented, and who have been nominated by their schools. Subjects include performing arts and theatre design, robotics and puppetry and a range of sporting activities, many hosted by local clubs. But here, too, the emphasis is on experiences that couldn’t possibly be fitted into the normal school routine - Royal Marines pulling sledges across De Montford University’s Bedford campus to teach cold climate survival skills, for instance. In any other context, such an activity would represent a timetabling nightmare.

But with a will, and a certain amount of cash, all things are possible at summer school. Which is why Andy Smith has persuaded 30 Norfolk youngsters to toss a blue ball high into the air simply by tugging in a co-ordinated way on the edges of a large, orange parachute. “It’s all about teamwork and co-operation,” he explains as the ball begins to bounce. And to the amazement of everybody present in that sun-dappled playground, it actually works.