Broomfield, an elegant 1830s mansion in leafy Essex grounds, is pulsating with mental activity. Forty 10- year-olds, with an average IQ of more than 140, are on a weekend course designed to stretch and enrich some of Britain's most gifted children.
For some it is the first time. 'Maths at school is easy and you tend to get bored,' says Jonathon. 'When I've finished what the others are doing I just have to go further on in the book.' Julian Whybra, the tutor at Broomfield, challenges Jonathon and a dozen others to find every possible hexomino (any combination of six contiguous squares) in the shortest possible time. Jonathon and Matthew get the full 35 in 16 minutes and 23 seconds: three seconds faster and they would have won a place in the Guinness Book of Records. Then they go on to heptominoes (seven squares) and octominoes (eight squares). 'Schools always stop polyominoes when they start getting interesting,' says Mr Whybra, as he asks the group to discover a pattern in the way that possible combinations increase.
Obligingly, they try subtracting, multiplying, squaring, and taking away the number they first thought of. Some stab at it, some think intensely, some say nothing but are clearly testing and discarding one theory after another.
'What's the answer?' they ask eventually. 'Nobody's found it yet,' says Mr Whybra. He adds: 'At school, if the teacher always gives you problems to which there is always an answer, then when you come across something to which there is no answer you're stumped. That's why I wanted to provoke you with something where mathematicians don't know yet if there's an answer or not. That's no reason not to look for an answer. Perhaps you'll be the one who finds it.'
After a game and discussion of the industrial uses of polyominoes, the group breaks for lunch with other groups doing science, drama and poetry. Here and there you see the little professor, the eccentric, the potential disruptive. Above the din, you catch words such as 'tesselate', 'substance', 'triumphantly'. But for the most part, the trainers and T-shirts, the chatter and laughter, look and sound perfectly ordinary.
'The most important result of this weekend is that children will swap addresses and telephone numbers,' says James Hind, the course organiser. 'These kids are the top 1 to 2 per cent in the country. There might be three of them in a school. Here they've got 40. At school they're under stress. Here they gain strength from the knowledge that something better is possible, that there are other people like them.'
Essex County Council used to be internationally renowned for recognising the needs of gifted children in its schools. But two years ago it stopped funding the team of teachers that ran courses for gifted children. So the teachers decided to carry on the work themselves. Mr Hind, Mr Whybra and James Senior, another former Essex teacher, set up a company called Gift, hiring teachers who had experience with exceptionally able children.
Children began to come from further afield than Essex; the last course had participants from Kent, Hertfordshire and Wiltshire. From next month Gift will also offer consultancy - advising and training schools to help their gifted pupils.
The courses are filled through school recommendation. They cost pounds 112, with a few reduced-price places for those who otherwise could not afford to come. Mensa and the National Association for Gifted Children also make recommendations for places. Parental applications are not accepted without supporting evidence of the child's ability - an IQ test score or school report, for example.
Courses are run for different age groups: 9-10, 11-12, up to 18. They cover subjects such as archaeology, freshwater ecology, astrophysics, population movements, geneaology, cartography. All combine new skills and discoveries with material unlikely to be covered at school. Students pick two subjects, usually from four or five running that weekend, spending a full day on each.
'It's much more open-ended than school,' says John Llewellyn-Jones, a secondary biology teacher who leads the 'build an organism' group as well as running an evening activity which involves building hot-air balloons with black plastic bags, alcohol and cotton wool.
'They can ask questions; they can combine their imagination with maths and art and science. The level of explanation and discussion is much higher than they usually experience. It makes them think.'
Tutte and Mark are certainly thinking as they slap papier-mache on to balloons and yoghurt pots. 'This is most triumphantly, utterly, completely and totally better than school,' Mark muses, to no one in particular. The paste up to his elbows suggests he is simply enjoying the mess; the notes on the blackboard - 'mass/volume/area'; 'brain/control system' - prove otherwise.
Each pupil has designed a complete set of systems - circulatory, nervous, respiratory - for the organisms they are building. These, of course, include improvements on the inadequate human one: Tutte's has glass- covered eyes; Mark's has a fully-fitting head and metal plates protecting each of its three hearts.
Later they must explain and defend their inventions to interrogators. Even startlingly articulate children such as Mark and Tutte have to think hard. How will the reserved, almost withdrawn Kelly manage?
Her teachers would be amazed: 'I haven't tried hard at school because I thought people would laugh at me,' she explains. 'But here I'm with people of the same ability and I know they won't laugh at my work. I think that will make me different when I go back to school.'
Gift: 5 Ditton Court Road, Westcliff- on-Sea, Essex SS0 7HG (0702-352886).
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