But the anti-intellectual prejudice that runs like a vein of fat through British culture is always exposed when one of these children is thrust into the limelight and, inevitably, this affects attitudes among parents and in the classroom.
A nice example of this deep-rooted suspicion of youthful talent appeared in the Guardian's letters page recently. Among responses to the story about 15-year-old Alexander Faludy, who has won a place at Cambridge, despite severe dyslexia, a woman warned Cambridge against accepting him, lest he become an "insufferable, pompous little adult" before his time. She recommended Alexander be forced to spend the next three years "as a classroom assistant in one of his parents' own schools". That, presumably, would serve him right for being so clever.
While the number of teachers who take this punitive line toward their brightest pupils is likely to be small, many, particularly at primary level, will feel unnerved when confronted with an eight-year-old who has the vocabulary of an A-level student (a typical characteristic of the very bright) - especially when they are having simultaneously to deal with children with learning difficulties, or who have English as a second language.
Teachers may also be unsure of their ability to identify bright pupils - especially as they often become disruptive or withdrawn when confronted with repetitive work, making them easy to confuse with those of lower ability. Others may feel ambivalent about giving special attention to pupils who appear to "have it all", when so many are struggling. This attitude is reinforced by the lack of any legal definition of special educational need covering extraordinary ability, so the school can claim no extra money for teaching time, special books or materials.
Earlier this month the Government acknowledged that the most able pupils may need special help by setting up an advisory group on gifted and talented children. The group's task is to design a "strategy" for early identification and support. Education minister Estelle Morris said: "We fail to identify many of our most able children and we don't challenge them enough. This can lead to disaffection and chronic underachievement. The attitude that gifted children can cope by themselves has let down too many young people."
In the meantime, the prospects for able children depend on the prevailing policies of individual schools and local authorities. Many secondaries now offer "extension" or enrichment classes for the top 15 per cent, but this is by no means universal. Likewise, some local authorities have created advisory posts for high ability, and some have set up Saturday classes and high-ability centres.
But for the individual teacher who is keen enough to seek out help for his or her ablest pupils, a wealth of information and support already exists. The National Association for Able Children in Education (NACE), for instance, produces literature to help teachers, runs in-service courses and has a list of publishers of books, software, extension packs and videos for teachers' information and for pupils to work on.
As NACE professional officer Colin Jarvis points out, there are two approaches to resourcing high ability. The first is to find publications aimed specifically at this group. The other is to adjust your own attitude and realise that the school may already have the resources, if you are prepared to accept that one child may be capable of reading adult literature while the rest work on a reading scheme.
"Many bright children are being ignored, or, if they finish a task fast, simply given more of the same," says Mr Jarvis. The organisation would like to see a co-ordinator appointed for able children in every school.
Hilary Heffernan is an education consultant for the Support Society for Children of High Intelligence (CHI). While this group was formed by MENSA members (an organisation some may consider no more than a mutual self-congratulation society), its purpose is to help those children who may not qualify for MENSA membership but are nevertheless exceptional. The group was set up to help frustrated parents but welcomes enquiries from teachers.
Ms Heffernan says the most common complaints from parents are about teachers who tell a child to "go and wash out the paint pots" if they finish tasks early, and that teachers stereotype them as "pushy parents" with inflated opinions of their child's ability.
CHI has a library of several hundred books about the needs of the most able. The society also runs summer schools and tries to put able children in touch with each other. "Some of these children are lonely, they find it hard to fit in with contemporaries, who may accuse them of showing off. We also show them how to take courses out of school," says Ms Heffernan.
Like Colin Jarvis, she believes a flexible approach is more important than finding specific resources. "Instead of feeling threatened when a child asks a question you don't know, it is better to say 'I don't know either, let's go and find out'," she says. This may seem obvious but, she says, a surprising number of adults feel threatened when a young child seems to be encroaching on grown-up territory.
Hilary Heffernan has written two books of brainteasers for able children - particularly suitable for those with logical and mathematical gifts - for the Brainwaves series from Folens. In October this publisher is bringing out a book for primary teachers (Able and Gifted Children by Chris Webster) to add to Providing for Able Children by Linda Evans and Gwen Goodhew, a comprehensive set of activities and issues for discussion for primary and secondary staff.
Commissioning editor Colin Forbes says the company's policy is to advise all authors to include extension activities for able pupils as a matter of course, rather than confining the able in a sub-group. "We risk pushing able children into a corral, ghettoising them," he says.
The National Association for Gifted Children was also set up to help worried parents, but is increasingly advising teachers and local authorities, running conferences and INSET courses. Educational consultant Edward Chitham highlights the difficulty teachers face when a child has a reading age far in advance of contemporaries.
"You might have a six or seven-year-old with a reading age of 12 or 13. The problem is that much modern literature written for teenagers deals with social or sexual problems that may be inappropriate or irrelevant to a small child. So we tend to advise teachers to turn to earlier authors such as E Nesbit or Arthur Ransome, or adult classics."
Like most educationists specialising in the able, he urges teachers to see able pupils as children whose development happens to be ahead of their chronological age, "not as a separate species". He also believes the pressure to fulfil national curriculum demands has made teachers wary or unable to stray from it, and that this has disadvantaged the brightest. "With able children, you have to be prepared to raid unusual areas in search of resources. A nursery child pestering you with questions about the human body might enjoy Dorling Kindersley's Human Body CD-Rom, for instance, even though it is designed for much older pupils."
He adds that the NAGC recommends enrichment activities rather than acceleration (moving the child up a class or two), so intellectual development does not outstrip social and emotional development.
One publisher that does concentrate on the able as a separate group is Able Publications (a branch of Pullens). Teachers may find its resource packs on subjects such as wind power, economics, industry and maths problems particularly useful, as they are reassuringly tied to the national curriculum.
Finally, try typing in "gifted children" as an Internet search. There are thousands of Web sites, many of them including useful contacts and links. If you are unsure how to surf, ask one of your pupils to show you (it won't need to be a gifted one).
* National Association for Able Children in Education, Westminster College, Harcourt Hill, Oxford. Tel: 01865 245657 * National Association for Gifted Children, Elder House, Milton Keynes MK9 1LR. Tel: 01908 673677 * Folens, Albert House, Apex Business Centre, Boscombe Road, Dunstable, Bedfordshire LU5 4RL. Tel: 01582 472788 * Children of High Intelligence, 5 Makepeace Avenue, London N6 6EL. Hilary Heffernan can be contacted by e-mail on HHilary@aol. com. Guidelines on identification, pupils' resources: http:www.users.dircon. co.uk * Mensa Internet links and resources: http:www.mfgc.org.ukmfgc Do you have a brilliant child in your class?
* Powerful reasoning; ability to generalise and deal with abstractions. Sees links between things * Rich and mature vocabulary, good grasp of sentence structure and accurate grammar * Good memory. Can distinguish between relevant and irrelevant information. Learns rapidly with little or no need for repetition * Creative and imaginative, interest in stories * Shows unusual intellectual curiousity, asks philosophical or religious questions * "Buttonholes" adults demanding information * May show precocious talent in certain areas only, such as maths or art, or have a very advanced reading age * Is original and inventive Negative indicators include * May fail to make relationships within class, preferring adults or older children. Conversely, child may try to conform by acting in an immature manner * Shows intense boredom in the face of repetition or reinforcement activities * May be highly disruptive or withdrawn