A t the age of 3, Jake* had already taught himself about multiplication, square roots and prime numbers. His mother, Louise Collins*, was proud of Jake's talents and gently encouraged his burgeoning interest in maths.
But when the time came for Jake to enter Reception at the age of 4, everything changed. A sensitive child, he struggled in the busy environment of school and was so overwhelmed that he misbehaved.
"It was horrific. He spent the whole time on the naughty seat," Collins says. "He had to shut down, he couldn't listen to instructions, he refused to sit on the carpet for two years.
"For him the environment wasn't really tolerable. It was very difficult."
Staff were initially resistant to the idea that Jake might be gifted, but Collins convinced the school that if her son could simply focus on maths, everything else would fall into place. The strategy worked: he settled down.
By the end of Reception, Jake had finished the primary maths curriculum. When he was in Year 2, the school brought in a specialist tutor so that he could work at his own pace. Now 11, Jake sat GCSE maths this summer and, despite his mother's concerns over selective education, will attend one of the UK's 164 grammar schools in September.
"I'm pro comprehensive education," Collins says. "But when we went to the comprehensive, they just said, `We haven't taught A-level for 10 years.' They were a bit rabbit in the headlights with it. Some of the provision for gifted and talented children seemed to be, `Oh, once a year you can go to a museum.'
"That's kind of OK, but it doesn't seem to me to be what is required. What is needed, every day, is someone in the classroom saying, `What does this child need?' "
A precious resource
Jake is a particularly compelling example of the millions of children around the world who display off-the-scale levels of talent or are extremely able in one or more subjects or disciplines. Despite their impressive skills, all too often they are viewed as a problem by schools.
In England and the US in particular, government policies have meant that many schools have been forced to prioritise getting the bulk of their student body to a basic standard, such as GCSE grade C. Indeed, to some schools, from some angles, an exceptionally able child might look more like a disruptive burden than a blessing.
Experts the world over insist that we neglect encouraging and developing our most talented children at our peril. According to David Lubinski, a psychology professor at Vanderbilt University in Nashville, Tennessee, "gifted children are a precious human-capital resource".
Lubinski's research compares the SAT college entrance test scores of highly gifted US students with achievement later in life. "This population represents future creators of modern culture and leaders in business, health care, law, the professoriate and Stem [science, technology, engineering and maths]," he says.
But Lubinski stresses that these children's success is not guaranteed. They need access to academic work suited to their faster pace of learning to ensure they remain motivated and reach their full potential.
Martin Stephen - former high master of St Paul's School, an unashamedly elite independent school in London - is soon to publish research into gifted and talented provision across the world, and describes high-performing children as "one of our last remaining natural resources".
But again he emphasises that their success is not certain. In the wrong environment, their talents might not be recognised or they might not want to develop them. Some even use their superior intelligence and ingenuity to avoid work.
There are no two ways about it: the picture for many students with high learning potential, particularly those from disadvantaged backgrounds living in the US and the UK, can be bleak.
In the US, where many of the most innovative and impressive gifted and talented schemes have been developed, provision is patchy at best. Critics complain that programmes are dominated by middle-class children of European and Asian origin.
A study based on 2006 data from Vanderbilt University finds that African-American students are under-represented in gifted programmes by about 51 per cent and Hispanic students by about 42 per cent, relative to their proportion in the nation's schools.
Meanwhile, a damning 2013 report by England's schools inspectorate Ofsted finds that non-selective schools - that is, the majority - are failing the most able. It notes that almost two-thirds of pupils leaving primary school with the highest grade (level 5) in both English and maths do not achieve an A* or A grade in both subjects at GCSE (see bit.lyOfstedAble).
There is no longer any ring-fenced funding in place for gifted and talented education in England, and it is left to individual schools and a mix of charities, private businesses and universities to provide services to meet students' needs.
A multimillion-pound national gifted and talented programme - which ran throughout the 2000s - aimed to pinpoint the cleverest students for a variety of enrichment and academic programmes. But it was shut down amid claims that it was a waste of money and was not reaching the children it was designed to help.
Critics - including those closely involved - say the programme was divisive, focused too much on identification of gifted children and lacked clear goals. Its disappearance has left a fragmented system overly reliant on the whims and priorities of headteachers and the proactiveness of parents.
High expectations for all
Meanwhile, in East Asia, results from the latest Programme for International Student Assessment (Pisa) tests in 2012 show that in certain education systems vast swathes of the student population are performing at a very high level in maths, reading and science. Success does not seem to be confined to a few lucky, specially selected children.
For example, an average of 13 per cent of students across Organisation for Economic Cooperation and Development countries performed at the top levels - 5 and 6 - in maths. But in Shanghai this rose to 55 per cent, followed by Singapore at 40 per cent, Chinese Taipei at 37 per cent and Hong Kong at 34 per cent (see bit.lyPisaGifted2012). It seems impossible to believe that this many children could be born with an innate talent for maths or any other subject.
Of course, some argue that these education systems achieve such results because they are little more than rote-learning hothouses where pupils do not receive the rounded education favoured by Western parents. But Professor Deborah Eyre, former director of England's National Academy for Gifted and Talented Youth and now education director at the Nord Anglia Education chain of international private schools, believes it is all about attitude.
Her own approach - which is being pioneered in the chain's schools - operates on the premise that every child is capable of the "advanced cognitive performance" that gifted children demonstrate. It is the perfect antidote to the British obsession with determinism, she says. The strategy is "goal-focused", with practitioners keeping an open mind about who will excel when they reach adulthood. The key, Eyre explains, is to set high expectations for all and encourage excellence in emerging elite performers.
"One of the reasons I'm interested in that is that when you look at different parts of the world where they have very high-achieving education systems, they don't get there by segmenting the cohort into more able or less able," she says. "What they do is say, `What we need is to set ambitious targets and we want everybody to get there and we need to focus on that and removing the barriers to everybody achieving.'
"In England we have these unique things that hold us back from that, which they don't have in, say, the Asian tiger countries. We don't kind of want everybody to do well because we feel that being in an elite group is a desirable thing, we don't want everybody sitting in first class. Other countries don't see it that way."
Others involved in gifted and talented education agree that in the West ideological resistance can often prevent us from giving gifted learners what they need. Denise Yates, chief executive of UK charity Potential Plus - which supports children with high learning potential and their families - believes the whole mindset in Britain is wrong.
"The issue in this country is that we are not supposed to say what we are good at," she explains. "We are almost the country of the underdog and you are fine to say what kind of special need you have but not that you might be gifted and talented. That's where it stems from, that's in our psyche."
So if some in the West have a distaste for elitism and can't or won't adopt the East Asian approach to education, what might work? And is there anything in the pipeline that offers hope?
On the intellectual fast track
Stephen is more optimistic than many others. He believes there are plenty of outstanding examples of gifted and talented provision scattered around the world that have been successfully established in non-selective systems. The most promising examples, he says, are not necessarily monolithic countrywide schemes but beacons of local and regional excellence.
Much best practice can be found in the US and Australia, Stephen says, singling out the Robinson Center for Young Scholars at the University of Washington in Seattle. Up to 16 young people under 15 go through its Transition School each year as part of its pioneering Early Entrance Program.
There, they take a module or two from the University of Washington's full degree programme while still living at home like normal teenagers. They then progress as fully fledged undergraduates to the university's full-time degree courses.
"This was the most surprising, staggering, earth-shattering insight: they showed you can intellectually fast-track children without emotionally fast-tracking them," Stephen says.
Among the other projects likely to feature in Stephen's forthcoming book is the Hungarian Genius programme, a national talent scheme run by the Hungarian government which works on the assumption that everyone has high potential.
"It is joyous," Stephen says. "They get the maximum creativity out of every student who comes along. It's an antidote to elitism. It will identify a brilliant young violinist and provide for them, but on the other hand it has prizes for folk dancing."
But why do we need to look abroad? Some experts believe that former education secretary Michael Gove's reforms may already be compelling schools in England to do more for the most able.
"The broad direction of coalition policy has been extremely supportive. The Govian philosophy was unashamedly elitist," says Tim Dracup, who was director of the now defunct Gifted and Talented Education Unit set up under Labour.
He points to the fact that today Ofsted looks at how well schools are teaching the most able, and says league-table reforms "will ensure that every learner's progress matters". In other words, headteachers will be forced to focus on gifted and talented students whether they want to or not. Changes to the national curriculum will make it tougher and more flexible, Dracup says, and scoring top grades in the new GCSEs and A-levels will also be harder.
But some would argue that what primarily needs to change in England is the attitude. The country has to stop seeing outstanding students as needy charges who could suck up time, money and resources.
"They need no more or no less attention paid to them than a child who needs a C grade," Stephen claims. Indeed, when able children are set on a path that motivates and appeals to them, they often require less attention, he points out, especially in the era of the iPad. "You have to find their enthusiasm, ignite it and let them run."
Jake and his mother would no doubt agree.
*Names have been changed