In the 1980s there was a five-year waiting list to escape the soulless tower blocks and semis of Kirkby. The town, built as an overspill for crowded Liverpool in the late 1950s, looked doomed. These days, such has been the transformation that there is a three-year waiting list to get into the recently revamped Tower Hill estate. There is a new spirit of hope about Kirkby.

A new spirit exists, too, in its local schools, where a group of primary heads has taken the radical decision to focus on their most able pupils. In a school such as Overdale community primary - a 350-pupil school where 90 per cent of the children are entitled to free school meals - the priority tends to be those with the most pressing needs.

The low-rise school is surrounded by pillar-box red spiked railings and stands amid a jumble of Sixties high rises and more recently built private homes. Children enter nursery often lacking basic social and language skills. Halfof Overdale’s pupils are on the special needs register.

Their disadvantage has been compounded by a deep-rooted anti-school culture. Steve Palin, head of Millbrook community primary school, says children who work hard are taunted as “meffs” (he can’t advise on how to spell it because no one’s ever seen it written down) and that some aspire to educational failure.

“Many of the parents had bad experiences in school themselves,” says Coleen Hibbard, head of neighbouring Eastcroft Park for the past four years. “Success has meant lasting until 16 without falling out of school, or not getting into trouble.”

Two years ago, the headteachers of six primaries in Knowsley LEA - Overdale, Millbrook, Eastcroft Park, Kirkby C of E, Ravenscroft, and Simonswood - decided to work together to give their brightest pupils extra teaching and enrichment activities with the aim of getting them to level 5 in the key stage 2 national tests. (Test results were fairly dismal at that point, with only 17 per cent of Eastcroft Park children, for instance, reaching level 4 at the end of their primary school careers.) The idea went against the grain with some. “Initially,” says Overdale head Cathy Parkinson, “people in the LEA needed convincing that it was justifiable elitism. I would describe it as social justice. It was recognising a need that was not being met.”

The result was the Excel High Achievement Project, in which the two or three highest-scoring children skip their usual classes every Tuesday to join their peers from the other five schools for accelerated learning classes.

Each Excel class contains about 20 pupils - Year 3 and 4 classes are at Eastcroft Park, and Years 5 and 6 at Overdale. Classes are organised on a secondary model, with separate teachers for each subject, and go on until 5pm. Parents have to bring and collect children, and are asked to be generally supportive.

In an upstairs classroom in Overdale, a Year 5 Excel class is having an IT lesson with Tony Highland, a teacher from the local comprehensive, Ruffwood. While the adults use words such as “most able”, the children do not mince theirs. “The people in this group are brainy,” says nine-year-old Elizabeth Hopley. “Excel is so they use their brains more and get a better chance of getting a better job when they’re older.”

Her friend, Judith Ashcroft, also nine, likes the group. “You don’t have to learn things you already know,” she says. Wonderful work on the wall - Sam Diamond’s L poem, about a “lepricorn” (sic) going to Libya with its luggage and ending up on a lamppost by the Liver building - is testimony to the stimulation the children receive in these classes.

Over the road at Eastcroft Park, the Year 4 Excel class is having fun with science teacher Kevin Lanagan. They are learning about objective description, which explains the words “tall, skinny, balding, human, old and green” on the board behind their teacher. Having run out of words to describe Mr Lanagan, they are now plunging their hands into the bottom of bin bags and describing what they encounter.

To add spice, Mr Lanagan has told them one bag might contain a tarantula. The atmosphere is not so much on-task as positively gleeful.

Nearby, Year 3 children are enjoying themselves just as much in Simon Woods’s IT class, where bottoms are bouncing on chairs and all hands point frantically ceilingwards. It says something about a man when he’s willing, in the cause of children’s amusement, to wear a tie like Mr Woods’s - with its faithful rendition of a computer, hard disk drive and plugboard with trailing flex.

Teachers find Excel rewarding too. “You go into a class and it’s like a little dream team,” says Mair Hindmarsh, deputy head of Kirkby C of E school, and until recently Excel project manager. “It’s children who want to learn, who gel with each other. There’s no reservedness about being with children from other schools; they genuinely do enjoy Excel.”

The initial impetus for Excel came from Ruffwood comprehensive, which ambitious parents in the area were in the habit of bypassing. “Our brightest 11-year-olds from our most upwardly mobile families - who had a car - would move to Maghull high school,” says Millbrook head Steve Palin. “Think of the impact that had on our GCSEs.” (Maghull comes under the neighbouring Sefton LEA; Knowsley has only 12 secondary schools.) Then in 1990 John Jones, aged 49, became headteacher at Ruffwood. Mr Jones has curly hair and a headful of ideas underneath. He grew up as a scally - “don’t write that down” - a working-class local boy, and now sits on three government advisory committees, including the headteachers’ task group on excellence in cities.

Over the nine years he was in charge of the school, John Jones (ironically he left last September for Maghull high) systematically attacked the low expectations he inherited at the 1,250-pupil comprehensive. Pupils were divided into four sets: Excel, Extended, Standard and Foundation. “We wanted to make sure the top end of the ability range were challenged and extended,” he says. “Nine years ago, if a parent said ‘my child is very able’, you couldn’t, hand on heart, say ‘Bring them here, they will succeed’. Now the challenge has changed from raising expectations to meeting expectations.”

Ruffwood’s job will of course be made much easier by the minor hothousing now going on at its feeder primaries. Raising standards of numeracy, literacy and ICT skills in primary school, says John Jones, “gives children the keys to the curriculum kingdom”.

GCSE results have improved dramatically at Ruffwood. The number of pupils gaining five A-Cs has risen from 5 per cent when Mr Jones arrived to 25 per cent last year, and the school was included on the chief inspector’s list of most improved schools in February last year.

There is no disputing the benefit of the Excel scheme to the participating primary school children. Last summer, when the first group to attend a year’s Excel classes took the national tests, more than 95 per cent achieved level 5 in science; almost 90 per cent got level 5 in maths and two out of three in English. All the children reached at least level 4.

These children are now “bounding ahead” at Ruffwood, says acting head Sandra Simm. “They arrive as a group and they’re very proud to have been involved.” Before, if a child arrived at Ruffwood with “straight 5s”, every member of staff would be aware of them. “Now, there are numbers of them,” she says.

Two things have made the Excel primary scheme possible in Knowsley. First, the fact that heads and staff here are accustomed to working together. The second thing is money. Excel costs pound;12,000 a term, mainly in teachers’ pay, and the start-up costs were met with a mix of local authority and government money. But the start-up period is now over, and the heads have had to approach local universities and businesses for sponsorship.

Whatever the future of the scheme, the question nags though - what has been happening to the pupils who are not part of the Excel group? The headteachers say Excel has given other children something to aspire to. At Overdale, they now set for English and maths from Year 3. Test results have improved generally at the school, with an average 53 per cent reaching level 4, against 23 per cent two years ago, before Excel. “Our three upper groups are benefiting considerably,” says Cathy Parkinson.

But what of the bottom group? “We’ve got finite resources,” she says, “and we’ve recognised as managers that we’ve got to put them where we can make a difference.”

Mid-morning on a wintry Saturday and it’s time to play Countdown at the Solihull Year Six curriculum project. David Harding, the teacher at the front of the class, writes numbers on the board - 50, 14, 9, 7 and 3. Beside them goes a bigger number - 327. Just as in the television game show after which the activity is named, the children have to use cunning combinations of addition, multiplication, subtraction and division to turn the smaller numbers into the bigger one. The 18 pupils, working in twos and threes, pounce on the problem eagerly, and hands are going up in seconds.

But Mr Harding knows who he wants to step up to the blackboard - two boys who throughout the session have been, shall we say, pretty confident. He thrusts a piece of chalk at one in the time-honoured teacher’s “go on, show us then” gesture, and the room falls quiet as the boys discover that having to work something out on a blackboard before an audience is a good deflator of the ego. Mr Harding has exactly the right words for them, too.

“Take care now!” he warns, “And remember that we are all hoping you will get it wrong.”

We know he doesn’t really mean it. The children, aged 10 and 11, from a local primary, are already on good terms with Mr Harding, a mathematics graduate whose more usual audience is a high-flying sixth-form group at fee-paying Solihull School, where today’s session is taking place. They just know he is going to say things like that. (“I don’t believe you,” he says later to another eager child. “I think you’re wrong. Convince me.”) The idea behind the Solihull Project is simple enough. The most able children from Year 6 classes in primary schools across the borough are gathered together on Saturday mornings for three-hour enrichment sessions with specialist teachers from the primary and secondary state sector and from Solihull School. Three Saturdays are devoted to each of four curriculum areas - maths, English, science, history, creative arts. (ICT, originally a separate module, is now integrated with the others.) Up to 90 children attend each session, and because different children are chosen for each subject, the project involves around 400 children a year.

Now in its second year, the project was devised to take advantage of a Department for Education and Employment fund to support projects that link the state and independent sectors. In the event Solihull’s pound;27,000 bid failed, but the headteachers were reluctant to forget the idea and found a group of businesses to provide sponsorship. The money pays for the teachers’ time (pound;50 a session) and for supply cover so they can meet during school time for planning sessions. A steering committee involved secondary heads from the start and helped allay fears that Solihull School might use the scheme to poach potential pupils.

The children are chosen by schools largely on the basis of their predicted performance in key stage 2 national tests. Steve Taylor, head of Dorridge junior, and chair of the project’s steering committee, says: “They have to be well up in level 5 or at level 6. The school picks two, plus two reserves. A letter goes out to the parents seeking consent. They are always very supportive.”

The authority, he explains, has for some years had an interest in helping able children, with an inspector responsible for the brightest pupils and a tradition of weekend enrichment projects.

The present scheme continues the spirit of previous ones by aiming to enrich and broaden the children’s experience rather than fast-track them through the curriculum.

So the Saturday morning sessions are “not the national curriculum”. But the projects will sharpen children’s basic skills. One of the maths group’s tasks this year, for example, is to design and make a package for six tubes of Rolo which is efficient, cost-effective and attractive, and tessellates in all three dimensions. It involves a great deal of work with shapes, and concepts such as visualising 3-D objects from 2-D drawings, all of which appear in the maths curriculum.

As well as this there is work on computers, and number games. One involves an alien race (Zircons) who have seven fingers, and so work to a number base of seven rather than 10. By the end of the third Saturday, the children’s work, including the Rolo packs, will be on show for visitors - and the children get to keep the sweets.

Other subjects share the same creative approach. The science group carries out a murder investigation using microscopes, data-logging techniques on computers and the analysis of anonymous letters, while the English sessions home in on poetry, debate and genres of writing. In each case there is an end product - an exhibition or a stunning anthology.

All the projects have strong cross-curricular links. Other connections are made, too, because on arrival, the children are split up and put into mixed gender groups with children from other schools. Lucy Simonds, Solihull’s numeracy consultant, who is heavily involved in the maths programme, believes this is an important ingredient of the scheme.

“They gain the ability to work well with other children,” she says. “In their evaluations at the end they write things like, ‘I discovered I could work with boys’, or ‘I found I could work with people I’d never met before’.

“They also have their first experience of working in a big group of the same ability.” At the end of the class, the children gather in the hall to wait for their parents or the minibus. There are big smiles all round. Nicholas Lunn of Coppice junior says: “It was really good to be here and use the facilities and the computers. It was much better than I expected.”

Parents like the scheme. Chris Mitchell, meeting her daughter Joanne, says:

“We were honoured to be asked. We’ve put everything aside for this. And see how she came down the corridor grinning from ear to ear.”

Equally obvious is the enjoyment of the teachers, who are given the opportunity to devise and lead challenging work outside the national curriculum. David Harding, his love of mathematics making him bounce eagerly about the room, says: “Three hours here is like a full day in school. They really move. It’s like the top third of my sixth form.”

Solihull School headteacher Patrick Derham says: “Just watching their brains work is remarkable.”

Mr Derham has worked hard on the project and was influential in raising sponsorship and in management meetings. As well as hosting some of the Saturday sessions, the school’s staff teach on all the modules, and its minibus transports children whose parents cannot bring them.

On the morning of this first session Mr Derham is outside supervising the arrival and departure of pupils. “It’s wonderful to see children here from all over the borough,” he says, looking at the traffic jam in the car park. “Lots of them stay in e-mail contact with each other afterwards. The least I could do was provide the facility.”

Deciding to run a Saturday enrichment project is one thing. Making it work so that everyone knows what to do, and that energetic children are kept on their toes, is something else.

Steve Taylor says: “You have to gather an enthusiastic team. They have to be committed to the concept of partnership because there are many stakeholders in this: authority, schools, the independent school, businesses. Like so many other things, it comes down to the qualities of the people involved.”