It's a maths class at HM Brinsford Young Offender Institution and Remand Centre, sited on flat, motorway-crossed countryside near Wolverhampton. Eight boys are losing concentration as the end of the afternoon looms. They are chatting, tipping their plastic chairs back under the fluorescent light and staring out of the barred, smeary, non-glass windows through which there's nothing to look at except more low-lying prison buildings.
One boy, a figure familiar from most secondary school classrooms, is squatting on the teacher's chair, cursing the food and the officers to anyone who will listen. He is pale, small and wary, and looks even younger than his 15 years.
The number of 15-year-olds in prison in England and Wales has more than doubled over the past five years, to 261 in January this year. Many are held on remand, and not given a custodial sentence when their cases come to court.
With the new Labour Government promising an end to repeated cautions - the most common method of dealing with juvenile offenders - numbers may be set to rise still further. But can prisons, particularly in the face of relentless budget cuts, offer young teenagers a reforming experience?
Brinsford, opened in 1991, was purpose-built for young offenders. Roger Tucker, head of regimes, is responsible for what prisoners do with their time. A bluff, cheerful figure with 27 years in the prison service, he sits at his desk behind a golf club paperweight and a mug bearing the message: "Old golfers never die, they just lose their drive." Mr Tucker is well aware of the responsibility he and his staff have towards the young prisoners.
"To me, with this age group, care is still not a dirty word," he says. "I feel a responsibility, because they are young men and we have a duty of care." He says staff try to find time to listen to prisoners' concerns, and he is proud that Brinsford offers more than the statutory minimum of 15 hours' education a week for 15 and 16-year-olds, despite spending cuts.
Once sentenced, juveniles are meant to be separated from older prisoners aged 18 upwards. But at Brinsford, as in other young offender institutions, overcrowding makes this impossible. Built for a maximum 448 inmates, with 29 hospital places, on the day of The TES's visit, Brinsford was holding 503 young men aged 15-21, one in five of them juveniles. Does Roger Tucker worry to see younger prisoners mix freely with older ones?
He says: "Some juveniles are 15 or 16 going on 28 - others are going on eight or nine." He rejects the suggestion that all 15-year-olds are impressionable. "They're well-versed in the system. They see this as an occupational hazard."
Persistent bullies are segregated for the protection of the vulnerable. The prison also has what Mr Tucker describes as a "fairly sophisticated" programme to stop young men committing suicide, although there is much self-harm. "It's more attention-seeking than attempted suicide," he says. "You don't usually have to go far back in a young person's history to find the reasons for it."
Do the teenagers serving sentences at Brinsford leave in better shape than when they arrived? Mr Tucker hesitates for a long time. "It's constructive in as far as there is a routine," he says. "If they want breakfast, they have to be up by 7.30am. If they want to go to education, they have to be dressed and have their cell cleaned. If they want visits, they've got to get out of bed to see their mum or their girlfriend. The skill of staff is to encourage people who might not be motivated to do these things."
For some, he says, the benefit of prison might be in learning to eat with a knife and fork, after a lifetime of eating takeaways with their fingers. For others it might be coming off heroin. "The experience is one of discipline - of routine," he says.
"Facilities are available to address problems - drug courses, drink courses, courses dealing with theft, and taking and driving away. You can make a start, but they're not with us for long enough to undergo any significant change."
Despite the best efforts of many prison service staff to help young offenders, the results are not encouraging. While 62 per cent of adults re-offend within five years of a custodial sentence, in the 14-17 year age group the rate is 90 per cent, according to the Trust for the Study of Adolescence.
In recognition of the brutalising effect prison can have on youngsters, the 1991 Criminal Justice Act says 15 and 16-year-olds should not be held in custody on remand except where it is deemed unavoidable, and that in such cases they should be held in local authority secure accommodation, not prisons. Local authority secure accommodation is subject to the provisions of the Children Act and runs primarily along care lines, rather than security ones.
Despite past government pledges to address the desperate shortage of secure accommodation for young people, few new beds have become available. The planned five new "secure training centres" are for incarcerating even younger children, aged 12 to 14. (The contract for building the first one has just been awarded to a Group 4 subsidiary, ominously named Rebound.)
Many juveniles end up in adult prisons, which lack the necessary resources and expertise. Are they seen as children, or men? "They're children," says Juliet Lyon, of the Trust for the Study of Adolescence. "But many will think they're men, and they will have led a life which is in some ways adult, either criminally or socially. But they are in transition. They're not fully-formed adults, and you have to work differently with them." The TSA has developed well-regarded training materials for prison service staff working with young offenders.
In 1993, after several boys committed suicide in prison, the Howard League for Penal Reform set up a project to "rescue" 15-year-olds from custody, focusing on Feltham Young Offender Institution and Remand Centre, Middlesex, where four youths died in the early 90s. Barrister Mark Grindrod worked on the project from its inception. "Prison is never the right place for a young person," he says. "You look at what's happened in their lives, and the level to which they've been marginalised - particularly if they're black - and realise the prison service is being asked to pick up on the problems we've failed to address earlier in these kids' lives. "
A report from the Howard League introduces a selection of the 650 children the organisation has worked with, through case histories which make pitiful reading. There is "Andrew", sexually abused by an adult outside the family, prone to attempted suicide, and serving a six-month sentence for attempted robbery. And "Eric", from a chaotic family, a heavy user of drugs and pre-occupi ed with visions of death, nearly succeeded in his attempt to hang himself in his cell. Then there is "Dan", physically big but with a child-like outlook, unable to read and spending much of his time in a fantasy world derived from comics.
The list goes on. The Howard League project helped its clients in ways ranging from basic support - such as befriending and supplying them with crayons and drawing paper to help pass the time in their cells - to organising appeals, securing their release from prison and, often, obtaining the psychiatric treatment they needed.
Many of the 15-year-olds were found to be in prison illegally. "Grant", for instance, was remanded in jail after a burglary charge by a magistrate who said it would "teach him a lesson". But juveniles can legally be sent to prison on remand only where the offence is sexual or violent. Grant tried to kill himself in prison, before the Howard League secured his release through a successful court appeal.
The project at Feltham, which operates with the support of the prison governor, has been taken over by the Children's Society. But it is unique. Most of the 15-year-old Grants have no dedicated criminal lawyers looking out for them. A high proportion - around one in three - come from care and may have no one who is interested in them.
"No part of the prison population causes me more concern than the juveniles, " wrote HM Chief Inspector of Prisons, Sir David Ramsbotham, recently. Young offender institutions vary dramatically, and the Inspectorate is about to embark on a review of the whole young offender estate. In March, it published a report into a young offender institution in Dover. The findings were shocking.
"The six-bed dormitories in which the majority of young prisoners were housed, apart from being ramshackle in appearance, were the setting for untold bullying and criminal corruption," said Sir David. "They were a veritable jungle, in which the strong preyed on the weak, and where most who entered the establishment had to physically fight to survive, or exist as a vulnerable prisoner, subjected to continual intimidati on and insult."
The prison, a Victorian fortress around some 1970s blocks, contained at the time of the inspection almost 300 young men aged up to 21. Conditions there "offend the most basic standards of a civilised society", warned the Inspector.
Relationships between young prisoners and staff at Dover were said to be good. But the design of the dormitories made supervisio n difficult, and cuts to the prison budget meant they spent long hours locked up together, and were inadequately supervised.
Diane Abbott, MP for Hackney North, was a barrister before she was a politician, and once worked with the Prison Service. "Anyone who knows anything about the criminal justice system knows prison doesn't work," she says. "But it's hard for politicians to be intelligent about law and order.They get swept away with the public wish for retribution."
She says the problem cannot be addressed without including schools. "You have to look at the rising tide of suspension," she says. "Where do these people go? Half the time, they end up on the street corner getting up to no good. If they're in school, they won't be nicking your video, or selling crack."
The evidence tends to support her point of view. Three out of four excluded pupils offend, according to last year's Audit Commission report into young people and crime. Eight out of ten of the 15-year-olds the Howard League tried to help were either excluded from school at the time of their arrest, or were not regular attenders. This is a chicken-and-egg situation, where teachers point out that the young people would not be out of school if they had not shown anti-social behaviour. But no one disputes the rise in the number of permanent exclusions.
Former Home Secretary Michael Howard, in a recent Green Paper, mooted some constructive if belated ideas about intervening earlier with young offenders. Labour has promised to reduce the delays in bringing young offenders to court. But in the recent election, no party trumpeted plans to help the damaged teenagers who increasingly fill prisons. "It's a perverse situation," says Mark Grindrod of the Howard League. "Most people who work with young offenders are on the same wavelength. But they are getting nowhere because the popular belief that prison works is so saleable. No one's prepared to get on the hustings and say it doesn't - so we are stuck in a punitive cul-de-sac."