The two boys are playing Twiddleums. You're not familiar with Twiddleums? How about Spiral Ludo, then? Or Quartette? Or Climbing Everest (the one where you must roll a six before making it to the summit)? They're all here, permanently set up on individual tables.
To be honest, it doesn't really matter which of the games the boys are playing. It's the way they play it that's remarkable. No sneering or swaggering or putting each other down. No embarrassment because I am a stranger and they are teenagers and this is a silly parlour game. Instead, they encourage each other. They explain the rules for my benefit. At one point, they even smile.
Did I expect anything less? Well, frankly, yes. The lad on my left, you see, has been barred from every school in the area for punching his headteacher. And the boy on my right? No one could handle him. He was out of control. Not every teacher's choice of pupil - damaged and disturbed, damaging and disturbing. And yet here, in a renovated Victorian schoolroom in Lichfield, Staffordshire, they are the nicest boys you could wish to meet. For this is the Stowe Teaching Unit, a mixed pupil referral unit that opened nine years ago and where 18 children with emotional and behavioural difficulties aged from 12 to 16 come to be remoulded - made ready, if at all possible, for re-entry into mainstream education. And here, the rules of play are as clear as in any parlour game.
"Put a smile on your face. You're looking miserable. Is everything all right?" "Yeah."
"What did you say?" "Yes, Sir."
That's Kevan Paylor, blending pastoral work with a spot of manners coaching. He's a big man of 50, smartly dressed but jovial, like a jolly town mayor on a semi-informal visit. But Kevan ("I don't want any of that Mr Paylor nonsense") is not visiting. He's been head of the unit for two-and-a-half years now, and he's here to stay.
Kevan is justly proud of what he, his colleagues and pupils (all boys, at present) have been achieving at Stowe, and he is keen to talk about it. But first he's needed in the old school yard, where it's time for Chain Tag.
Chain Tag, like The Great Limpopo River and Hot Rice and Stuck in the Mud, three other Stowe playground favourites whose rules the children themselves helped to research, involves a great deal of calling out and running around. There are shouts of "Get Mrs Ellis!" and "You know the rules. Get on the end!" Soon there are 14 boys (four are away today on work experience or at college), three teachers - including Kevan - two support staff and a voluntary helper, the entire Stowe establishment, in fact, spread out and linked by the arms like revellers on some holiday hokey-cokey.
"It doesn't matter who wins or loses," says Kevan when he's got his breath back. "It's the taking part. In fact, we use the games to remove the fear of losing from these kids. It's a very safe environment here, because they can make fun of themselves. It's safe and it's fun. But they know what the boundaries are, and they know that they are very firm." Pupils who step outside those boundaries lose the right to carry an activity card. This means he must remain in the schoolroom all day; his card will not be restored until an application is passed by a meeting of the staff.
Along with their activity cards, the children are handed their school ties each morning. (For safe-keeping they also hand in smoking materials, referred to by staff and pupils as "groceries".) The ties are part of a general grey, blue and white dress code that excludes denim, baseball caps and jewellery. The dress code is part of an overall philosophy, a calming philosophy that excludes activities like snooker and pool and replaces them with parlour games, co-operative playground games and chess.
"Chess is compulsory at Stowe," says Kevan. "There's a set in every room, because mastering chess is a useful learning experience." (They play the local high school, but never pick a team, on the basis that "any child who wants to play plays".) Apart from more obvious mental skills, chess teaches them how to play by rules they cannot change, says Kevan. And in the canteen area, Paul Simon and Art Garfunkel are busy doing something rather similar.
Bridge Over Troubled Water is not everybody's choice of dinner-time listening, but the album is in Kevan's tape collection, with Vivaldi, Gilbert O'Sullivan and a compilation from the Big Band era. And all this week, the hymn board in the corner of the eating area plainly says "Simon amp; Garfunkel". So Bridge Over Troubled Water is played and if the kids don't like it, they must learn to lump it.
It's a little tongue-in-cheek, even a little self-mocking, like several of the rules and rituals at Stowe. But as Kevan explains, in addition to exposing the children to a broad range of music, it teaches them that, sometimes in life, "they just have to listen to what other people want to hear".
It's not all mind games here, however. The ambition of every pupil at Stowe - motto "Forward Together" - is to get back into mainstream education, and so the staff teach English, maths, science, IT, art, history, geography - "as balanced a curriculum as we can with our limited resources", says Kevan.
His deputy head, Jean Davison, teaches four of those subjects. She leads me into a classroom whose walls are alive with paintings, a room in which boys are busy writing or drawing, or helping each other master the intricacies of a computer program in such an atmosphere of calm and co-operation that it's easy to forget that most them have been excluded from other schools for extreme and difficult behaviour.
She shows me examples of their work, and they tell me what they are doing, politely and with self-assurance and genuine enthusiasm. There is a characteristic emphasis on presentation here, with a printed set of rules which must be applied without fail to each work folder. But there is creativity too: poetry, photography and abstract art. And the frequent visits to galleries and theatres and special activity workshops are recorded in illustrated booklets, produced by staff and pupils.
"We take a holistic approach to education," Jean explains, "and the ethos of the whole place is based on mutual respect." The pupils watch how the staff get on with each other. "They see how we enjoy working as a team, and they pick up on the ambience," she says.
Even the furniture has a role to play. Nigel Peckett, the maths, science and IT teacher, says they had the height of all the cupboards reduced so they would seem less overbearing.
Pictures of former pupils are all over the unit, and Kevan gives me a guided tour. "This girl was an absolute gem," he says. "She's a nurse now. And this lad is a salesman. They both come back to visit us." In the wall of one room, there is a huge display of framed certificates "for continued excellence in all aspects of unit life", "for an excellent attitude to helping others". They are awarded to the children at end-of-term ceremonies, to which parents are invited. "We have a proper presentation," says Kevan, "and the youngsters really love it. Nobody has ever presented them with anything before." (Needless to say, he finds a reason for every child to win a certificate.) And then there is the museum of education. When Kevan, a historian with a love of museums, found himself teaching in a Victorian school, he couldn't resist the temptation to research its past and to assemble a collection of historical school artefacts, with the active help and participation of the pupils, of course. There are bells and slates and a wooden egg-and-spoon game ("it's harder than it looks. Here, have a go"). There are pens and ink, registers and punishment books, and even a tableau with mannequins dressed in Victorian clothes. The children love it, as do the elderly residents of the flats next door, some of whom were pupils when this was plain St Chads C of E.
The pensioners visit the museum, and children from the unit help with their gardens. All in all, it turns out to be another of those learning experiences which just seem to materialise at Stowe, but which Kevan assures me are actually the result of detailed discussion by staff once the children have been taxied home.
Does it work, this eccentric - at times almost surreal - blend of fun and games, held together by a framework of detailed rules and contained within clear, unyielding boundaries? "We do have failures," says Kevan. "If a child uses violence against staff or another pupil, I recommend permanent expulsion." It's a threat he has only had to carry out once in two-and-a-half years. "But when we say 'no violence', they have to know that we mean it."
Meanwhile, he has lost count of the times parents have said "he's completely different now" or "she's so much more considerate" of a child attending the unit. And one member of staff told me how, on a recent trip to the theatre, the doorman approached him and said, "Are that lot with you? If so, then I commend you."
"We still have the odd one who's arrested," says Kevan. "But a lot take a considerable amount of what they have learned here back with them."
Staffordshire's new inspector for special needs, Janine Murphy, is impressed. "We're very proud of Stowe. It's a good unit catering for an important need," she says.
"Kevan took the unit, which was very run-down in terms of the buildings, and he used his budget creatively. He got community help and did a splendid job in making it a vibrant learning environment. Pupils who before were reluctant to go to school are now very happy to go."
She is impressed too by the judicious mix of arrangements, with schools, colleges and work placements, which extend the Stowe pupils' education, but also mean Kevan can cater for more pupils.
"Now we're hoping to develop it even further so that the unit can do more work supporting children in mainstream schools," she says.
"At the centre of it is good education and curriculum. But they also spend time developing the children as individuals. They've taken some difficult children and done a wonderful job with them."
The average stay at Stowe is less than a year, but some remain longer - repairing damaged children takes as long as it takes. And once they fly the nest, it's not always the end of the story. One lad achieved his ambition of returning to mainstream education, but still insists on having his dinner at the unit on a Friday. He has even invited Kevan to his mum's wedding. Kevan is clearly touched.
"We like to refer to ourselves as a family," says the head of this extraordinary unit. "Although so do the Mafia."