Traditionally, teachers have stepped in to patch up arguments that spill into the classroom or waded in to separate playground fights.
Now, new schemes are emerging that encourage children, sometimes as young as eight, to settle their grievances with the help of other children.
Earlier this year, posters went up around Walworth School, an inner-city comprehensive in south-east London, advertising a novel service - the Walworth Conflict Management Scheme.
'Are you involved in an on-going conflict or dispute? Have you experienced bullying or harassment?' ran the slogan. If so, help was available in the form of one of the first full programmes of child mediation in a British school - a scheme designed to help children to settle their own arguments peacefully and rationally, without adult interference.
Walworth School's neighbourhood is hardly renowned for its peaceful approach to problem solving - the 'Murder Mile', the stretch of Old Kent Road that backs on to the school, has one of the highest murder rates in the country.
Last year, a man was stabbed in a gang fight, and staggered in through the school gates; the police helicopter that landed in the playground to pick up the body was 'a distraction' for the children, concedes Martin Pring, the deputy headmaster.
Not surprisingly, the atmosphere within the school - a run- down concrete building - is often strained; staff complain that bullying is rife, and petty arguments often escalate to violence. Causes of disputes vary - from name-calling, fighting and bullying to 'going out with someone else's boyfriend'.
In January, Year 10 - the 14- and 15-year-olds - elected six of their number to train as mediators, and Thomas Daffern, who studied mediation at the Community Boards in San Francisco, began to instruct them in the art of resolving disputes.
Susanna Kelly, 16, one of the students chosen to become a mediator at Walworth, says: 'There's a lot of tension and jealousy here. You see all the fighting and arguing that goes on around the school, and nothing gets done about it because people are too afraid to go and tell the teacher. With someone closer to their own age, they might be more comfortable sitting down and talking about it.'
Last term, the school set aside a classroom and two morning sessions within the timetable to give the children a chance to approach the mediators. Three or four informal mediations were completed last term, and formal sessions begin next week. This term, the number of children chosen to train as mediators has increased to 15.
Other schools are beginning to implement their own mediation programmes. The first project involving children as young as eight years old has begun at Jessons Church of England Primary School, in Dudley, near Birmingham.
In January, Charlie Hilken, a staff teacher, and Hilary Stacey, a former French teacher who is currently doing a PhD in child mediation at Nene College, Northampton, introduced all the eight- and nine-year-old children to the basic principles of mediation.
In a series of workshops, they studied affirmation - 'learning to say nice things about each other' - co-operative games and communication skills.
Staff believe that the children benefited from the training. Ann Stone, another teacher involved in the programme, says: 'Obviously they still have their arguments, but they seem much more mature when it comes to settling them.
'They work together very well, and they are vastly different from children in the year above, who haven't had the training.'
Once the general training was completed, the children elected 16 of their classmates to train as full- time mediators. Coincidentally, the children chosen by their school friends were the ones the staff felt would make the best mediators. Formal sessions of mediation began this term.
By acting as 'lightning rods' to dissipate tension in the classroom and the playground, a handful of mediators may improve the atmosphere in the whole school.
At Jessons, where the children are much younger, the scope of the mediation sessions is more limited: violent disputes will be dealt with by teachers, and if a mediation uncovers violence or abuse, or provokes a threat of suicide, then it must be taken to a member of staff.
Teachers at Jessons say good mediators require confidence and self-esteem.
Some of the children have other suggestions: 'You have to be able to stick up for yourself, and you have to be able to keep a secret.'
Ms Stacey argues that children often make better mediators than adults, for they can be truly neutral - unlike teachers, who always have a vested interest in seeing a dispute resolved.
Nevertheless, it is a process that requires patience. 'It's much easier to have a fight than to try to settle your differences,' says Mr Daffern, who is also director of the International Institute for Peace and Global Responsibility at London University's Institute of Education.
He hopes to see one or two cases a week going to a formal mediation at Walworth - and, if the pattern in American schools holds true here, then 90 per cent will be successfully resolved.
Lucy Griffiths, headteacher at Jessons, hopes it will also make more time available for teaching. 'Even small disputes end up taking up a lot of the teachers' time,' she says.
Eventually, both schools hope that the children who have trained as mediators will pass on their skills to those in the classes below them to minimise adult influence. At Jessons, Charlie Hilken hopes to see workshops introduced throughout the school from nursery level upwards.
If the success of the schemes depends on the enthusiasm of the children involved, then the signs are good. Ms Stacey says: 'They become aware of their power to solve their own problems among themselves without any bullying. All we have to do is to make it possible, and then they do all the work.
'Children will always bully and name-call, and all the rest of it, but they can also be amazingly open and generous and loving towards each other. It's up to us, as teachers, to bring out these qualities.'
TEN MINUTES LATER, FRIENDS AGAIN At 1.15pm Marique and Lyndsay, both nine, make adjustments to the layout of the four chairs in an empty, brightly painted classroom in Jessons primary school. Then they go to the door together.
'Would you like to come in?' says Marique, formally, to the two nine-year-old girls waiting silently outside. Victoria and Rebecca were once good friends, but they have fallen out over a petty dispute that has grown out of all proportion. Marique and Lyndsay - the mediators - hope to help the 'disputants' settle their differences.
The girls - two black, two white, in grey skirts, white shirts and red pullovers bearing a Jessons crest - take their seats nervously, and the mediation begins. Posters advertising a circus decorate the walls of the special needs classroom, the venue for the mediation. Chalked on a blackboard are the steps they must follow: 1 Rules. 2 Problem. 3 Solution.
Marique and Lyndsay take it in turns to list the rules. Mediators will not take sides, nor offer a solution; it must arise during the discussion.
Confidentiality is guaranteed, and swearing, name-calling and put-downs are out.
In a broad Black Country accent, Lyndsay invites Rebecca to tell her side of the story: 'I'd come down from PE, and I was looking for the key for the cupboard, and Vicky went up and got it, and got the jewellery, and she wouldn't give me my watch and then she threw it on the table,' says Rebecca, breathlessly.
Lyndsay repeats her account, and Marique invites Vicky to tell her version.
It is rather different: 'I came in and I saw Rebecca looking for Miss, and I knew where the key was, so I went to get it, and I got the jewellery box, and I got three watches, and I gave out two, and then I put Rebecca's on the table.' After a moment, Marique repeats it back to her.
Now that the source of the argument is clear, both girls look sheepish.
Lyndsay invites Rebecca to suggest a solution: 'If she'd just ask me to help her with the jewellery . . .' she says, tentatively. Vicky has another idea: 'Maybe we could take it in turns to hand it out.' With prompting from Marique and Lyndsay they soon reach a compromise: one will get the key, and the other will hand out the jewellery. 'Do you accept that? Are you both friends?' asks Marique.
They shake hands and smile. Then Lyndsay completes the form relating the dispute and the solution, and invites them both to sign it - an important step, says Marique: 'Otherwise they could break their promise and say they hadn't done a mediation.' The mediation has taken 10 minutes; in a week, they will return to review the situation.
All four are enthusiastic about mediation. Rebecca is a mediator herself and decided to try the system when she and Victoria fell out. Victoria says: 'It helps us to sort out our arguments and make school a better place. It helps us to be friends and understand each others' feelings.' Marique says: 'It helps teachers understand our feelings and they don't have to waste time shouting at us.'
It is the fourth mediation at Jessons - the others included disputes over the ownership of a packet of crisps and a lost PE kit. 'They might seem petty arguments to an adult, but they're very important to the children,' says Ann Stone, the teacher in charge of formal mediations.
She attends all the sessions but from Christmas it is hoped the children will run them all themselves, and go on to mediate more serious disputes.
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