What to do with them? It's no good shouting - many of them live in a world that's just one big 24-hour yell. What difference is it going to make if teacher weighs in with "STOP IT MARK!"?
Some schools, of course, plug on in a state of permanent semi-confrontation with their most difficult children - a war of attrition, using up teaching-assistant time, invoking the special educational needs procedures, having meetings. Then, maybe, back to three-way shouting (parent, school, child), an insomniac teacher and a head despairing of the effect on community relations.
Increasingly we're beginning to meet heads who are searching for something else -a way of reaching around the confrontation and finding the child on the other side. As heads are determined people, used to finding what they want, they're actually coming up with answers.
Jane Blacklock, for example, at Newtown primary in Carlisle, uses Cheiron Trust's idea of "the Quiet Place". It's both a concept and a physical space - a room decorated like a tropical island that looks, feels, sounds and smells entirely different from the rest of the school. "You walk in and find yourself in a wonderful, magical place," she says.
In the Quiet Place, six children at a time, over a half-term, meet a psychotherapist and a therapeutic masseur (both trained by Cheiron) learning how to recognise and deal with their feelings in a calm and quiet atmosphere. The effects, says Jane Blacklock, spread through the school and the community.
"The children's parents have massage, and the staff when the masseur has time," she says.
Another Quiet Place enthusiast is Phil Doyle, head of St Margaret Mary's Catholic junior in Liverpool. "Two hundred and fifty of our children have been through the Quiet Space, and every class uses it on a regular basis.
We get fantastic comments from the children. We couldn't imagine life without it," he says.
Also addressing self-esteem is "Paths" - "Promoting Alternative Thinking Strategies", from the United States, which is being used in a number of authorities and education action zones, including East Manchester EAZ.
"Paths" is a two-lessons-a-week programme of problem-solving that puts the responsibility on the children for thinking through the answers to issues that affect their feelings and reactions.
Jane Ferguson, Paths co-ordinator at Seymour primary in Manchester, says:
"When children come into school not knowing basic things like their colours we don't make judgements about them, but when there's a deficit in social skills we actually blame the children for that."
Not a million miles from this approach, and also spreading through authorities, is Investment in Excellence (IIE) from the Pacific Institute.
Originally used with staff - often including education officers and advisers - to build up their confidence, there are also programmes for key stages 1 and 2. JohnJCorbett at Summerbank primary in Stoke on Trent has used them with staff and children.
"It promotes good-quality discussion," says Mr Corbett. "The children think and talk about the way they learn and think about themselves. Children listen to a lot of negative talk in their lives. We want them to be saying, 'I can do. I can achieve.'"
There are other approaches that you might, for want of a better term, call a "Third Way" to the primary curriculum (as between target-driven formality on the one hand and simmering underachievement on the other).
The International Primary Curriculum for example, based on "brain friendly" principles and originally taken up by international schools looking for alternatives to the UK national curriculum, is now established and proving popular in a number of UK schools; and Jenny Mosley's "quality circle time" is much more than a 10-minute interlude in the day.
None of these is going to transform a school overnight - but then, no primary head or teacher would believe anything could. As Jane Blacklock says of a Quiet Place: "It's not a magic wand. It's provided quite dramatic changes in some children and more gradual understanding in others."
It also, she says - and users of Paths, and of IIE make a similar claim - helps children to put words to their feelings. "It's very effective for emotional vocabulary," she says. "They can talk about their own behaviour in a much more structured way and analyse it."
Even more importantly, says Ms Blacklock: "It sends a message to the children that they are not just scores on a test sheet, but that we value them as people."
That's the key isn't it? The more we bang on to children, saying, in a well-meaning way: "With a bit more effort this work could be a level 4," (and how often have you said that this term so far?) the more they will suspect that our motives are to do with the school's priorities and not with their own worries and concerns.
A Quiet Place: www.cheiron-quietplace.com. Paths http:www.channing-bete.compositiveyouthpagesPATHSPATHS.html.
Investment in Excellence www.thepacificinstitute.co.uk. International Primary Curriculum, www.internationalprimarycurriculum.com, Jenny Mosley's Quality Circle Time, www.circle-time.co.uk