We know them when we see them - hoods up, trousers halfway down to their knees, swaggering along the pavement in small groups, playing loud music on their phones, swearing, spitting. These are the children Michael Gove described in September as the "educational underclass".

Most of the teenagers arrested in last summer's riots were in this group. There were a few exceptions, where a young adult was pulled into crime by a temporary shifting of the moral compass, a moment of madness. But the rest were the usual suspects. Most had no qualifications. Many had been expelled from school or were serial truants. They were attached to gangs and living a life of crime, drugs, computer games and fast food. Look at the shops they raided and you see what their values seem to be: trainers and mobile phones.

The state came down hard on them, and rightly so. Although a short custodial sentence is unlikely to do these youngsters much good, the courts needed to send a message that the public should not be intimidated. If you see these children on their own, there's often much less of a swagger. Look into their tired eyes, and you will see mistrust, fear and anger. Whether we feel pity for the awful lives many of them have led, or rage because of the fear they cause, we cannot afford to ignore them. If we are to protect ourselves, we must do more to change their behaviour.

Many of them have been thrown out of school and have ended up in Pupil Referral Units (PRUs) or other alternative provision. Their future is then not good: barely one and a half per cent of pupils in PRUs get five good GCSEs with English and maths. Many of these institutions are simply holding pens. They may keep the children off the street for a few hours a day, but when they leave at 16 they have no meaningful qualifications or skills. One brilliant head I visited described her PRU when she took it over: "It was run like a holiday camp, the children never did any work and they spent their time out on trips, playing pool or on Facebook. I think the staff were frightened of the pupils and they were never challenged either about their behaviour or with any academic work."

As part of my role advising the Government on pupils' behaviour, I have been reviewing the provision of education for children who have been excluded from mainstream schools. In writing my review, I have been able to see some fine schools, with inspiring head teachers and staff. The best of these PRUs transform the lives of pupils: the children are helped to manage their anger, deal with their feelings and change their behaviour. At the same time, these units provide teaching that is as good as any in the country. They also work closely with local schools so they can intervene early, before things get so bad that the child is expelled.

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If we want to improve all our PRUs then the best of them must be given greater freedom to do their job. They should be permitted to convert to become academies and allowed to innovate and develop. They should be able to take over failing PRUs, and set up new provision in other areas. Then they will come up with ideas that no one in government or local authorities has thought of - because these are some of the elite school leaders in the country. PRUs should be able to train their own teachers, so we can develop a workforce of experts in behaviour, who have the understanding to teach the most difficult children.

Mainstream schools should have more choice about where they send their most troubled pupils. At the moment their budget is cut to pay for the local authority PRU. Schools have to pay even if the PRU isn't any good. That's wrong. Schools should be allowed to use any good independent provider, whether it is a small independent school or a charity. The monopoly of the local authority's default PRUs should be ended.

With this freedom for schools comes more accountability. At the moment they often send some of their children with behaviour problems out of school to receive support, but some of the providers are as bad as the worst PRUs. I have recommended that the Department for Education and Ofsted set up extra inspections of schools, to ensure they are not sending their most vulnerable children to this sort of low-quality, out-of-sight, out-of-mind provision.

My recommendations are challenging, but necessary. The behaviour and attitude of some of these youngsters can be appalling. There's a temptation to push them into the background and hope they will go away. But they won't. If we don't give them what they need to get their lives on track, we will all pay, via the cost of prisons, mental health services, crime and welfare benefits. If we don't begin to solve this problem, we will continue to pass it on through the generations.

Charlie Taylor is Expert Adviser on Behaviour to the Department for Education