EBD is a national problem, so Hull is not on its own here. The authority had used two schools in neighbouring East Riding for its special provision for behaviour, but last year one closed and the other could no longer admit Hull's problem children.
"We had to put them in our pupil referral units," says Colin Herrick, Hull's child protection officer. It has obviously put strains on the system.
The authority is consulting on ambitious plans: a new primary referral unit, a new EBD day school and a headteacher panel to monitor the new arrangements.
Many of Hull's heads see behaviour as the biggest obstacle on the way to raising standards in their schools. They are willing to work hard to include children with challenging behaviour, but argue that children with severe problems should be educated in special schools.
"Mainstream classrooms are not the place for these children," said one primary head.
The education authority points out that secondary schools in Hull receive more than pound;1.5 million of funding, from Excellence in Cities monies and the pupil retention grant, to help them cope more effectively with challenging behaviour. The consultation paper proposes delegated funding that aims to help primary schools establish their own in-school inclusion units.
Secondary inclusion units, such as the one at Hull's Winifred Holtby School, have had a great deal of success in dealing with challenging behaviour.
Jan Vogel is the co-ordinator of behaviour support at the school.
"I don't teach," she says. "I'm completely support. We run a series of programmes that are proactive behaviour modification programmes, and there is a lot of parental involvement."
The school pays a counsellor to work with families, and there are drop-in sessions for parents and staff. When a child is at risk of exclusion, Ms Vogel works hard to find the positives.
"Look at their timetable," she says. "Give them a green marker pen and ask them where it is going right? You can guarantee that 60 per cent of that kid's timetable is green. So we ask how we can spread that?"