Its head, John Botham, is the director of a 10-school project in Nottingham which has measurably raised standards of both academic work and behaviour for inner-city children through careful planning and the setting of precise targets.
At Greenwood, seven to 11-year-olds are taught in ability groups for maths and English, but there is other targeting as well to meet the particular needs of this largely Asian Muslim school, such as special teaching for pupils who have been away for extended holidays and separate science teaching for girls.
These were cited by Tony Blair in a lecture at the University of London last week which skilfully blended the values of the old and new Labour. "We know our objective: to maximise opportunities for children to develop themselves, " said Mr Blair. "And we know too the two extremes that we must avoid - divisive selection on the one hand and teaching to average ability on the other. "
Differences in capability needed to be addressed, he said. "'Setting' in different subjects as children proceed through the primary years, or 'target grouping' as they call it in Nottingham, has a role to play and we should not shrink from this".
He urged flexibility. Flexibility is central to Greenwood's success. When the Raising Achievement project began in 1992, "We looked at the organisation of classes," says Mr Botham. "What we said was that we were convinced that you didn't have to have the same organisation all the time. You needed an organisation that fitted the purpose." They also felt that children didn't always have to sit in groups. "We sometimes work lecture style." There is a place for some didactic teaching, with junior age children, he believes.
Sometimes there is a case for imparting knowledge to information-hungry youngsters. "We expect teachers to have a tad more knowledge than seven-year-olds".
There are also arrangements to make sure children get the benefit of a variety of teachers' expertise. "In the afternoons we break down class barriers", he says. Children shouldn't miss out on the motivation of a music enthusiast, for example, just because she is not their class teacher.
Mr Botham, an inner-city boy himself from the London Docklands, began to question the orthodoxy of the "busy" classroom, with a multitude of activities going on at once based on discovery by the children, because he did not believe it helped most inner city children thrive.
"Children don't naturally achieve their potential. They need help," he says. But everything done at Greenwood and the other Raising Achievement schools is based on evidence.
In addition to small-scale class tests and teacher assessment, children are screened in maths and English using NFER tests, and these show the "value added" by the school since pupils entered in 1992. Their scores went up from 83.2 per cent of the national average in maths to 90.5 per cent in two years, and from 79.1 per cent to 88.3 per cent in reading.
The Raising Achievement project was set up in 1992 under a Grants for Education Support and Training project to raise achievement in urban schools, and was then continued under City Challenge funding, with a slightly different group of schools.
Nottinghamshire county council hopes to extend its lessons throughout the county. One of the few inner city projects geared toward setting targets and value added assessment in the primary sector, it was written up by Professor Michael Barber of Keele University - an important influence on Blair's education thinking - in his study of achievement in inner cities for the Office for Standards in Education. "One was tempted to conclude, 'I have seen the future and it works'," he wrote.
School inspectors have consistently highlighted low achievement and mediocre teaching in junior lessons, but John Botham says there is no reason for key stage 2, with bright, eager pupils, accustomed to school and ready to take in knowledge, to be a "wasteland".
The Nottingham project focused on three areas of improvement: "achievement in school", behaviour, and home-school links. Specific targets were set, for example to boost reading scores by a set number of points. Behaviour, too, was targeted. They found a way to measure bad behaviour, by counting things like punches and kicks, and developed policies to suit each school.
"We found even though schools could be very close to each other, they could have very different behaviour problems. Greenwood found that most of their problems were emanating from lunchtime scuffles, which in turn related to problems before school. They zoned the playground into different areas, including a quiet one with picnic tables, put down games like hopscotch, and taught the children to play them. They also established a consistent, whole-school system of sanctions and rewards, where all the rules are very clear to the children.
The result is a calm school with orderly play times. Home-school links are harder to measure, but they have found that children are the best people to involve their own parents. "They're much tougher on their parents than we can ever be", says Mr Botham. Several of the project schools are producing their own videos (research showed that every home had a video recorder) to lead more able children, working in small groups at each other's homes, into science or maths tasks.
Teachers at Greenwood said that far from stigmatising children, ability setting made them more content. "They see success within each day because the work is geared to their need, and that success sometimes transfers into other subjects", says Section 11 teacher Kathryn Twigger. Behaviour also improves. In addition, children know they can move up. Nothing is fixed.