The 18 state school pupils in the maths classroom at St Paul's looked out of place – with their pink pencil cases and polyester sweatshirts – but they were having the time of their lives at one of Britain's top boys' private schools where parents pay nearly £18,000 a year to educate their sons to enter the leading universities.
These teenagers were getting lessons for free from the school's star-studded maths department as part of a controversial programme by St Paul's to help out neighbouring state schools that can't give their children the high-quality maths teaching that St Paul's pupils get.
The St Paul's teachers are amazingly well-qualified, including an Olympiad champion, a chief examiner and the editor of a prestigious journal of mathematics. No pupil at St Paul's in south-west London gained less than an A grade in maths GCSE this year and a large number of the quarter of pupils who get into Oxbridge annually study maths, engineering or science. The fact that the school is sharing its expertise with local state schools by inviting in their most able pupils is a novelty. It is controversial too on first sight – will the St Paul's parents think fee income is being used to educate children from state schools? – but it is certainly good for the children and for the school, according to the high master Martin Stephen.
"We're interested in the raw ability of the children to profit from the type of education we offer," he says. "We are asking very experienced graduate maths teachers of able children to teach graduate maths to other very able children."
Aged 13 and 14, the teenagers have to take a stiff test to qualify for the weekly lessons. Only the top 20 are selected. Nearly two-thirds of the 18 are girls, mostly from single sex girls' comprehensives.
It has taken almost two years to get the scheme off the ground after a false start with Saturday master classes that were abandoned largely because many pupils on the gifted and talented register willing to give up their weekends were not good enough at maths to benefit. The maths department had to tread carefully and enlist the help of gifted and talented co-ordinators in three neighbouring boroughs to avoid putting out a negative message about maths teaching in state schools. Some teachers were opposed to the idea of a leading independent school picking off their brightest mathematicians, as if state schools were not good enough to teach them. Others welcomed the opportunity to stretch their most able mathematicians.
The pupils say it is not patronising for a selective school to offer extra help to comprehensives that are teaching a wide range of ability. Their own teachers give them extra support but they usually have to work on their own or with much older students, they say.
"It's a lot more interesting than the stuff we usually do in class and it will give me a head start with A-level," says Sam.
Aysha, 14, agrees. "Everyone has heard of St Paul's," she says. "It's the great big independent school and I found it intimidating at first but now it is quite nice." Last year she followed a GCSE course with a top set three years older at her Fulham comprehensive but they have now left the school.
St Paul's sees the lessons as a key part of its community outreach that includes opening up its facilities through sports, music and drama clubs, Latin GCSE and Oxbridge entrance tuition.
There are thousands of students in state schools who have never met a graduate maths teacher because of the shortage of specialists in the subject, says Stephen. "We know we are very fortunate here. What I see in my maths department are people who are evangelical about maths in the nicest possible way. To be able to pass on your enthusiasm to a wider group is a natural progression."
St Paul's has bent over backwards to show that it is not threatening state schools. Paul Motion, the head of junior maths, says he is not aiming to fast-track the students to A* at GCSE. "We sent out a letter to schools assuring them that we were not duplicating what they were doing in their maths classes. What we do is not syllabus based. It's the sort of extension work we do with our Year 9s."
In practice he has found the students do not have the grounding in some maths topics to be able to tackle the challenges and sometimes has to stop to teach them. "The first lessons I wanted to do used simultaneous equations but fewer than half had done them. A lot of them don't have the algebraic skills they need to solve problems so I have taught algebra," he says.
"I am not criticising the state schools in any way as teachers are bound by the curriculum. There is certainly a case for challenging the national curriculum. These are very able students and we are expecting them to work at a higher level which at times means having to strengthen and reinforce their algebraic, numeric and geometric platform."
The scheme is open to the nearest boroughs – Richmond upon Thames where St Paul's is situated and neighbouring Wandsworth and Hammersmith and Fulham. Some of the schools sending pupils serve a deprived catchment, such as Fulham Cross and Phoenix but others, such as Lady Margaret and the London Oratory, are solidly middle class.
St Paul's has made it clear that this isn't a recruitment programme, says Stephen. "The department felt it had a duty to do something for the community and if they are getting students who are not gifted and talented then it's a waste of time for both them and the teachers."
How do parents of pupils at St Paul's, who pay for their sons' education, feel about other children getting it for free? "Only one mother has raised the issue and when I explained that the money doesn't come from fees but from the independent/state school partnership fund she was satisfied," says Motion. "As long as their sons are getting a good education, they are not wanting to deny opportunities to others."
Both head teachers' unions say they support extra help for very able children. "Bringing the best young mathematicians into contact with each other and with excellent mathematicians is an excellent idea," says John Dunford, the general secretary of the Association of School and College Leaders.
But he adds: "This won't work if the independent sector uses it to criticise maths teaching in the state sector. They might say it privately but I don't think there is a need to say it publicly because otherwise state schools will be less willing to take part."