The conference comes at a time of great uncertainty for the private sector as it awaits the outcome of the next general election. The abolition of the assisted places scheme by a Labour government could have profound effects on a system that educates some 7 per cent of secondary pupils in England and 5 per cent north of the border. But Lindsay Paterson, professor of education policy at Moray House Institute of Education, says: "Even if we accept that all those benefiting from assisted places are from relatively poorer backgrounds the vast majority of pupils attending private schools are from middle-class backgrounds. "
A quarter of Edinburgh's 68,000 pupils are at independent schools, a higher proportion than any other city in the UK but parents remain happy with the state sector, Professor Paterson says. "One of the reasons is ironically the Government's placing request legislation which allows parents the free choice of schools. It has allowed certain state sector schools to become open to choice by parents who might otherwise have sent their children to private schools. We have a situation where the middle class are more supportive of public education in Scotland. What happens in the future depends very much on the outcome of the general election."
So far opting out has not been taken up widely by parents north of the border. Professor Paterson says: "There are suggestions that the way the Conservatives would like to go is to place the onus on parents to opt in so there might be ballots, compulsory by law. In such circumstances a lot would choose to opt out. As far as funding is concerned a lot of middle-class schools in the state sector are finding that their budgets are being cut."
He adds: "If these schools do leave local authority control they are of a very similar status to independent schools but they are not charging fees. In some parts of England some independent schools have tried to come into the local authority sector precisely because they see now the problem of competition from grant-aided schools."
Judith Sischy, director of the Scottish Council of Independent Schools, says: "There is unanimity within the independent sector that what we are doing is fine but we have to consider what we will look like in the 21st century as a sector as well as each individual school."
Of the 30,000 children at independent schools in Scotland, only 3,000 are on assisted places and if a Labour government phases out such assistance Mrs Sischy does not anticipate schools closing.
She says: "What will happen is either children will be replaced by full-fee children, which I do not think will be possible in all 3,000 cases, or schools will do their best to offer bursaries and scholarships. But this won't match the money available now in the final analysis."
Mrs Sischy stresses the variety of scholarships available, in music, art and sport and estimates that around 20 per cent of secondary pupils, including those on assisted places, are receiving help of some sort or another. "If the money is not available from the Government, how do you keep the door open for that 20 per cent? I think the schools will make a very good attempt to do that. When you speak to heads you hear that they don't want to become exclusive schools just for those who can afford it."
Elizabeth Maginnis, education convener in Edinburgh, believes there will always be private schools to meet the demand for a particular kind of ethos but state schools remain overwhelmingly dominant because they have a wide range range of abilities among staff and remain attractive to parents.
This was recognised by the independent schools that approach local authorities to buy into staff and curriculum development programmes. Private schools in Edinburgh are increasingly undertaking projects with the state sector.
"All of this underpins a mutual recognition of need between the two sectors, " Mrs Maginnis says. "I think we have to demonstrate within the state sector that our results continue to improve and children of all abilities leave with the maximum qualifications they could expect to achieve in any system."