Today, I am going back to my old school - Robert Gordon's College in Aberdeen - and I have some questions for the teachers and pupils, questions that have bothered me over the years as a former pupil of a private school.

Such as: is private education fair? Could state schools learn from private ones - or the other way round? Does a private education mean you are more likely to attain an influential position in society? Are Scottish private schools different from English ones? And the most important question of all: do private schools make society better or worse?

My plan is to walk round the school and put those questions to as many of the staff and pupils as possible, but first of all I have to walk around in my own past, which is disorientating to say the least. On the surface, not much about the school has changed. The buildings and interiors are the same, more or less, the uniform is the same, and even some of the staff are the same. One of the first teachers I meet, in the chemistry department, points at me and booms "I remember you!" and it's not for a good reason: chemistry was not my strongest subject.

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Elsewhere, the school has undergone some fundamental changes since I was a pupil in the 1980s. When I was here, it was all-boys and was run pretty much as it had been since its foundation in the 18th century. You were known by surname only, you had to salute the teachers, and if you stepped out of line, you were punished physically: by the belt, the boot or the hand. Twenty-five years on, the school is much more relaxed and less formal, although there is still the same emphasis on extra-curricular activities, sport ("clearly not his favourite subject," according to one report of mine) and an all-encompassing encouragement/pressure to take as many subjects, and sit as many exams, as possible.

If you like the sound of that and would like to send your children here, it will cost you about £11,000 a year for secondary (excluding the costs of the uniform and equipment), although about 5% of pupils have the fees paid. Last week, the writer Alan Bennett launched a strong attack on private schools, saying that "to educate not according to ability, but according to the social situation of the parents, is both wrong and a waste", but the funded places mean schools such as Robert Gordon's can call themselves charities and save many millions of pounds in tax. Which brings up one of the other questions I want to put to the staff: should a school that charges many thousands of pounds for its services be allowed to call itself a charity?

One of the first teachers I meet, Stuart Farmer, who is head of physics, has an interesting perspective on private education drawn from experience of both private and state sectors. He grew up in Cupar in Fife and attended the local comprehensive, he has taught in comprehensives and independent schools, and he sends his daughters to Robert Gordon's because, he believes, the expectations are higher than they were when he was at a state school. From his conversations with parents, he thinks there is concern that the Curriculum for Excellence is narrowing the range of subjects; in a school like Gordon's, he says, pupils are pretty much guaranteed to do any subject they wish at all levels, which is not the case in the local state schools.

"The other thing about Gordon's is the peer group. Coming here, you're in with pupils from homes that on the whole care about education - it means that while we are still teaching adolescent kids and they have issues, on the whole we've got a motivated, supported group of pupils."

Farmer also believes that in many state schools expectations can be low. "One of my colleagues met a barrage of 'you can't expect kids to do that' in a state school and she said: 'Why not?' When she came here, she saw that difference - it was an environment that expected high standards. When she tried to do that in state schools in a deprived area, that expectation wasn't there, even though the kids could have done a lot more. Schools have a role in trying to break that cycle and I'm not convinced that all state schools do that."

Some of the other teachers I speak to in the science department agree with that position, but others accept the resources of a private school help. In one of the chemistry labs, for example, I watch some pupils conduct an experiment and the teacher tells me the facilities and equipment are much better than he experienced in a state school and that helps his job; if you lack resources in a comprehensive, clearly that can grind the teachers down. Farmer, though, believes resources are only a small part of the issue. "Obviously, we are well resourced," he says, "but it depends on having vision and drive, and that happens more naturally here." So is that what it's about? Vision? Drive?

At which point, the school bell goes - loud and shrill like I remember it - which means it's time for a meeting with the head of the school, Hugh Ouston. He is based in the oldest part of the school, the Auld Hoose, and over tea and biscuits in his office, I ask how much the peer group in a private school has an effect on how the school runs. Doesn't it make it easier for a private school, I ask, when the pupils arrive confident and ready to learn? "That's a crude thing to say," he says. "I think it's too easy to say: 'Because you're rich, you're confident.' It's easy to fall into this crude stereotype that the children in independent schools think they are superior."

Some of my other questions irritate Ouston too. Are private schools fair, I ask? "I don't have a view on that," he says. "We do the best we can with the people we have in front of us." Do private schools deserve their charitable status? "We are a charity and have been for 250 years," he says.

So what of Ouston's view on the access that private schools reportedly give their pupils to the upper levels of society? We already know, for example, about the Eton effect in the Cabinet, and recent research by the Sutton Trust, a think-tank that campaigns for social mobility through education, showed that 10 private schools in England produced more than 10 per cent of the UK's professional elites and that pupils from top private schools make twice as many applications to the UK's leading universities, including St Andrews.

But is Scotland different? Possibly not. For a start, 20 per cent of pupils in Edinburgh are taught in private schools - the highest figure of any UK city. And although Eton-educated boys dominate the Cabinet, it also includes a former pupil of Robert Gordon's: Michael Gove, the Education Secretary, who was two years above me. Recent research by The Herald also showed that 17 per cent of MSPs were educated independently - much higher than the national average of 4 per cent. However, it is also much lower than the number of MPs who went to private schools - at Westminster, the proportion is 34 per cent - and Ouston believes there is a big difference between England and Scotland, something a few teachers who have taught in both countries also tell me.

"There is a big difference between the culture of the public school in England and the independent school of Scotland," says Ouston. "You don't get a feeling that the school here is separate from society."

As for any idea of a network of old boys and girls that might, or might not, make it easier to succeed after school and reach the top of society, almost everyone in the school denies its importance. There are many successful former pupils of Robert Gordon's - Sir Ian Wood, the former chairman of the Wood Group, many politicians, a few celebrities including the singer Sandi Thom, sportspeople, especially rugby players - but who knows if they would have succeeded without private school, and it is hard to know to what extent any kind of network helped (although there is a former pupils association, The Gordonians).

Stuart Farmer, the head of physics, is the only one to admit the possible connections can be a consideration for some parents. "The whole Gordonians structure is there, and while that is not necessarily something that is flagged up as a big issue, that is a consideration," he says. But the headmaster dismisses the idea. "There's a strange delusion or prejudice that there is some magic thing that you buy when you go to an independent school - it's all graft, hard work, principles, standards and attention to the pupils as individuals. That's all there is to it. There's nothing else."

On the subject of the possible effect of schools on the wider education sector - good or bad - the headmaster believes independent schools keep up the collective standards of education and that there should be more of them. However, a common argument from critics is that they cream off the best and that pupils are taken out of schools where they could have a positive influence. Some of the teachers I speak to say there may be a marginal effect in some comprehensives but recently Lindsay Paterson, professor of educational policy at Edinburgh University, said he thought private schools did not improve attainment in the system as a whole but neither did they harm it.

Which leaves the question of whether state schools can learn anything from private schools - a question to which I seek the answer in the modern languages department, still tucked away as it always was in a gloomy part of the school known as Crooked Lane. On the way there, one of the deputy heads, Mike Elder, points out that an independent school such as Robert Gordon's is insulated from most of the change and upheaval caused by the Curriculum for Excellence - they have a lot more flexibility in how they take it up. But even if that means independent schools have it easier in some ways, most of the teachers here believe some state schools could learn from private ones.

They include Tom Cumming, a warm, lively man who tried to teach me French (another one to add to the list of my least favourite subjects) although, like some of his colleagues, he is wary of patronising the state sector. "There is a corporate identity which you buy into here," he says. "There is a work ethic, so you buy into a package which has different components."

And can you transport that to comprehensives that don't have it? Cumming believes you can, but also thinks Gove has come unstuck with his free schools programme. "If you listen to what Michael is saying, a lot of the things he's putting forward are a lot of things he experienced here at Robert Gordon's, and that's what he's trying to implant somewhere else. But it's not as easy as that because you've got to change a vision, a way of thinking, you've got to get rid of a different culture, to some extent you have to get over negativity that exists, and that's one of the biggest hurdles."

For a while, Cumming and I talk about what the school was like 25 years ago - it has changed for the better, we agree - but then we get talking to a few fifth- and sixth-year pupils, all 17 or 18 years old. Some of the group have more awareness of the place of independent schools in wider society than others but one of the most impressive, Kenneth Watt, has thought a lot about the issue. Watt has been at Gordon's since he was four years old, starting at the nursery, but is conscious of trying to think outside the private-school bubble and he says he often wrestles with the fairness question.

"I'm not necessarily supportive of the principle of private education," he says. "I'm here, but my parents made the choice when I was four. I feel very lucky and my parents have sacrificed a lot for me and I should make the most of it. But I'm not sure whether I would send my kids to private school. It would depend where I live. At the moment where I live, the local state [school] is in one of the deprived areas of Aberdeen so my chances are naturally reduced, so it would depend on my circumstances."

In his spare time, Watt works for the local Labour party (where he gets a bit of good-natured stick about being a private school boy) and says his fellow Gordonian Michael Gove has it wrong in thinking that a private school model can be easily used to improve state schools. "It's an insult to state schools for Michael Gove to say: 'You're doing everything wrong.' I see someone who falls out of education as a failure of the state. If you come from a background where you can't be whatever you want to be, there should be a support mechanism there."

Watt also thinks a good social mix in independent schools is important and says the mix at Gordon's is good. A couple of pupils I speak during the day are on 100% bursaries but the vast majority are from families that can afford to be here and my impression, then and now, is that the social mix is not nearly as wide as the mix in wider society - by definition, it is going to be that way, whatever the protestations of the staff.

And they do protest: over lunch in the school dining hall (the food is a little better than I remember), one of the deputy headmasters, Stefan Horsman, says there is a good social mix and that it is much broader than at some of the English public schools where he has taught. And some of the teachers argue the mix at Robert Gordon's is similar to that at some comprehensives such as Cults in Aberdeen or Jordanhill in Glasgow. This is helped by the number of bursaries, which help secure the school's cherished charitable status.

But even after talking to so many pupils and teachers, here I am still struggling with the idea of an independent school as a charitable service to the community: it is a school for well-off people that offers a relatively small number of free places. Which doesn't necessarily mean we should reform private schools or abolish them. Private schools may well help to raise standards generally to a small degree - particularly in modern languages and the sciences, where cut-backs have been made in the state sector - and they certainly help individual pupils who might otherwise go to a school where they might struggle. That's a point the head of chemistry, Jane Kennedy, raises: the school is, she says, a chance for some pupils to get out of a disrupted environment and improve their chances of going to university - and why would you deny that in those circumstances?

As for fairness as a whole, teachers and pupils say that is a matter for government: if state education is underfunded, they say, the government should spend more on making it better. And there is another important fact that all schools - well funded or not - have to deal with: society will always be unfair and there will always be parents who will push their children hard. Getting rid of independent schools would not change that fact. In other words, if you want to abolish private schools, you will have to abolish middle-class parents too. n