THERE ARE certain polling questions that always make me chuckle. One of them is asking the public to estimate how much of the government's budget is spent on overseas aid. The result, whether in the United States or the United Kingdom, is invariably comical. Many voters assume something like one pound in six is spent on international development. (The actual answer, of course, is less than one pound in 100).

I sometimes wonder what results would be produced by asking the public to estimate the percentage of Scottish school children educated privately?

I suspect most people would get it wrong by at least an order of magnitude. The actual numbers are tiny. Fewer than 5% of Scottish kids are educated at private schools. The total number of children educated privately in Scotland is roughly 30,000. Yet, to hear some people talk, you could be forgiven for thinking independent schools are a big part of the problem with Scottish education.

They are bastions of elitism and privilege and they exacerbate inequality and societal division. None of this, you will understand, is good. And perhaps it is not. Nevertheless, it might be better to ask why private schools perform so well. Then it might be useful to ask if it matters.

That they perform well is not in doubt. This year fifty-six percent of highers sat in Scotland's independent schools resulted in an A grade with an A-C pass rate of 93% compared to a national figure of 76.9%. Had those privately-educated pupils who sit A-levels sat highers instead these results would be even more impressive than they already are.

Is this just a matter of money? A little, but not entirely. It is a question of culture, of competition and of aspiration. And perhaps most importantly of all, it is a matter of expectation. Excellent resources, supportive parents and a demanding, disciplined environment all play a part. But so does this level of expectation. Expecting success is one of the conditions for producing success.

Some of these things are easier to achieve within the confines of a carefully controlled educational penitentiary masquerading as a hothouse of excellence for tomorrow's leaders (i.e., a boarding school) than they may be at your local comprehensive. But not every aspect of private education's success is reliant upon financial resources or parental expectation.

Perhaps the difference in expectation is most apparent when it comes to extra-curricular activities. At many, perhaps most, private schools these are both a large part of what the parent is paying for and a considerable part of what the teaching staff is expected to deliver. My experience – based on that of friends and family teaching in both the private and public sector – is that, as a general rule, teachers in private schools are required to devote much more time to their pupils out of academic hours than is the case in the state sector. I don't know if this makes them better teachers but I suspect it contributes to making good schools.

What private schools do enjoy is independence. Though subject to regular inspection they are, as their status suggests, given a freer hand than their state counterparts. It would be odd if this had no impact or was of no importance at all.

In any case we should cease thinking about education in terms of the private-public divide, however. After all, a private day school in the city may have more in common, in certain respects, with a state school drawing upon a wealthy, middle-class catchment area than that state school has with a comprehensive in a tougher, less affluent, less employed part of the city.

And it really is a matter, in Scotland at any rate, for cities. Private education is very popular in Edinburgh and quite popular in Glasgow but there are only a handful of significant-sized private schools outside the country's two biggest cities. Proponents of school choice - that is, fans of the let a hundred flowers bloom approach to education – should, however, admit that these are theories best suited to metropolitan areas. They are of little use in small towns in which there's never likely to be need or demand for more than one school. That's not an argument against reform; it's simply a question of noting that not every school can be assisted by competition.

Nevertheless, if this limits the usefulness of school choice arguments it also demonstrates the considerable nincompoopishness of those who think private education is a problem that needs addressing. Curbing private education will do nothing whatsoever for single high school towns across Scotland from which no-one (or almost no-one) is sent to private school anyway.

The argument over private schools' charitable status is so bogus it is neither red enough nor sufficiently herringesque to meet EU red herring standards.

Class-warriors claim this "subsidy" is unjust and that it contributes to inequality. It may be that charitable status helps keep school fees lower than they might otherwise be. Nevertheless, it is also the case that the greater "subsidy" is afforded to local authorities who would otherwise have to bear the cost of educating those children presently schooled privately. Private education makes state education cheaper.

Moreover, objecting to non-profit, fee-charging, selective, independent schools enjoying charitable status while defending the charitable status of non-profit, fee-charging, selective, independent universities is an interesting test of intellectual consistency. It's a curious view of "public good" that doesn't allow education to fall within it.

As for the conditions in which at least 19 of every 20 Scottish kids are educated well, let us merely observe that Margaret Thatcher's education reforms were too much for Scotland. So were John Major's. So were Tony Blair's. And so are David Cameron's. It may be that Scotland had no need of any of these changes; it may also be that Scotland has benefited from being insulated from English reforms.

After all, supposing that reform is naturally preferable to the status quo is simplistic silliness. On the contrary, change for the sake of change is first cousin to the something-must-be-done school of witless politics. Nevertheless, the more open-minded type of Scot might wonder if perhaps our southern brethren are on to something.

It is notable, for instance, that London's state schools are now the best in England. That is, poor children in London's state schools perform better than poor children in Kent or Manchester or Norfolk or any other part of England.

As always, we should resist the temptation of monocausal explanations. These are complex matters ill-served by simplistic explanation. What might be said, however, is that competition in London has been good for London's children.

Moreover, giving schools greater freedom - whether as academies or, now, as Free schools - has played (or in the case of Free schools, will play) a part in transforming London's educational performance. I suspect some of London's excellence is also driven by immigration (immigrant families placing a sensible emphasis on the importance of education) and there are doubtless other factors to consider too.

Nevertheless, it bears repeating that the Academy programme pioneered by Labour in England (but not, of course, Labour in Scotland when they had the chance to do something similar) has been proved a success. Moreover, despite predictions to the contrary, school liberalisation is a particular boon to so-called disadvantaged communities. The academy revolution is more important to Hackney than to Hampstead. Similarly, in Edinburgh, Currie doesn't need education reform as much as Craigmillar could benefit from a new approach.

Competition is not, despite left-wing assertions to the contrary, necessarily a "race to the bottom". The competition between Edinburgh's great and ancient independent schools improves performance at each of them. Comparably, competition for pupils in London has helped sharpen standards for the benefit of poorer pupils in particular.

Again, competition is not enough on its own. Systems still depend upon people but systems can be designed to help people deliver upon their potential. That is the point of the Academy and Free School movement. One day, perhaps, Scottish politicians will appreciate this too. But not yet, alas, not yet.

Scottish state schools are, on the whole, quite good but they could be better still. Arguing about private education will do nothing to change or improve the performance of state schools; setting them free just might.