By Mike Baker BBC education correspondent

Is it hypocritical to send your child to a state school while paying for extra private tuition? Does resorting to private tutors mean you have no confidence in state education?

Or is all the fuss over the alleged extra coaching received by the prime minister's sons just political opportunism allowing commentators to spout their favourite prejudices about the state of our schools?

In an ideal world, all children who need individual help would get it

The outspoken former Chief Inspector of Schools, Chris Woodhead, is not one to sit on the fence.

He said of the Prime Minister: "What stinks is the pious pretence that all is well with the state sector, when in fact he is buying tuition for his own children even though he has got them into one of the best schools in the capital."

Hang on a minute, though. Isn't this the same prime minister whose press secretary talked about "bog standard comprehensives" and whose education secretary said there were some schools she "wouldn't touch with a barge-pole".

So who exactly was pretending "all is well" with the state sector?

Sinking to the depths

The Liberal Democrats' education spokesman, Phil Willis, was equally forthright.

He said it showed the "depth to which Labour have sunk in abandoning their principle of a state education system for all".

Tony Blair's sons are reported to have had private tuition

He added that the prime minister might as well "go the whole hog" and send his children to private schools.

Did he really mean that? Would it truly be better for our leading politicians to have no stake at all in the state school system?

As a well-known former tennis-player might have put it: he cannot be serious.

However, once we get past some of the hyperbole, there are some interesting aspects to these claims (neither confirmed nor denied by Downing Street) that the prime minister's sons received extra tuition from teachers at a top private school.

Tuition on the rise

Although there are no official statistics to prove it, head teachers have voiced their belief that private tuition is on the increase.

Chris Woodhead: Critical of the Blairs' decision

Tutor agencies claim to be busier than ever with anxious parents not only seeking help with A-levels, GCSEs and secondary school entrance tests but even wanting coaching for the national tests for 7-year-olds.

Does all this mean that our schools are getting worse or that public confidence in state education is declining? Possibly.

Yet it could equally be that standards are the same as ever, possibly even improving, but that parents' expectations or anxieties have increased.

Testing schools

The great irony about the national curriculum tests (or SATs as parents have come to call them) is that one of the main reasons for their introduction was not so much to test children but to test schools and teachers. Hence the use of test results for league tables.

The idea was to tie teachers to teaching the national curriculum and to give parents an indication of the relative success of schools.

The test results do not have any implications for the individual child. The tests at age 11 are not used to determine secondary school admissions. Yet many parents feel it necessary to resort to coaching to boost SATs results.

If, as researchers have suggested, some schools in London have a majority of children being privately coached, then how reliable are school test results as an indicator of their teaching quality?

If the Prosperous Suburbia Primary School has 60% of pupils receiving private tuition while the Deprived Inner City Primary has none, then how much of a guide are the league tables to the relative quality of teaching at these two schools?

More tests

There is one fact we can be sure of: pupils today sit far more formal, externally-set examinations than in the past.

In England, there are the compulsory national tests at seven, 11 and 14, plus increasingly a range of voluntary intermediate tests too.

Then there are GCSEs at 16, AS-levels at 17, and A-levels at 18.

The increase in exams could, alone, explain the increased use of private tutors.

Then there is secondary school entrance.

In areas where the 11-plus survives, private coaching has long flourished. I know.

I live in one of those areas and I know of a house not far from mine which is a minor cottage industry of 11-plus preparation.

Capital problem

In London the pressure to get into independent schools has grown in recent years.

This is partly because affluent Londoners no longer want to send their children away to rural boarding schools.

The competition for private day-school places is another reason for the growth of private tutors.

So what of the main charge against the Blairs: that it is hypocrisy to make a show of supporting the state sector while having so little confidence in it they are resorting to private tutors?

Remembering, of course, that we do not know for sure how much, if any, tutoring they have received, and for what reasons, it is hard to make this charge stick.

It is surely possible to be content with the overall quality of your children's school whilst being concerned about their progress in one particular subject.

In an ideal world, all children who need individual help would get it. But there just aren't enough teachers to go around. So, with private tuition, we have rationing by ability to pay.

Equality in education

If this episode tells us anything it is not that schools are getting worse but that equality in education is still a long way off and, maybe, is not achievable.

Even if we had ever achieved a genuine comprehensive school system, there would still be schools in more affluent areas where admission would, effectively, be by mortgage.

However, if Gordon Brown needed a reminder of the social and economic inequalities in education ahead of this month's spending review, the issue of private tuition should serve as one.

If the government wants to do something to improve equality of educational outcome then it needs to remember that there are some schools, and some families, which should get extra help because their students will never afford private tuition.