Scottish schools are undergoing changes to meet the demands of the 21st century

Scottish independent schools are as famous for their sweeping grounds and world-class facilities as they are for attracting the sons and daughters of the rich and powerful. Tony Blair, Alistair Darling, Prince Charles and Zara Phillips were all educated privately in Scotland, and the top establishments are still responsible for teaching more than 30,000 children.

One might think that their impressive alumni lists and impeccable academic records would justify a bit of laurel-resting. But more and more of the schools seem to be acknowledging that they need to move with the times in order to survive.

Mark Pyper has been the principal of Gordonstoun, the exclusive boarding school near Elgin in the north of Scotland, since 1990. The school has played host to three generations of royals, including Charles and Zara, and was once famed for its militaristic regime and rock-hard beds. But Pyper insists that this reputation is no longer deserved.

"I think we've succeeded in changing our image significantly," he says. "We've built drama and music centres, and theatre studies is now one of our most popular A-levels. People will probably be surprised to hear that for all our younger pupils, boys and girls, it's compulsory to do dance – 15 years ago, people would have only associated the school with cold showers, early morning runs and the royal family."

Some of the school's policies are indeed startlingly modern. All pupils are automatically enrolled on the "international citizenship" course, a direct response to founder Kurt Hahn's original mission statement: to prepare his students for "a full and active role as international citizens in a changing world." It covers subjects as diverse as cookery, recycling and understanding the media, and is internally examined up to GCSE level. The school doesn't worry about making its pupils sit an extra exam, because it refuses to take part in any academic league tables.

"You won't find Gordonstoun on any list, because we're not just an exam factory," says Pyper. "I won't enter the school into any tables, because if a pupil gets two Ds at A-level he or she is viewed as a failure, whereas in the real world, they will often go on to succeed. We've always been an independent school, and I'd rather we stayed that way."

The Scottish Council of Independent Schools is a representative body that promotes the contribution each school makes to the community. The director, Judith Sischy, is convinced that these ancient centres of learning should not be faulted for retaining their core beliefs, and that modern misconceptions about their methods should be challenged.

"Some of the tenets which independent schools have always held on to – such as homework acting as a link between the teachers, the child and the parents – are now becoming popular nationwide," she says. "When they go out of fashion they stick out like a sore thumb, but the schools shouldn't drop their core values just because they are no longer trendy."

One school which has embarked on a serious programme of modernisation in the face of parental pressure is the Edinburgh Academy. It was established in 1824 to promote classical learning in the heart of the city, and the Greek influence is still evident in the impressive Doric columns of the main building and the motto printed above the doors. Yet next year, for the first time in its 183-year history, the school will become fully co-educational. Girls have been admitted to the sixth form since the 1960s, but now they will be allowed entry at all levels.

"We could see that a single-sex education was outdated," says John Light, the school's rector, "and we also didn't appeal to parents who wanted to send their sons and daughters to the same school. We were cutting out a huge part of our market. The age of educational apartheid between the sexes has no merit over the next 25 years, and I don't believe we were right for all those millennia when males treated females with a degree of condescension."

The school has also set about changing its image in other ways. Traditionally, pupils were required to don hairy green tweed jackets every morning during the winter months: these have been replaced with sharper blue blazers, though the school's blue-and-white striped tie is unchanged.

"We had to review it some time," says Light. "It was a uniform which had been operating since the 1960s, and although some might have liked it, for others it looked absolutely awful. It was emotive to start with – some parents felt they didn't want that change, and there was a major furore – but this soon died down."

And that's not all. They've also ditched the old school crest – the head of Homer, the Greek poet – and replaced it with a bolder logo displaying the school's initials. This move proved to be just as controversial as the others, but Light insists that the school is just changing with the times: "We will only survive as schools if parents feel that the job being done equips their children well for the 21st century."

But travel just a few miles across Edinburgh and you'll find two single-sex independent schools with no desire to change their gender intakes. Merchiston Castle School is set amidst lush grounds on the outskirts of the capital, with stunning views of the Pentland Hills. It is the only all-male school left in Scotland, the closest equivalents being Eton, Radley and Harrow in the south of England. Andrew Hunter has been Merchiston's headmaster for the past ten years, and is certain that single-sex education can be just as progressive as co-education.

"We did a review of our position about two years ago, and we're very happy with what we're doing," he says. "Boys are sometimes slower to develop than girls, and here they're allowed the time and space to find themselves. How can you be sure, in a co-ed school, that the boys are learning and not switching off? Of course I believe in the sexes working together, and we have strong links with many girls schools: this way I think we get the best of both worlds."

Merchiston is almost exclusively a boarding school, and has just invested £8m in a new accommodation block of en suite single-rooms, more likely to be found at a university than a secondary school. Pupils are given the run of the city at weekends, although most are more likely to be found on a rugby or cricket pitch: the school's sporting record is second to none. Merchiston is trying to keep its traditions whilst embracing modernity, according to Hunter. Mandarin is being taught, but they've stuck with Latin as well.

St George's School, also based in Edinburgh, has been all-female since its foundation in 1888. The head teacher, Judith McClure, is proud of the way the school has adapted to become more internationally orientated: pupils from Year 9 onwards spend time at partner schools in Canada, China and Australia.

"Today's young people have to operate in a global society, and get on with people from all over the world," she says. "And we're not just creating hard-edged career women, but women who will also be at the heart of families, bringing up the next generation. This is what the 21st century is about."