Sounds impossible? Not in the Falkland Islands, where Mrs Rendell is director of education, and life itself is improbable. There is no unemployment to speak of, very little crime - 92 people were charged last year, mainly for speeding - and sheep outnumber people by 350 to one.
Mrs Rendell is in charge of two schools, 30 teachers and 310 pupils. Class sizes are comfortably small, truancy is unheard of and the nearest OFSTED inspection team is 8,000 miles away.
In the newly-prosperous islands, Mrs Rendell's main worry is not so much where the money is coming from but where to spend it. Her worries may be about to increase, because next year explorations for oil begin in earnest off the coast.
Born and brought up on the Falklands, Phyllis Rendell went to primary school in Goose Green and completed her education at boarding school in Derbyshire and Goldsmith's College, London. She taught in south London before returning to the islands. She was appointed director of education for "Camp" - the local term for everywhere outside Stanley - in 1984.
As one of the Falklands' most senior officers, she is in London on behalf of the islanders to monitor the negotiations with oil companies which could make the Falklands the Saudi Arabia of the South Atlantic.
But not for another five years at least. Meanwhile, she is taking advantage of her brief stay to catch up on a bit of culture, visiting London's museums in her lunch hour. "The biggest problem with living in the Falklands is isolation - culturally as well as geographically. You can get starved of culture if you like that sort of thing," she says.
Suitably replenished, she will return to the islands, on an 18-hour flight, loaded down with Christmas presents, materials on the national curriculum and computer teaching manuals, looking forward to a new year of celebrations and exciting developments in one of the most unusual education systems in the world.
As an antidote to the barren cultural landscape, the United Kingdom Falklands Islands Trust launched the Shackleton Scholarship Fund Appeal which pays for islanders to travel abroad and for artists, performers and sports people to go there. The next visitor will be ex-Status Quo drummer Geoff Rich, who will be giving a percussive masterclass to schoolchildren. Mrs Rendell heard of him through a feature in The TES. "It's my lifeline," she says.
Three-quarters of the islands' 2,100 population live in Stanley. A village by anyone else's reckoning, in Falklands terms it is a city. The capital has a 150-pupil primary school and a slightly larger 11 to 16 community school, which operates along broadly similar lines to any UK comprehensive except that the curriculum features agriculture, and Spanish in place of French. Built at a cost of Pounds 14 million and opened in September 1992, it offers 16 subjects to GCSE level.
Far older, and much more unusual, however, is the education system for children who live in "Camp" which will be celebrating its centenary in 1996. Camp is an area the size of Wales which is served by a team of six travelling teachers.
The travelling teachers spend two out of every seven weeks at small settlement schools or farmhouses, where classrooms have been fashioned from Portakabins left over from the war in 1982.
The rest of the time, children are taught by two-way radio from the Camp Education Unit's headquarters in Stanley, a medium that has proved surprisingly adaptable - recorder lessons and even swimming tuition have been conducted over the airwaves.
It's a job that requires special skills, Phyllis Rendell explains. "Teachers must be flexible, resourceful and resilient. Teaching one child, or two children of different ages and abilities is quite different from teaching a class of 30."
Teachers are recruited from the UK and New Zealand on two-year renewable contracts; some stay on to become permanent residents. Although the mode of transport has changed from horse to plane, this peripatetic tradition has been maintained in the Falklands while similar systems in other sparsely populated parts of the world, such as New Zealand and the Highlands of Scotland, have been superseded. "We have taken on board technology but we still feel that human contact is the most important element of education," says Mrs Rendell.
Television arrived in 1986. An upgrade of the telephone system two years later signified a communications revolution in the islands, allowing people on remote homesteads to communicate by fax. The modern world's next incursion is scheduled for a couple of years hence when the islands link up to the Internet.
The conflict in 1982 was a turning point in the islands' fortunes, not to mention those of Mrs Thatcher, who is remembered in street names and even has her own commemorative day, "Maggie's Day", on January 10. Relations with Argentina, Mrs Rendell says, are nowadays "cordial". The South American country they are closest too is Chile, and student exchange links are being fostered with schools there.
"There is no animosity towards Argentina. We recently allowed relatives of soldiers killed in the war to visit the site of a crashed plane. That kind of thing is good on a human level."
Things have changed a lot in the past 13 years, not least the islanders' attitudes. "There is a feeling of permanence and of something worth working for and building on. Education plays a key role in that."
The islands are now financially independent thanks to an agreement signed with the British Government in 1986 which allows them to grant fishing licences. The licences now generate annual revenue of Pounds 25 million, a welcome addition to the recession-hit farming economy and a small but growing tourist trade.
The money has paid for new roads, a hospital shared with the 2,000 British soldiers stationed there and a sports centre. The Falklands compete in the Small Island Games, but individual sports (darts is a favourite winter pastime) are more practical than team games. "It's quite difficult to get a bunch of squaddies to play netball," she jokes.
The primary school is being extended in anticipation of a population surge should oil be discovered. But a shortage of skilled workers means all other building plans have to be postponed while work is in progress.
"We have quite a booming economy, but no spare houses. We need more skilled people - builders, plumbers and electricians. The reason the school was so expensive was that we had to import every last brick and piece of wire, and fly in the labour to build it."
Before the war, sixth-formers were educated in Argentina but now a formal arrangement exists with Peter Symonds Sixth Form College in Winchester - one of only two boarding colleges in England. Pupils who pass five GCSEs have an automatic right to study here for A-levels with their fees paid for by the Falklands government. "Children grow up in a community where they feel valued and appreciated. We really want them to do well and to contribute to the future of the Falkland Islands," says Mrs Rendell.
Among the 19 students at the college, the feeling is mutual. Eighteen-year-old Bernadette Lang is in the final year of her Spanish, modern history and maths A-levels with ambitions to be an interpreter.
"When I first came here I found the amount of people very frightening. There's a lot of things for young people to do like bowling and ice skating, which we don't have. What I like best about England are the trees - back home we only have a few bent ones."
Sacha Clarke, who is 17, is taking biology, chemistry and mathematics and "really enjoying it". She has a grandma and uncle in England but, like Bernadette, she is going back to spend Christmas in the Falklands with her mother, twin brother and sister on their farm. She misses the fresh air and wide open spaces of the countryside, where she likes to ride her motorbike. "It's very different here. It's busy and loud and you can't walk around on your own at night like you can at home. I think of Stanley as quite a big place but to people over here it's tiny - just a cluster of houses."
Living in England has its advantages, however. "At home, everyone goes around wearing the same clothes so I like to go shopping and buy things nobody else has. I've got my mum some perfume for Christmas which is very expensive and hard to get hold of there."
The islands' investment in her education looks like being rewarded. She hopes to go on to university to train as a paramedic and eventually return to work in the Falklands. "I love it there," she says.