Louis and Lilly don't work to a formal timetable. The whole of London, and beyond, is their classroom. They spend as much as two-thirds of their time on activities outside the home. And none of these is compulsory - everything is chosen by the children themselves.
Ten years ago, disillusioned by her son's experiences of nursery education, Leslie took the decision not to send five-year-old Louis to school. She had no training in teaching.
"I remember that day - September 6 1988. I was so worried; I thought the school inspector would arrive at the door any minute. I was sitting there thinking, How can I teach geography? I don't know any geography. Eventually we went to the park."
Gradually over the weeks things fell into place, with Leslie involving Louis in all her daily activities on the principle of learning through doing.
"We would make a cake together, we would go to the launderette and he would put the money in the machine, we would visit our Japanese friends and talk about where they came from. It wasn't trying to turn everything into an educative experience, just learning through life."
Now Louis and Lilly are older, they have a rough weekly pattern of activities, based around fixed points such as music lessons. But Leslie firmly believes that education comes through trusting the child's inbuilt desire to learn.
"This idea that you have to go in and beat the child up in order to put knowledge into its head seems the wrong way round. Children want to be part of the world - you don't have to motivate a young child to walk and talk. If you wait until the child says 'Yes I want to write', they will learn."
The range of activities the Barson children choose to fit into their lives is quite startling - especially to many parents who believe their offspring would spend their entire lives slumped in front of a video or computer game if given half a chance.
As well as his Maths `A' level (having achieved a GCSE Grade A at 14), Louis is currently working for his GCSE in Drama and English, and his Grade VIII violin exam. He attends a weekly Shakespeare performance group and sings in the English National Opera's children's chorus.
Lilly, at nine, plays the piano, attends singing lessons and writes her own songs. She recently won a prize from the National Trust after throwing a fund-raising Yorkshire tea party for 23 friends, baking five different types of Yorkshire cakes, and raising pounds 50 for the Yorkshire Coastline appeal. She also sings with the English National Opera.
Home-based educators bring in expertise from where they can, and find no shortage of people willing to help, says Leslie. She runs the Otherwise Club for home-educated children of all ages up to about 16, which meets every Thursday. Pottery and drama, felt-making, country dancing, and a talk on owls are just a few of the things they've been up to recently.
Leslie also runs a Duke of Edinburgh award scheme on Tuesdays for the over 12s. Their current range of activities includes volunteer work with local learning-disabled youngsters, canoeing expeditions, go-karting evenings, and workshops in mediation and conflict resolution.
For the home-educated 8-to-11s there's a weekly history group where they're currently learning about the ancient Egyptians - through crafts, dressing up as mummies, and visits to museums rather than deskbound study.
Lilly also attends a science group run by a top scientist who happens to live locally, and a 'mother and daughter' reading group which Leslie runs once a month. On top of this there are one-off visits, and talks or workshops taking in anything from church history to a mobile planetarium.
Leslie is fortunate in having an income which, although modest, means she can afford not to go out to work. She's immensely happy in her role as a home educator. But her positive experience has made her critical, not merely about how we educate our children, but the whole way we as a society relate to them.
"People say to me 'How can you stand being at home all the time with your kids?' I love being with my kids. Children only get on to you if they don't get good attention for some of the time. Home-educated children are involved in what's going on, they don't need to be noisy and demanding.
"When children come home from school, and parents from work, everyone's tired and stressed out. I've had people say to me that by the end of the summer holidays they actually feel they're just beginning to relax and get to know their children."
Leslie is also critical of the way conventional education segregates pupils. "Children in home-based education have the world on which to model themselves - not a very small internal isolated group of 30 kids they might spend 12 years with. They're out all the time doing all sorts of things, seeing all sorts of people. "
But can the experience of home education adequately prepare people for the harsh realities of life in an intensely competitive world? - "We place so much emphasis on academic work," says Leslie, "but we're not all going to be academics. In a world where things are changing all the time, what people need is research skills, and the confidence to know who they are.
"People say, 'Life is hard out there and you've got to prepare them for it'. But if you're going to send someone out to a country that's starving, you don't starve them first - you build them up."
Leslie is doing PhD research on home-based education and its effect on parents, with the Open University. She will be leading a discussion on Is there a role for the teacher in creative education? organised by the London Forum of the OU's Creativity in Education Community, at Kings Cross Conference Centre in London on January 12 at 5.30 pm. .
HEAS, PO Box 98, Welwyn Garden City, Herts AL8 6AN; tel. 01707 371854; Education Otherwise, PO Box 7420, London N9 9SG; tel. 0891 518303. The Creativity in Education Community is a national network, based at the OU, of teachers, academics, parents, researchers, home educators and others interested in exploring alternative theories of education and creativity. It is in the process of establishing a series of regional forums; the London Forum is the first of these and meets monthly. More information about the activities of the Creativity in Education Community is available on the Internet at http://soe.open.ac.uk/SIG/creativity. For details of London Forum meetings contact Mike Leibling on 0171 328 3746