You said "Some subjects are dry and dull but learning them is what makes you a rounded individual. The danger with this child-led approach is surely that the child does not do what he or she hates and ends up somehow lacking in skills in those areas?"
This hasn't been my experience. What has happened with my children is that they have put off doing things they hate until they feel equipped to deal with it, and then tackled it then, always assuming that it is something that they really have needed to know.
My son (now 22) did not like writing, so he didn't do it until it became necessary (when he had a term's try out at Secondary school) whereupon he picked it up within a couple of weeks and was writing in a legible cursive style. His writing is still very untidy, but as he is now in the second year of a biomedical research PhD, it obviously hasn't been a huge limiting factor. He has said that if it ever becomes a real problem he would spend a couple of weeks studying caligraphy and sort it out, but it has yet to worry him enough to bother.
My daughter (12) does not like maths and so had done no formal maths until a few weeks ago when she came to me and said that she was now ready to tackle it as she could see it was a subject she would need to get the qualifications she wants to do her chosen career (Psychologist). She has chosen a structured course on a cd and is steadily working at it in a self imposed regime of one hour per day. I don't remind her or nag, it is her choice, although I do help if asked to.
you said "I hated mathmatical and scientific subjects at school but worked very hard at them because - well, I had to. And that in itself is one of life's lessons - that sometimes you can't just go to a museum, you have to sit down and do something that's thoroughly boring and turns you off."
I believe that by allowing my children the choice of when and what to work hard at or to choose not to work on at all I have allowed them to come to these subjects with a free mind, and strangly enough the very subjects that you look on as boring are what my son chose freely to study in great depth, without anyone pressuring him, but because he found them vital and fascinating. The subjects that he found dry and boring for instance history and geography, he probably hasn't studied much, and yet he seems to have built up an amazing depth of knowledge on all kinds of subjects without formal study. He now lives in Manchester, and often flies off at weekends to various destinations around the world, so I would guess his geography is adequate, and for fun he visits National Trust properties, so no doubt history is getting covered too. He does not in any way believe that his learning has come to an end, and is constantly trying new things, for instance he has just taken an Italian exam after blagging himself onto the last 8 weeks of a two year course - he says it doesn't matter if he passes, all he wanted was to be able to speak Italian better. He studies ju-jitsu and has a teaching qualification in it. He set up a skills swap where he got piano lessons from an international concert pianist in return for teaching her husband to play guitar (he has a grade 8 in guitar), and he has also just signed himself onto a diving course. He intends to spend his whole life trying to learn everything there is to know
"Also - I can see how home educating in the primary years might be OK but I know there is no way I would be equipped to teach some GCSE and A Level subjects - how do you manage when the complexity of a subject exceeds your own abilities?"
I have never sat down and made my children learn anything they have not wanted to know. I have never pretended to have the skills to teach them anything. All I have done is to enable them to learn the things they have expressed an interest in. They have never been told that learning is "hard work" or "boring" so they don't know that it can be - to them it is interesting and vital, and something to be earnestly desired. They have learned that they can do anything if they really want to.
My son decided to go to college to do the qualifications that he needed to get the job he wanted. He started at 14 doing GCSE's and A levels side by side. He left with 5 GCSE's and 4 A levels 3 years later.
When my son decided at 13 he wanted to use his body more, after being a computer geek for all his life, he first went to a local community hall and asked the ladies there if he could join their gymnastics class - he went along and queued in line (at 6' tall) with 3' tall girls in leotards, and learned the basics. The ladies were very dubious at first but singing his praises by the end of the session. Soon he searched the internet and found a gymnastics class for university students, then rang up and asked if he could join that. After going there for a couple of years he joined a ju-jitsu club - I paid for the first year and after that he paid his own way by working as an assistant tutor. When he was 17 they offered him the job of running the citywide operation running in 15 locations - he turned them down as he was due to start at University.
When he decided around about the same time, that he wanted to learn guitar, he approached a local home ed dad and negotiated a special rate to learn, without asking me for any funding. He funded it by selling on ebay and by doing odd jobs. He worked with the same tutor until he passed his grade 8 4 years later. He tutored others in his turn for cash, or as a skills swap for drumming tuition and piano tuition. He also played in a band for a couple of years.
My daughter recently expressed an interest in learning Japanese, co-incidentally we chatted to a Japansese stall holder at a car boot sale. My daughter asked her if she would give her lessons, so for the last few months we have had a small group of children in our front room learning Japanese or making sushi in my kitchen. In a charity shop last week, she bought herself "Memoirs of a Geisha", and finished it in one go as she found it so vitally interesting. She spends some time each day seeking out lessons on the internet and Manga cartoons to watch and is now quite good at the language - if I had imposed this on to her, I doubt she would have had the same desire to learn.
I could go on, suffice it to say that learning does not have to be hard work, or dull and boring, if it is never presented in that way. When my son was at college and university he never missed a single class except when he was ill. He never overslept or decided not to go. When he managed to take an extra module at Uni he was double booked for some lectures so arranged to tape one with the lecturers permission, and listened to them later.
It is the children who are forced to learn and told it is hard work instead of thatlearning is fun who are the ones who don't turn up to lectures or are still in bed at midday when they are expected elsewhere, in my experience.