Sam does a lot of this – along with Lego, taking things apart and asking a lot of questions. It's called "child-led" or "autonomous" education, which means children follow no external curriculum and study what interests them. This style of learning is rare in schools, which is why I am teaching Sam and his siblings Zena, five, and Matty, four, at home. When I say teaching, I mean facilitating – that is, I offer support, resources and instruction, if needed.
It's radical stuff. How can a child left to direct their own education possibly knuckle down to hard work and fulfil their potential?
Louis Barnett is doing both. Louis, 16, struggled through his early school years due to undiagnosed dyslexia. In desperation, his mother, Mary, from Kinver, West Midlands, pulled him out of school when he was 11.
Given the freedom to pursue his own interests, Louis discovered a talent for making handmade Belgian chocolates. "I made a cake for my aunt's 50th birthday. After that, her friends kept asking for cakes," says Louis.
Driving ambition and a stroke of ingenuity shot him into the big league, when his edible chocolate boxes won a contract with the supermarket Waitrose. Since then he has had a personal audience with Gordon Brown, addressed 3,000 people in London's Lyceum on the use of palm oil in chocolate and launched his Biting Back bar in Sainsbury's, which highlights the plight of Borneo's orang-utans. His business, Chokolit, is such a success that Mary, and Louis' dad, Phil gave up their jobs to work for it.
Louis believes life is about opportunity. "When I came out of school I started working as a volunteer with a falconer. He told me, 'You're only 12. You have to prove you're worth taking on'. He gave me the worst jobs and I stuck it out until I worked up to doing displays. That experience taught me you have to work hard for what you want."
It is clear that Louis has turned his life around since the days when he believed he was "stupid" in school. However, what is unclear is whether spending so much time cooking would be deemed a "suitable" education under revised guidelines to local authorities being issued by the Department for Children, Schools and Families.
The right to educate your children at home is enshrined in the words "or otherwise" in the 1996 Education Act, which states: "The parent of every child of compulsory school age shall cause him to receive efficient full-time education suitable; a) to his age, ability, and aptitude, and b) to any special educational needs he may have, by regular attendance at school or otherwise."
In its revised guidance, which is out for consultation until October 24, the DCSF is seeking to help local authorities identify children who are at risk of "missing education".
There are children who are undoubtedly at risk. But the home education group Education Otherwise is concerned that the guidelines appear to categorise home-educated children with these "vulnerable" groups, and fears that local authorities will take the guidance to mean it is they who decide whether or not education is suitable.
"We are concerned that the wording of the draft leaves room for misunderstanding," says Fiona Nicholson of Education Otherwise.
The trouble is that what is deemed a "suitable" education is arbitrary. Home educators have long complained of a postcode lottery in which much depends on the ethos of the relevant local authority.
Cambridgeshire's elective home education manager, Martin Smith, believes local authorities find it difficult to balance the need to respect the rights of home-educating parents while carrying out their legal duty to identify children who may be missing from education. Smith is surprised that the new guidelines appear to place home-educated children alongside vulnerable groups: "I'm not sure how helpful that is," he says.
"The vast majority of home educators we come across do a great job. However, we have concerns about a minority who refuse to engage with the authority. But it's important we don't allow our policy to be dictated by this minority."
By appointing a single "adviser", Cambridgeshire has done much to offer a consistent approach to families, but other authorities' inspectors can be wedded to traditional schooling. The skills needed to teach 30 children of mixed maturity, ability and backgrounds are not needed at home. Similarly the sort of interest-based learning common in home education would not translate to the classroom.
Or would it? Dr Ken Spours of the Institute of Education has called for the national curriculum to be broadened to allow more creative learning. He believes even a small shift, favoured by many home educators, would reap rewards for teachers and pupils, as well as universities and employers. "If just 10 per cent of time were given to project-based learning stemming from pupils' interests and passions, we would see an incredible difference," he says.
In a recent report for the Nuffield Review, a six-year consultation on the education and training of 14-19 year olds in England and Wales, Spours and co-author Ann Hodgson called for an overhaul of the exam system. Spours claims the emphasis on GCSEs and A-levels throttles creative learning. "This approach doesn't help students when they go to university and need to take an independent and analytical approach to learning," he says.
This is something Alex Dowty, 19, knows all about. He received an unconditional offer to study law at Oriel College Oxford, armed only with Open University courses and Grade 8 harp. It was a dream come true. Dowty, from Leytonstone, Greater London was home educated after being removed from school aged eight. He believes his child-centred education has stood him in good stead at Oxford.
"University is a shock to everyone, but being home educated probably helped me settle in more quickly than some people, who felt uncomfortable initially with the change from more directed learning," he says. "Every week we attend a tutorial. At the end, we are given a list of 20 books to read for the next week, which you have to get on with. It's great, like home education but with tutorials."
Meeting Louis and Alex has made me realise that, if you place trust in children, they will respond. Recently I have been further convinced by going for long walks with my children and our new puppy. Having uninterrupted time together has given scope for wide-ranging conversations that have served as springboards for learning. On one walk recently we discussed clouds, vast East Anglian skies, the artist Constable, 180 degrees, the agricultural revolution, and, coming from left field, Mount Etna. Then we went home, looked it all up and made a model of a volcano with erupting bicarbonate of soda.
It's tremendously rewarding and I see the children learning – in their own way at their own pace.
This is why my son Sam can spend as much time gazing into space as he likes. In fact, he's just come out of his latest trance and is preparing to speak. I wonder if he has developed a Theory of Everything.
"Mum," he says "I hate my new shoes."
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