I'm home edding my ASD DS.
Autonomous education is not suitable for him, as the very nature of his disability means he needs more scaffolding & structure than the average child. You could say we are at the opposite end of the pedagogy spectrum through sheer necessity. However the methods I use are not those practised in all but a very few state schools either.
However if my DS learns best via directed, precision teaching then I can easily see how a different type of thinker might thrive best doing the opposite. Neurodiversity is something to celebrate not abhor, as it's those individuals at the edges of the bell curve who invent new things, and forge new advances for the rest of us in so many areas. (We are constantly being told how Einstein's brain was structurally different from the norm for example!)
Mainstream state education is designed to suit those children who sit in the middle of the bell curve - that's great for the majority, but may help to explain WHY 1 in 6 who leave 12 years of compulsory school without the functional numeracy and literacy skills they need out there in the modern world. I met one to many NEETS to want to sentence my child to that fate without putting up one helluva fight.
It may not be fashionable to say so, given that we have entered the era of the nanny state - but parents almost always instinctively understand their own child's unique learning style better than anyone else. Home education one of several legal options for those square pegs in the round holes of the state school system.
The Queen was homeschooled - her social skills are universally acknowledged to be beyond reproach
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As for specialist subjects - well my DS is a science geek, and homeschooling via a live online school is giving access to the specialist science teacher he wouldn't get in a state school aged only 9. Technological advances make it possible to go all the way thru to degree level at home nowadays in most subjects. It's worth pointing out that just because education is being delivered at home, it doesn't mean the parent has to teach every single subject. Tutoring is a growth industry even for children who do attend school! (oh the 11+ angst!).
Academy's are not required to follow the national curriculum or to employ qualified teachers so the quality standard that parents used to rely on just doesn't exist in many local authorities now (many have all academies at secondary level). Schools vary too from Summerhill, to the local comp to Eton - not all are created equal by a long shot. Gove has officially fallen out with Ofsted as quality control has become a political football following the recent failures of several free schools and academy chains.