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out of the school environment is a hard sell for me.
... ability or willingness to learn new skills is probably going to be fostered better outside of a formal education...
One the first, there is a bit of disingenuity to the HS argument in that by enlarge they still teach the curriculum. The basic framework as I understand it is still piggybacking off the national curriculum.
Re your second point it's hard to know isn't it? Parental attainment is the no.1 indicator of a child's outcome.
This I agree with very strongly, numeracy and literacy are the fundamental building blocks to communication.
Geometry, percentages etc are tools to use in life, and it's hard to argue that picking up such a variety of skills is more likely out of the school environment is a hard sell for me.
Having said that, the ability or willingness to learn new skills is probably going to be fostered better outside of a formal education. It depends on picking up the basics I suppose.