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ChristianKl comments on Interesting critique of British education by outgoing advisor (warning: some politics) - Less Wrong Discussion
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That leaves the question about which outcomes you measure. I think it's okay to have a world with some school that run like KIPP where there a lot of measurement and others that run like Sudbury Valley with has feedback principle like internal elections and reviews how many of it's student succeed at college.
When it comes to the specific example of teaching integration I think that will be done best via some computer tool.
I guess that 20 hours of time investment into practing a well developed Anki deck on integration would leave most students with more knowledge of integration afterwards.