Feels like the Khan Academy apps do something like this. You progress through a tree of knowledge and can’t move to any next node until you master the one you’re on, demonstrated by solving problems. It also gives you all the help you need to achieve that mastery.
> and can’t move to any next node until you master the one you’re on
Oh that's the absolute worse way of teaching people (or, ok, that's my pet peeve in education)
"but how do you expect to learn stuff without knowing the basics blah blah blah" well, because maybe actually knowing how it is used in the end helps with learning. Instead education seems to focus on wasting a lot of time with "basics" disconnected from reality then finally teaching things how it is.
Calculus was the worst for this: in my first class we spent literally two months dissecting the minutiae of limits and Lipschitz conditions and infinitesimals and blah blah etc, only to get the the punchline, "and you find the slope of a function by doing the obvious thing, which works in the obvious way every time you'll actually be using it in practice". I get it in a college level analysis class or something, but as an intro in high school that's just a great way to make students hate what is at its core a very simple and useful subject.
Not sure if I'd agree. Khan Academy is firmly rooted in the American tradition, it teaches facts, but it's like Feynman in Brazil, it does not integrate the concepts. For that you need problems tailored to your level. A good tutor can do that.
Feynman's complaints will be familiar to anyone teaching university in the United States. Obviously Feynman makes a distinction between the science education that he knew and the travesty that he saw in Brazil, but today's education in the US is exactly like what he complained about. What happened, and when?
The Russian tradition of "math circles" (https://www.msri.org/people/staff/levy/files/MCL/Zvonkin.pdf) is altogether more productive than US-style kindergarden (no resemblance to the German original) where the 3-year olds sit in rows and have the ABC beaten into them. Of course the Russian approach relies on individual attention and problems, and class sizes are smaller.
