Ask HN: How to learn math from zero for adults?

On academia and grades: yes, it's a "dark time" (as in "Dark Ages" for what we mean by it, regardless of the veracity of that historical perception). I often summarize all those collective F-ups by remarking that most people, either individually or collectively as institutions, have lost their purpose, they "have no mission in life" so to speak. Thus, we lose sight of the endgame, of the actual purpose of education for instance.

That's not about to change if the now widespread intuition that most institutions have been rotting too much for too long is true, so the solution might be some historical disruption of the domain — I think Khan was an early ripple in those foundations.

Careful. This can sometimes be counterproductive. It is often the case that one concept taught when learning a subject will be applied as part of teaching the next concept.

The best way to learn that first concept in many cases is not to focus on it until you really "get" it but rather to just get enough of it for how it is used for teaching the next concept. Then you move on to the next concept and the application of that first concept there gets you experience using the first concept which solidifies your grasp of the first concept and makes you truly "get" it.

The application of earlier concepts throughout the subsequent material can be in effect a kind of natural spaced repetition for learning the earlier concepts.

I think that deciding when to move on is one of the hardest things in self-learning, especially if the subject is new enough to you that you can't use your experience in a related subject to help guide you. You don't know enough to know when you've learned enough to go on.

- Bruner's work on spiral curriculum, and follow-up work. Spiral curricula are mis-implemented in most schools which claim to use them; it's not review. It's successive passes going deeper.

- Cognitive work on progressions such as surface->deep->transfer learning (Hattie) or chunking

- Physics education research on complex multiconcept problems

- Spacing effect. You can go all the way back to 1885 with Ebinghaus, but the esoteric author of supermemo seems to have done the best work here. If you prefer the academic establishment, there's a ton.

- There's a bunch of science that about 2/3s of what we learn, we're not aware we're learning or teaching. Concepts support each other, deeply. Kaplan, back when Bror was there, did a bunch of nice work there. It's easier to learn long division if you know a bit of algebra, and vice-versa. Chemistry helps learn physics, and physics helps learn chemistry. This was supported with pretty independent methodologies in independent domains (data analysis from tests, cognitive task analysis, etc.).

... and so on. This has very little to do with affect. It's a very well-established, rarely-applied set of results.

A complete lit review here would be book-length, at least.