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by conwy 793 days ago
> this is one big hurdle in learning math backwards. You discover new missing pieces at every corner. Each missing piece leading to another missing piece.

Yes this is exactly what happening to me.

E.g. I got up to Week 2 of the course and suddenly made the big (to me) discovery that sqrt(a/b) = sqrt(a)/sqrt(b).

It seems trivial I know when you see it written like that, but the problem is to recognise and apply that principle in the context of a broader problem such as factoring.

> Just keep at it.

Thanks, this gives me confidence that I'm not wasting my time haha

I am beginning to get better at it, to the point that I can often work out why I got a question wrong on my own without referring to the answer.
2 comments
password4321 793 days ago
This tool begins with a diagnostic to determine the missing pieces: https://news.ycombinator.com/item?id=40081541#40082722

https://hn.algolia.com/?query=mathacademy&sort=byDate&type=c...

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gofreddygo 793 days ago
It's really frustrating how every single person I know who got (really) good at math or programming got there the same way, but never even hinted about it to me till I saw them use the same techniques. The clever ones figured out the important parts faster and spent more time on repeating the common idioms, theorems and required prior knowledge (e.g. the sqrt(a/b) = sqrt(a)/sqrt(b) piece for you) instead of the problem or spending too much time on conceptual understanding

The really important part for me was to rip these small but critical parts out and form somewhat like mental workout routine that I kept repeating multiple times per week. By week 5/6 I could solve the same/similar/related problems which weeks ago took me several minutes with ease and I had more brain power left to think about higher level and related concepts and techniques that formed more connections, making the experience a lot more fruitful, productive and faster. Without that mindless, disciplined mental routine to get the basic and critical stuff in muscle memory, I do not believe I could have made it through.

Good luck.

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