I find that I learn immensely more in even tiny little tasks where I care about finding the result, compared to any assignment or exercise. Suddenly you look at the resources in a totally different light, critically evaluating what they are saying. Like, I'd pull some lecture slides or papers from the internet and read them in a very different way, compared to actual lectures. The roles are changed, I suddenly see the math (or whatever the topic is), and evaluate what it can do for me in the particular case. Not like what I need to do for the math to conquer it and learn it to the satisfaction of a teacher.

This also applies to computers. Just get your hands dirty, try to build something and you'll find yourself learning about so many things and tools incidentally while trying to fix something.

I can learn much better this way than going chapter by chapter in a book.

But interestingly, even graded, project-style assignments don't accomplish the same effect, only if I'm really onboard with the topic. I seem to need a spark of excitement of "this is not exactly the way you're supposed to be doing things" and just breaking things and playing.

Couldn’t have said it any better. Whenever someone is asking me if I have been introduced to a tool needed to do a job, I tell them “no, but only because I never had a reason to learn it. I’ll pick it up.”

I can pick something up very quickly when I have an actual reason to know it, and getting a good grade in a course is not a strong enough reason compared to “Learning this will help me save the world”. I’m not going to be passionate about it or inquisitive or asking myself the extra questions I normally ask myself when I’m learning something in order to apply it to a problem. And real problems are better than made up problems.