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Is it okay to prioritize problem-solving over theory when studying physics or math? (sh.itjust.works)

submitted 5 days ago by leonine@sh.itjust.works to c/asklemmy@lemmy.world

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I have a unique way of studying that seems to work well for me, but I’m curious if it’s a good long-term strategy.

Whenever I start a new topic in physics or math, instead of diving into the theory or derivations, I first skim through a variety of solved problems to get a sense of the types of questions typically asked. I take notes on the key concepts and methods I encounter, focusing on recognizing patterns across different problems.

Once I’ve built a mental "map" of the topic through problem-solving, I attempt unsolved problems using my notes and keep adding new observations as I go. By the end, I feel confident about most question types and can solve them quickly. After that, I might revisit the theory with a sense of curiosity, wanting to understand the "why" behind the formulas and patterns I’ve observed.

This approach has helped me become faster at solving problems compared to my peers. However, I sometimes worry that I might miss out on deeper conceptual understanding, especially for rare, extremely challenging problems.

The reason I lean toward this method is that I tend to forget theoretical details over time, but problem-solving strategies stick with me much longer. It feels like I develop an intuitive "second brain" for tackling problems.

So, is this a valid way to study? Or should I switch to the more conventional approach of learning theory first and then solving problems?

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[–] hendrik@palaver.p3x.de 4 points 5 days ago* (last edited 5 days ago) (1 children)

I'd phrase it differently: make a map of how the topics / information relate and are interconnected. Keep track of what you already know and what you'll have to learn. Then focus on the latter.

I think that's a sound strategy. And you need some means to evaluate how you're doing. That's often applying your knowledge and doing some excercises. Also this makes it stick. I think those are the main reasons why professors hand out homework assignments. Because just reading the theory book won't even get you half way, and the human mind doesn't really learn by passively reading something.

So I think your strategy is the a bit more organized and self-reliant variant of what you're supposed to do. Just don't skip the theory or reading the book. Because you're not an expert yet, and you don't know what you don't know. Usually books and education material have been written in a way that teaches you the stuff in the correct order. And the right amount for a time. Otherwise you might get lost in detail. Or have a hard time because you yourself didn't get a connection. Or you'd miss a large chunk. I'd say you don't need do follow it 100%, you might be better off learning your way, but be aware of what the official material says.

[–] leonine@sh.itjust.works 2 points 5 days ago (1 children)

The thing is that I’ve always struggled with passive learning, like watching lectures or reading theory books, because they don’t keep me as engaged, to make them fun I used to first understand what the lectures trying to teach me and then I'd make notes on my own understanding, but at the same time, I prefer doing problems since it forces me to think actively. I’ll definitely try to stay mindful of the structured material.

[–] hendrik@palaver.p3x.de 1 points 5 days ago* (last edited 5 days ago)

Same same. Also makes a huge different if it's applied science, or academic theory. And I can relate. Takes me a huge amount of effort to learn something if I think it's not interesting, uninspring ... But once I'm interested and have some application, I read a full book on theoretical concepts. Or I apply it once and it's stored in my brain for the next 5 years. It just doesn't work at all if someone gives me a pile of information and says"here, learn this for the upcoming test".