Is it okay to prioritize problem-solving over theory when studying physics or math?
Is it okay to prioritize problem-solving over theory when studying physics or math?
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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Depends on what your ultimate goal is. Being able to solve common problems? Sure.
My immediate goal is to become as efficient as possible at problem-solving, especially for exams or competitions. But I do wonder if this approach might leave gaps in my understanding in the long term.
The theory makes you understend why a method works for a certain problem. A lot of exams try to trick the taker by giving problems that are almost solvable with just the toolbox but need a bit extra trick to solve which theory can help. But there again i find that simply knowing the specific trick is enough to do well.
But personally believing that is in any way important to succeed in exams has lead me to waste too much time. If you find that you have prepared well enough to solve any problems across math for an exam, it would then be ok to then cover the theory.
So in essence, just keep doing what you're doing.
It’s reassuring to hear that focusing on problem-solving isn’t necessarily a drawback, as long as I’m prepared for a wide variety of questions. I think I’ll stick with my method for now and revisit theory selectively when I feel gaps or curiosity arise.