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?
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.
Do what works if your goal is to pass exams / tests.
BUT
just be aware that past papers are not a full guide to what you might be asked, sometimes a novel question comes up that would require you to make use of the theory to find your way through
Oh, I’m very well aware of this, I’ve faced these situations in the past, but the thing is, I solve a ton of problems, including medium to hard problems, also after some rigorous practice, I become good enough to visualize the path I’ll take to solve easy problems and become efficient enough to solve them in my head.
Only the very hard problems, where I have no clue how to tackle them and have to bang my head on the wall for 2-3 hours, get the better of me. I always end up seeing the solution, and then I just take notes and make sure that if the same or a similar problem pops up (which rarely happens), I’m at least able to find my way. But that never happens, I usually end up forgetting the method or approach due to lack of practice. I feel like even if I read the theory very well and learn the derivations by heart, I still won’t be able to complete those problems. Maybe it has to do with reasoning and general IQ, but I’m not sure.
Yes of course, it’s not only ok, but it’s important. Even when studying theory. You get to understand theory by solving problems about how the theory works. Problems aren’t just about formulas but also about reasoning.
Thanks for the reassurance, i’ll keep doing what am doing. :)
So, is this a valid way to study?
Yes, but what’s your goal?
I call you an engineer. If you want to be a scientist instead, you better fix your ass on a chair and sweat all these details, one by one.
My current goal is more aligned with being efficient at solving problems, especially in the context of exams or competitive settings, so I guess that leans more toward the ‘engineer’ approach.
If it works, it works. Not sure what level of math and physics we are talking about here, but university mathematics usually doesnt have “problems” in the common sense. Sure, there are going to be questions on the exam which you can solve using the theory or by remembering similar questions. But, upcoming topics are going to heavily rely on the theory, not on the applied methods for problem-solving. So you might start having problems there. But again, if your system still works for that, who cares.
Also, if you are aiming to become a Doctor / Professor / stay at university, youre going to need to remember the theory. Pretty sure there wont be a way around it.