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.
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.
I highly recommend NOT changing a working and tailored to your brain strategy into what you believe others are doing.
As an autistic though i am heavily biased to rely on my own systems of interpretation because what is normal is alien to me
The only thing I’d do is go back and look to see if you are applying the theory you are supposed to learn after you solve the problem. Applying a novel approach isn’t bad in the real world, but a lot of problems provided can be solved multiple ways.
Otherwise, I’d keep doing what you’re doing.
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.
The thing about learning from educational institutions is that they typically give you a box of tools rather than a specific method for solving specific problems. It’s not always obvious at the time why they teach a particular method or a particular way when there are easier or more efficient ways, but often it is because it’s prepping you for something later or because it also teaches you something else useful at the same time.
There is nothing wrong with your strategy, just don’t let it interfere with what they’re trying to teach you, even if you’ve skipped “ahead” and found a “better” way.
