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?
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.
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.
I’m the same way for humanities, I prefer the empirical then use theory to understand it.
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
What u said reinforces my confidence in sticking with my approach! Thanks :)
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.
I would say… This is exactly how you should do it, and the “conventional” way is pretty stupid.
Everything we’ve discovered so far in science was to “solve” some kind of “problem”. I don’t mean “solve problem” in the way it’s usually used, like idk figure out what’s the most efficient way to travel from A to B, but in the way “there’s some unexplained phenomenon here and our existing models don’t cover it, so we gotta figure out a solution that works (predicts it)”.
For all these new problems, it doesn’t help you to be able to understand a theory by reading, it helps if you know how to problem-solve, i.e. figure out ways to apply your existing knowledge in previously non-existent combinations. Of course you got to have the knowledge of the previous theories or concepts to not go down routes already traveled, so you gotta learn your theory. But the methods you’re building by being problem-focused is imo exactly what you need to build to actually work in the real world and not just in an academic, “get your degree” kind of way.
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.
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.
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.
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".
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.
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. :)
