Poor at problem solving -- I'm looking for changes to my approach

[physicsgirlie]

I've found myself in a bit of a frustrating position: I never seem to do particularly well when it comes to solving problems. It’s not as straightforward as it might appear. I often reach a point where I have a solid, deep understanding of the material—I can explain it clearly to anyone, regardless of their level of background—but when it comes to actually tackling problems, especially under exam conditions, I tend to fall short.

I study at a top university in the UK, where assessments are almost entirely exam-based, and you're expected to demonstrate your understanding by solving problems. I know there are students who manage to get through by following the right steps to arrive at the correct answer, even if they don’t truly grasp where much of the underlying theory comes from. I’m the opposite: I understand the theory extremely well, but can’t seem to convert that into marks.

Another issue I face is that I tend to overthink problems. Rather than applying a method and moving forward, I often second-guess myself, get stuck analysing what the question is really asking, or explore too many possibilities before committing to an answer.

What sort of changes should I make to my study approach in order to perform better in exams or any problem based assessment? Has anyone been to a similar situation?

 

[berkeman]

Welcome to PF.

One thing that helped me a lot in undergrad was to try to work as many problems as I could. That meant that I tried to do every problem at the end of every chapter*, especially the last ones which were usually the hardest. I could generally only check my answers on half of the problems (odd or even, depending on the textbook), but even so I could still try to judge whether I understood enough to know how to start working on the problem and try to get a reasonable answer.

In one of my favorite UG Physics classes, the prof handed out a set of about 150 problems on the first day, and said that many of the problems would show up on the midterms and the final. I worked through all of those problems on my own that semester, including doing them all again during the week before the final. There were a couple that I was not able to figure out before the final, and sure enough one of those was on the final. I actually figured it out during the final, and was super happy about it.

I guess my point is that you get better at doing problems (and handling hard ones in exams) by doing more problems.

* Every different type of problem. There is no reason to do 5 problems in a row that involve the same concepts.

 

[fresh_42]

I know the overthinking aspect. I often think of using heavy machinery when a simple thought would do. It reminds me a bit of Bohr's barometer question. As @berkeman said, all you can do is practice as much as possible, and maybe trying to think of easy solutions first. Exam problems are rarely so complicated that they involve difficult solutions. Nobody wants a high failure rate. It's more likely that problems have a twist that has to be figured out compared with the textbook theorems and principles. Exams are always stressful situations, so you could try to better deal with that pressure, but that is a very indirect approach.

 

[fresh_42]

We had oral exams and I protocolled around about 250 or so for a dozen different professors. Oral exams have their own rules, but I remember a student who could quote any theorem or definition in a book, but was rather helpless when asked about an example. This shows that there are several levels of understanding, and knowing the subject and solving a problem are two different skills. They have to be trained differently.

 

[TensorCalculus]

I've found myself in a bit of a frustrating position: I never seem to do particularly well when it comes to solving problems. It’s not as straightforward as it might appear. I often reach a point where I have a solid, deep understanding of the material—I can explain it clearly to anyone, regardless of their level of background—but when it comes to actually tackling problems, especially under exam conditions, I tend to fall short.

I study at a top university in the UK, where assessments are almost entirely exam-based, and you're expected to demonstrate your understanding by solving problems. I know there are students who manage to get through by following the right steps to arrive at the correct answer, even if they don’t truly grasp where much of the underlying theory comes from. I’m the opposite: I understand the theory extremely well, but can’t seem to convert that into marks.

Another issue I face is that I tend to overthink problems. Rather than applying a method and moving forward, I often second-guess myself, get stuck analysing what the question is really asking, or explore too many possibilities before committing to an answer.

What sort of changes should I make to my study approach in order to perform better in exams or any problem based assessment? Has anyone been to a similar situation?

Ohhh I struggled so badly with that...

My way of getting over it would be to build up problem complexity: like start with problems that are as simple as just applying a single formula, and then do some where you have to rearrange that formula, then build up to more and more complex problems that tie in more areas of physics. Try at first to do problems which are tricky, but that only test basic concepts (maybe for a 1st/2nd year, trying some of the IPhO problems would be nice. Or maybe by then they are too simple, not sure.)

And then it's just about practice... getting used to what the exam wants (the British system... grr... it rewards writing in a very specific style, making sure you get "key words", working through the mathematical problems the way the markschemes like it...). And of course, if you are ever struggling, you can ask the PF community :-). The more problems you do, the more you start to spot patterns between them.

Oh, one more thing. If you're overthinking a problem, go do something else for a bit, distract yourself, and just come back to it and look through your workings with a fresh mind. Sometimes even just that does wonders.

 

[gleem]

At what point are you in your program? I assume your major is Physics. Is this an issue with every subject? Can you give an example of a difficult problem?

 

[vela]

Problem solving is definitely its own skill, and like everything else, you have to practice to get good at it. It's pretty easy, for example, to understand Newton's laws of motion conceptually; it's quite different to apply them to solve problems.

To add to @berkeman suggestion above, after you solve a problem, you should review what you did. Were some of the steps you did unnecessary so they can be omitted? Can you do the math more efficiently? What's another approach you might take to solve the problem? Is it better than the one you used? And so on. It helps to imagine that you will teach your solution to the class. You want it to be clear and concise.

As far as overthinking goes, just commit to an approach and go for it. Don't hesitate because you're not sure if you're doing it right, etc. The worst that happens is you realize you need to take a different approach. So you just start again. This is part of the learning process.