Need advice on the efficiency of a particular study habit that I have.

[ImAstudent]

Hi, I'm not sure if this is the correct sub-forum to post this question, so I apologize in advance if this post is misplaced.

Anyways, a little about my self: I'm a Junior in high school, My passion is in physics and mathematics and I plan to major in physics and preferably get a PHD in it in the future. My goal right now is to improve as much at physics and mathematics as I can.

Now to my question:
I've been noticing lately that I sometimes fixate my self on a difficult physics/mathematics problem and would spend hours at a time trying to solve it (sometimes it can take up my entire day). 99% of the time my attempt is in vain and I feel like I just wasted my time doing a problem when I could of spent it on something like doing my homework or solving problems that I have a higher chance of solving.

So I've been wondering if there is any benefit to spending hours doing a problem only to get no solution at all, or would it be more beneficial (learning wise) to just do problems that I can solve confidently?

Any advice(even unrelated to my question) will be highly appreciated! Thanks!

 

[serllus reuel]

It really depends. Doing easy problems can be a waste of time, but so can spending hours on a problem that you can't solve. Problems should be challenging but solvable. What book are you using? Something like Serway or Halliday?

 

[ImAstudent]

I am using Halliday for Physics right now. Most of the problems that i get super stuck on are the ones that i find on online forums like AoPS. I feel that the problems in Halliday's are challenging but still solvable in a reasonable amount of time. Should I just focus on working on problems in there instead?

 

[homeomorphic]

I think the trick would be just not to get stuck. There are a lot of strategies for that. Take a break. Solve an easier version. Solve a special case. Solve a more general case. Come up with a new idea instead of digging the same whole deeper. You can always come up with a different idea or a different way of looking at it, instead of the way you are trying to do it that is getting you stuck.

Getting stuck and practicing these kinds of strategies can be very beneficial. What you don't want to do is just sit there spinning your wheels.

 

[djh101]

I would say the trick is to be able to realize that you are stuck. Often times when you get stuck, you end up going in circles (e.g. applying trig identities over and over hoping to get to something solvable) and don't really get anywhere. Finding the solution on your own will, of course, help you learn better than consulting Physics Forums or the solutions manual, but sometimes you just can't solve something without help and applying trig identities for hours straight or waiting for an epiphany to happen (or whatever) is really not the best use of your time. Try your best, but as soon as you notice that you aren't making any progress and probably aren't going to, that's when it's time to check the solutions manual, post to a forum (and move on to another problem while you wait), or ask the instructor/TA/friend/etc.

Of course, always research the problem at least a little bit before turning to the above. Reread the chapter or search Google for some insight into the problem's background.

 

[462chevelle]

i have this same issue. usually going to a teacher for guidance can do wonders. you would be surprised what stupid thing you forgot to consider. some of those harder problems bring some concept in that is totally unrelated to what your working on and you can focus to hard on something and miss something else.

 

[mpresic]

I think that if you think that the Halliday / Resnick type problems are challenging but doable, then this is the level that you should be treating solving and examining. I think when you enter college / university, your professors will feel the same way. Most likely, they will not be trolling the online physics forums for problems for their tests. Most instructors select straightforward H/R type problems, or perhaps one with a little twist.

One danger in taking unusual amounts of time to solve the most difficult problems will rear it's head during the physics GRE (4 years or more later). You are expected to solve perhaps 50 (relatively easy) problems in three hours. Solving the 12 most difficult problems will not get you very far.

On the other hand, once in graduate school, you will need the attention span to solve fewer very difficult problems.

I do think your short term goal to learn physics and math in depth is an excellent one. I think a junior in high school setting a life goal to get a Ph D is farsighted. You may want to talk to researchers in the field to find out about what they find good or bad about their profession. If you see yourself in this career, then good. If instead (for example) you get an internship doing (for example) robotics, GPS, or project management, and later get an offer of employment, and encouragement to make this your career, and you think this is better than research, that's OK too.

I think you are young enough to be flexible in your long term goals. (I would giver different advise to graduate students in their fourth year post-graduate studies, who have a significant time investment already.)
Best of Luck

 

[Calabi_Yau]

I think that is a very common problem. For me, it works to be sure I master the basic concepts first and do all the "compulsory" homework, and then treat myself with challenging problems.

Why do this? For me, I found that while I could solve hard problems, the exams always had some direct questions or problems that involved basic concepts and details that sometimes I overlooked in favour of doing some more hard things. The result was me spending more than I should have on those easy problems because I hadn't practised any of them, and then had fewer time for the last one which is usually the one that serves to distinguish students.

Start with the basics. When doing hard problems don't worry if you can't solve them. What you must aim is to learn something out of it every time you try. Be it a new approach, or why your reasoning wasn't leading you anywhere, etc. Reflect on each problem and the solution, and understand why it has to be like that and what could have possibly have lead you to come up with the right approach.