Understand it or burn I have a big problem when I study math,namely when I am stuck on some problem I can't go on and I won't keep studying other material till I haven't solved the problem I've been stuck on.
I am referring to the kind of problem of which I know the "tools" with which it can be solved but I can't see how to apply them or understand how they've been applied if the solution is provided.
This is really a devastating feeling ,it is like if I can't understand that specific problem I won't be able to understand any other thing if I leave it and keep on with the material.
It is literally as I've stated methaphorically in the title:understand it or burn.
This attitude is really bad in general  for me because I know I am wasting time that could be used efficiently on other topics and because I haven't really much time to waste.
That's  because I've decided to take a gap year after high school to learn some mathematics on my own since I knew I wouldn't have been ready for college mathematics  given that  for the last years I've been studying arts(also I can't afford a tutor).
So really I have no one which can help me and I have to find a way on my own to solve all my problems and  this is the only site which really can help me in the way .

So I am asking not how much I should struggle with a problem,but
  rather what is the best way to struggle with a problem (I hope you get
  what I mean).

 A: It happens with me but only when am practicing at home . During exams , the adrenaline in me kicks off and I do whatever I know I can . Then with the remaining time I approach the problems I left and fortunately I have solved all in most of my exams . But during practice , there isnt much focus . I feel sleepy if I dont get something and cant proceed further . And let me tell you in most of the cases , its the wrong approach . You can waste hours with the wrong approach . So these days , I mark the problem that I cant do and proceed to the next and repeat the process . After finishing whatever I could do , I retry some that I think will be solved with a different approach . Finally I use Google , stackexchange , quora for ' Expert ' advice . 
So what you need to do is . Dont think that you are worthless if you couldnt solve a problem . Think about how many problems you did solve without any help . When you are stuck in a problem . Take at most 3 approaches for the time and that too within 5 minutes and then skip if you cant . Retry after you finish everything you could . If still no luck , Theres " Stack exchange " , " Quora " , " Google " , " Yahoo Answers " . Good Luck 
A: Some things to consider:


*

*To a various degree this happens to all of us.

*It is an essential skill, to be able to leave a problem behind, even if only for a few days. It is fine to skip a problem, esp. if you have solved almost all the others from the section. If it is really bugging you, get help from math.SE. Time is precious—get things done, and get done with things.

*Perhaps you are one of those people who could benefit a lot from reading "How to solve it" by Pòlya (already mentioned in comments by @mt_). Some say it's a collection of obvious and useless (and actually I don't disagree that much), but there is a difference between just following intuition and consciously being aware of some methods and heuristics. Unless you have years of experience, it does help (I do have years of experience, and I still view it from time to time, just to remind myself of some good habits).

*If I were to suggest one thing, then I would urge you to get somebody a bit more experienced (or even better, a few such persons) to show you how they solve problems, but including the internal monologue, that is, how they think (therefore a few people would work better, because you might find somebody that thinks similarly to you). To witness how they create possible approaches (in what way), dismiss some (how, which), from the rest pick the most promising one (why), try, fail, pick another one, etc.
This is a lot of work for that person, and actually some kind of tutor would be best (I am aware that you can't afford one). You can start asking for such a script here, although I doubt many would be willing to write such lengthy notes. Maybe ask for a help via chat, interactive discussion is much better. There are also bounties, but I don't know how effective they would be.


Good luck! $\ddot\smile$
A: I'd like to offer a suggestion from personal experience with math troubles.


*

*Sign up for classes at a community college(2 yr).
I managed to pay my way through my associates degree delivering pizzas for minimum wage + tips (Not much more the minimum wage). Community colleges are designed to be affordable and a helpful stepping stone to a 4 yr degree. I did almost all my Math and Science at community college and saved THOUSANDS!

*Sign up for high school type math classes like Algebra,
Trigonometry, etc.. To try and learn it again.
You'll be sorry if you move on to calculus without mastering these concepts first. (Personally all my Calculus problems stemmed from doing bad Algebra not the calculus concepts.)

*GET A TUTOR!
Most community colleges will give you FREE tutoring if you ask for it. Usually the only requirement is that you be taking a math class for that person to help you with. Just check with an adviser when you try to apply.
