Some questions about math education -- my time limit for solving a problem

[nmego12345]

Background about myself (Can be skipped)

I'm a gifted math student in the 11th grade, I studied Differential Calculus 2 years ago and I did pretty well in it, unfortunately I'm not studying math a lot these days, but I've gained a lot of experiences in life that made me more mature than I was 2 years ago, I'm 17 years old by the way, and while it looks like I'm kind of a little old for 11th grade, keep in mind that in my country kids enter kindergarten when they are 4-5 years old, and I've entered it at 5 years old, add to that 2 years of kindergarten and 10 years of school and you get my current age. As you can see, English is my second language, so I might make a couple of mistakes here and there. I also have some experience in programming (Python, C, some Javascript and some basic stuff like HTML and friends), I made a couple of minor projects (Chess game - Sudoku solver - Quiz game).

-----Background Done------

At first I used to try solving math problems for 15 minutes and if I got stuck I look up the solution and learn it, but now I've learned to give it a go for a hour or two, I might even stay at it for days --- But that would take too much time, It is really fun to try solving a problem for ages then to find the solution to it, but if I have to spend days for every hard problem, I would run out of days to live.

So that's my question:

"What should be my time limit for solving a problem?"

A.K.A

"How much time should I spend on a problem before I give up?"

And "Why?" <----- Very very very important because I require reasons for every single advice I take, it is something that I've learned (and that is to not take things for granted.)

Okay, I've got another question, hope you don't mind:

Solving Math problems require creativity, but sometimes I solve a problem, and see others' input on it, and marvel at the amount of creativity they have. So I look at their solutions, understand it and start to use them in my future problems --- "Does that decrease my own creativity?"/"Would that damage me in the future?" --- As by reading another solution, I completely remove the possibility of coming up of the same solution by my own in the future.

One last question, if you please.

Sometimes I see some very hard problems, that require knowledge of something I have not learned yet, then I have 2 options:

1. I wait until I learn that subject and then attempt the problem (I hate waiting)
2. I read an elegant answer to the problem that helps me understand the subject and add something to my "Ways of problem solving list"

"Which one would be the correct choice?"

 

[jedishrfu]

What defeats your creativity is not using it. Once you've found a solution by whatever means you used, you can still try to think outside the box and come up with an alternate solution. Try to approach the problem from different angles. As an example say you need to compute the volume of some object and decide that x,y,z coordinates are best and so you get an answer then look at the problem and solve it in cylindrical or spherical coordinates. You might run into difficulties but then you'll learn new approaches that may come in handy later on.

I've found that most talented math kids have investigated many areas of math before you see them solve some cool problem. They recall tables of numbers for all sorts of functions in their head which helps to streamline their work.(like knowing the sin, cos, tan of all common angles of the unit circle, the logs of numbers from 1 to 100 or 1000... powers of numbers, roots of numbers, factorials of numbers... knowing how to estimate solutions) From those earlier experiences they've seen and remembered things that can be used as shortcuts in solving future problems.

Feynman was one who battled his way through problems and from his comments it gets easier and easier while the problems get harder and harder. Checkout some of his videos on youtube to get insight into how he solved problems.

 

[JRMichler]

"How much time should I spend on a problem before I give up?"

If you can just go ahead and solve it immediately, it's just busy work and you learn nothing. If you spend forever on it and never solve it, you get nowhere. Somewhere in between is the best time to give up and move on to another problem. That time is specific to you and the subject.

Back when I was taking thermodynamics, my limit was 8 hours on one problem. Other subjects, maybe one or two hours. That's when you are in school. On the job, some physicists might work on one problem for their entire life...

 

[Salvador Sosa]

I would generally spend 1 or 2 hours on a problem for a time limit because I don't want to over stress so I recommend you do the same. I believe that seeing how others solve problems doesn't limit your creativity but just allows you to see a problem in a different point of view. And for the last question I would recommend you learn the subject and then attempt the problem so you can see the problem in a different viewpoint but if the topic you don't know isn't very complicated than I recommend that you do the other option so you can figure out how to solve the problem faster

 

[nmego12345]

What defeats your creativity is not using it. Once you've found a solution by whatever means you used, you can still try to think outside the box and come up with an alternate solution. Try to approach the problem from different angles. As an example say you need to compute the volume of some object and decide that x,y,z coordinates are best and so you get an answer then look at the problem and solve it in cylindrical or spherical coordinates. You might run into difficulties but then you'll learn new approaches that may come in handy later on.

I've found that most talented math kids have investigated many areas of math before you see them solve some cool problem. They recall tables of numbers for all sorts of functions in their head which helps to streamline their work.(like knowing the sin, cos, tan of all common angles of the unit circle, the logs of numbers from 1 to 100 or 1000... powers of numbers, roots of numbers, factorials of numbers... knowing how to estimate solutions) From those earlier experiences they've seen and remembered things that can be used as shortcuts in solving future problems.

Feynman was one who battled his way through problems and from his comments it gets easier and easier while the problems get harder and harder. Checkout some of his videos on youtube to get insight into how he solved problems.

I posted this question in another place, and got this answer:

As for the second question: no, it does not decrease your creativity. You may be surprised to learn that, in fact, this is what people call learning, and it's how everyone builds intuition. What people do when they come up with a solution to a seemingly hard problem is think "oh, I've seen this kind of problem before", or "I've seen something before that might be of use here." Answers don't just come out of thin air.

Can you explain why is the above argument wrong?

The thing about trying to find multiple answers to a problem, I mean it is a fun thing to do, but what is the time limit for doing that? and if I try to find different ways to solve a problem, for every problem I do, that would take forever.

Cool, I'll check out Feynman.

"How much time should I spend on a problem before I give up?"

If you can just go ahead and solve it immediately, it's just busy work and you learn nothing. If you spend forever on it and never solve it, you get nowhere. Somewhere in between is the best time to give up and move on to another problem. That time is specific to you and the subject.

Back when I was taking thermodynamics, my limit was 8 hours on one problem. Other subjects, maybe one or two hours. That's when you are in school. On the job, some physicists might work on one problem for their entire life...

I get that, but are there any other factors that help in determining the time limit?

By the way, you said your time limit was 8 hours on problem, you said you were taking thermodynamics so I'm pretty sure that you had a lot of problems to solve, how would you cope if you encountered a problem that would take you 8 hours?

Okay, Most people suggest 1-2 hours at school, what do you think is the reason for that?

Thanks.

I would generally spend 1 or 2 hours on a problem for a time limit because I don't want to over stress so I recommend you do the same. I believe that seeing how others solve problems doesn't limit your creativity but just allows you to see a problem in a different point of view. And for the last question I would recommend you learn the subject and then attempt the problem so you can see the problem in a different viewpoint but if the topic you don't know isn't very complicated than I recommend that you do the other option so you can figure out how to solve the problem faster

I've read about this subject in different places, and most suggest 1-2 hours like you said, I might try that.

That is an interesting viewpoint, I'll keep it in mind, thanks

I see your point there.

 

[jedishrfu]

The second comment is not wrong. It's just another way of explaining how folks solve problems by pulling in ideas from other places.