Hey there!
That's my first post in here. The first thing which comes to my mind as what topic of this post should be is the following question:

They say the best way to develop and train problem solving skills is by creating one's own problems.

I'm still a "passive" problem solver but I'd like to learn solving problems in an "active" way.

Could you give me some advice, name some guidelines on how to create new, own problems?

Thanks in advance. :)

Okay...

Now there is your first problem, figure it out on your own.

Sorry, probably a little rude. Whenever i am faced with a problem i simply walk around in my house, often talking to myself at the same time. And i focus on the problem, because whenever i have a problem i solve it. But sometimes the solution to problems comes when you least expect it.

I always tell myself that the problem is the solution. Not sure if that will help you, or even mean anything to you.

Thank you very much for your reply, but sorry I didn't get what you mean... °_°

oh...now you can ignore the previous post...alright...well that was a little bit rude yes ;)

yes, I agree with you that any problem, mathematical or physical, is equivalent to its solution, but I'm talking basically about inventing new mathematical/physical problems to help you learn the corresponding material better.
The main constraint is that whenever I'm up to create my own problem it tends to be automatically formed to an analogous one I've solved before...it sort of happens simultaneously in my mind.
You can say that it's all about training creativity in general. So I'd like to do it on the basis of mathematics. I sort of can't find an effective way to start the creative process...and that's why I asked for a piece of advice. :)

Your purpose is just develop your problem solving skills or to have better understanding of the subject thro' solving problems?

If you are thorough (reasonably) with the subject, problem solving will not be much of a problem; you can create your own problem that would be a problem for others.

If you want to learn more on the subject, better search for problems and try to solve them. creating own problems may not help in the early stages.

Your purpose is just develop your problem solving skills or to have better understanding of the subject thro' solving problems?
Well, both are interrelated, aren't they?
I imagine inventing new problems improves problem solving skills and shows you to what exent the subject has become clear.

If you are thorough (reasonably) with the subject, problem solving will not be much of a problem; you can create your own problem that would be a problem for others.
If you mean encoding known facts so that they become a riddle for those unacquainted with them, this is not what I am actually looking for. It is merely how to invent a problem whose solution uses known facts, but for which it is not enough to know the facts...I don't know if it's clear enough, but hope you understand. :)

If you want to learn more on the subject, better search for problems and try to solve them. creating own problems may not help in the early stages.
Well, I think I have a fairly complete grasp of school topics and have some background in calculus and linear algebra, some higher geometry (I mean projective and affine geomtery). In my case, does inventing new problems help or not. If it's still "no", then why? :confused:

When it comes to creating your own problems, well i invent stuff, therefore they become my problems and i always solve my problems, some more sucessfully than others of course. If inventing is what you are interested in then i guess i could tell you how i proceed when first comming up with the problem and then solving it. But usually these kinds of ideas springs to ones mind when they are least expected, unlike most my co-workers in this field i have a tendency to solve any problem related to the bigger problem by merely sitting down for a little while and think, takes me 5 seconds sometiems and sometimes several days, weeks, even months. But the actual "big problem" is usually very difficult to create unless you have a topic for your invention, but that often turns out to be total crap in the end, the best ideas are the ones that either come on their own, sometimes also the ones that you force to come to you when you are trying to fall asleep. At least that is how it works for me.

So id suggest that you come up with a subject, think about it for a little while, will probably not turn out to be that great. Go to bed, lie awake for about an hour and think about that same subject, hopefully it works, otherwise repeat the same procedure at least for a week and see what you come up with.
The only real advice i can give really is this. Since i am a capricorn and therefore never give up i have a slight advantage i reckon, therefore never give in to the oppinions of others. Allways listen to them though, but never give up, take a defeat, but come back victorious the next time when you have gotten some time to think the problem over and solve it, lose the battle but win the war. That is my strategy. I have various experts in my team, people who know far more than me in certain fields, i have something that einstein valued, i have imagination, and i am bloddy stubborn, a great combination if you ask me, and since i am posting, you do :p

well, thats all i can provide you with, how it applies to your fields i do not know, hopefully it helps some.

I feel it's about curiosity and asking questions. I've made some of the problems for Cee Ann's Problems Pages from fascination with geometric shapes and relationships. I find an object and wonder what's its surface? ... what's its volume? ... what's different about it? ... what happens when we do this? ... can this be solved by another method? ... then I try to answer the questions I've asked. I enjoy finding clever solutions and mostly use Archimedian methods as I have no real math training. Has it helped me solve other problems? Yes. I've gotten my name on Dr. Delgado's solvers list for Bradley University's Problem Of The Week many times with initially no idea how to begin.
Here's the link if you want view my pages: http://www.geocities.com/fran3406/Cee_Ann.html
And here's the link for Dr. Delgado's POTW:
http://bradley.bradley.edu/~delgado/potw/potw.html