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Improving problem solving.
#1
Improving problem solving.
Does anyone have any good advice on how to improve problem solving/logical thinking regarding mathematics? I consider myself at least decent at mathematics and I usually have an easy time understanding mathematical concepts. But one problem I have is sometimes when I stumble upon a more difficult problem I just can't figure out what I am missing and when I find out the answer it seems like it was too easy to miss.

Usually someone must explain how to solve the problem to me and then I can solve similiar problems. But I want to be able to at least most of the times connect the dots and solve the problem on my own. In other words be more logical, better at connecting dots and have a better problem solving in general.

Are there any particular methods to improve those skills or does it just come with practice or is it mostly inborn?
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#2
RE: Improving problem solving.
I dunno... When I did higher maths at Uni, it simply took loooooong hours to come up with proofs, maybe 10 hours per sheet. Finding solutions to problem types you haven't seen before can take time. If you try long enough you will develop a better sense of how to approach new ones. Often it boils down to really clearly understanding what are the givens (be it numbers for a calculation, or theorems for a proof) and what the thing you want to show/calculate is exactly.
The fool hath said in his heart, There is a God. They are corrupt, they have done abominable works, there is none that doeth good.
Psalm 14, KJV revised edition

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#3
RE: Improving problem solving.
(10th April 2016, 20:52)Alex K Wrote: I dunno... When I did higher maths at Uni, it simply took loooooong hours to come up with proofs, maybe 10 hours per sheet. Finding solutions to problem types you haven't seen before can take time. If you try long enough you will develop a better sense of how to approach new ones. Often it boils down to really clearly understanding what are the givens (be it numbers for a calculation, or theorems for a proof) and what the thing you want to show/calculate is exactly.

Neil deGrasse Tyson, told in interview, something like this "process of problem solving in math by itself changes neuron networks in brain and thus improves the ability of brain to solve problems, even if you don't use math you know at all, your brain after being "trained" by math problems will preform much better at completing completely new tasks".

Alex K, can you please comment on his statement. Sorry for being lazy and not digging the google for actual scientific proofs of that statement.
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#4
RE: Improving problem solving.
or you could look for easier problems

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#5
RE: Improving problem solving.
I think what Alex said about getting very clear on what you're looking for and the givens is basic. Exploring tangental connections and noticing similarities to other problems encountered can also help.

Less helpfully, it is probably useful if you enjoy the process and have an expectation for success. But you acquire those or you don't based on past experience. So each new problem gives you an opportunity to earn those mindsets. If you are a little giddy at the prospect that's probably a good sign.
(16th February 2017, 18:16)TheOther JoeFish Wrote: So what you're saying is that I can harass all of the members I want for the next 168 hours, as long as I do so in my signature?
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#6
RE: Improving problem solving.
Roz, Google is your friend.

Seriously, if I run into a problem that I cannot get started on, I will look to Google or StackOverflow or WolframAlpha.

Someone somewhere has seen every problem in a math book. Also, you can always PM me with math questions. I'm a baller at that maths.
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#7
RE: Improving problem solving.
Thanks guys!
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#8
RE: Improving problem solving.
This doesn't have anything to do with math in particular but for me whenever I find that I need to work something out I try explaining what I'm doing to someone else. I have found that trying to explain it helps my brain sort it. Even if you just say it out loud what you are doing maybe the little things will click easier and you won't miss them?
“What screws us up the most in life is the picture in our head of what it's supposed to be.”

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#9
RE: Improving problem solving.
What I want is being good at is creativity, finding patterns and solving new problems that I haven't encountered a lot before. I feel like practicing is more like getting familiar with a problem and applying that to future similiar problems and that it doesn't really help with what I listed earlier, but I could be wrong.
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#10
RE: Improving problem solving.
(6th December 2016, 16:46)RozKek Wrote: What I want is being good at is creativity, finding patterns and solving new problems that I haven't encountered a lot before. I feel like practicing is more like getting familiar with a problem and applying that to future similiar problems and that it doesn't really help with what I listed earlier, but I could be wrong.

If you do a lot of math problems, logic puzzles, etc. eventually you go beyond the specific solution in each case, and start to get a sense of the general flavor.  I think the essence of high IQ is that some people skip the details and get straight to the underlying principles.
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