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I'm a sophomore in university and seriously feel that I'm bad at solving mathematical and algorithmic problems (be it discrete math, calculus or just puzzles). I noticed that I'm only good at solving questions that are similar to the ones that have been taught to us.

Here's how I generally approach it:

  • What is the problem? What do I need to do here?
  • Does it look like I've encountered this before?
  • Can I think of a smaller problem to solve instead?

If the answer is no to all the above then I sort of blank out. I stare at it and force my brain to run through a wide variety of stuff, almost like a brute force attempt of solving it. Obviously that leads me to nowhere everytime. I simply can't think "outside the box."

What can I do to improve my situation?

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    What kinds of questions are you talking about? I think a lot of it *does* come down to recognizing certain tricks and patterns, and you build up this ability with experience. How often do people truly think outside of the box?2012-11-01
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    "What can I do to improve my situation?" (1) Do A LOT of problems. (2) Read George Polya's "How To Solve It"2012-11-01
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    Hmm not exactly sure how to answer this. Just questions in general on any topic say textbook practice problems or questions in: http://projecteuler.net/problems although these are more math puzzle types.2012-11-01
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    I think that how we perceive ourselves, specifically how we perceive ourselves in terms of "what I'm good at" or "what I'm bad at" can be self-fulfilling. I think one's attitude when encountering novel situations, in general, like new problems, has a lot to do with how successful one is in handling the situation: if one develops confidence in one's competence, one is more likely to **persevere**. One can be fearful, intimidated (retreat); one can feel challenged and stimulated; etc...2012-11-01
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    I added a couple tags; hopefully, these tags will counter the "not constructive" close vote.2012-11-01
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    A lot of difficult textbook problems (at a proof-based level) simply take a lot of time, more than anything else. As amWhy said, you need to persevere. Don't expect to finish a problem in an hour, a day, or even a week.2012-11-01
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    The Art and Craft of Problem Solving is a great book.2012-11-01
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    The three steps you gave is how I would say I and most people I know do math. But after solving a problem, you have to pick at it and see why it worked. It's the same idea of "recognize small changes", but a more attentive person sees more ideas in a single problem. After many problems those "small changes" naturally compound into the kind of thinking you're looking for. And the next step should be something like "try random manipulations even if you don't see a solution in them, just to see how things work", rather than "blank". It's like being an artist: your worst enemy is the blank page.2012-11-01
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    The information is much too vague to diagnose your problem. I suggest that you take an actual problem where you failed to find the solution yourself after a long time, but understood the solution and describe where you were blocked and what you were thinking when you were blocked. Ideally, you do this in real life with an expert. Less ideally, you do it here. There are *plenty* of reasons why one might be stuck during problem solving. For example, you might not be looking at problems of the appropriate level, or you might not have any concept of playing with a problem instead of solving it.2012-11-01

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