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Testing How to get Aha moments in the middle of math exams?

  1. Jul 2, 2011 #1
    How to get "Aha" moments in the middle of math exams?

    I find that when I work on math homework, I usually spend hours (or days) on a single problem, with little success. I usually go around in circles, and end up frustrated and clueless, with a huge mess of scribbled paper in front of me. Then I go do something else completely unrelated to math and all of a sudden the solution just pops out at me, and I can write it in 5 minutes.

    The problem is - what to do on exams? If I don't get a flash of insight, I will probably just sit there and twiddle my thumbs, or randomly jot down any bits information I have that might pertain to the problem at hand and see if I can piece them together to form a solution (usually this strategy doesn't work, since the crucial missing piece is the not-so-obvious insight that comes when I'm not looking for it).
     
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  3. Jul 2, 2011 #2
    Re: How to get "Aha" moments in the middle of math exams?

    Well, the trick is you need to spit three times over your left shoulder, do a cartwheel, and then the rest just takes care of itself.

    No, but seriously, all you can do is prepare the best you can, try to relax and have confidence in what you know, and you're also already doing fine by actually jotting down stuff, rather than trying to keep them all in your head.
     
  4. Jul 2, 2011 #3

    Hurkyl

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    Re: How to get "Aha" moments in the middle of math exams?

    Practice lateral thinking. Practice solving puzzles. Anything that forces you to think in new ways -- to stop thinking "Grrrr, what do I need to do to solve this problem?" and to start thinking of things like
    • What can I do that isn't what I've already done?
    • What assumptions or biases do I have that are affecting my approach to the problem? I need to re-examine them to see if any are wrong.
    • My work lets me change the original problem into a new problem. What if I forget the old problem and now try to solve the new one?
    • Can I describe what difficulty I'm having in solving the problem?
    and so forth.


    Part of the advantage of switching to other tasks then returning to the problem later is that it gives you time to forget whatever mental block you've constructed that is keeping you from solving the problem. :smile:
     
  5. Jul 2, 2011 #4

    Vanadium 50

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    Re: How to get "Aha" moments in the middle of math exams?

    I would argue that hoping for an Aha! moment in the middle of a test is not the right strategy. You should be trying for those moments well before the tests. Additionally, you should be trying to categorize problems: understanding the similarities and differences between different problems so you know what to do when you see something new.
     
  6. Jul 2, 2011 #5

    DaveC426913

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    Re: How to get "Aha" moments in the middle of math exams?

    I was going to say something similar to Van; ideally, if you've studied well, there should be no aha! moments. The problems should be similar to ones you've learned already.
     
  7. Jul 2, 2011 #6
    Re: How to get "Aha" moments in the middle of math exams?

    I too agree with Van. Don't get too wound up in the problems themselves (while doing homework), but instead focus on the general approach used in the problems. There is a pretty limited number of different problems a given chapter can have. Do the homework, of course, but think of each problem in the general sense (after completing, perhaps) and try to group the problems by the approaches you used. Chances are that you will see a pattern between the questions asked and the approach used.

    This way, on your exams, if you take a step back from the problem you should (in the general sense) be able to recognize the different types of problems and the (general) pproaches associated with them.
     
  8. Jul 3, 2011 #7
    Re: How to get "Aha" moments in the middle of math exams?

    Funny thing is that I get Aha moments on exams that I don't prepare for and I never get them on the ones I prepare for...kinda sucks actually lol
     
  9. Jul 3, 2011 #8
    Re: How to get "Aha" moments in the middle of math exams?

    Don't make your math teacher angry, that way problems on exam will be easier.
     
  10. Jul 3, 2011 #9
    Re: How to get "Aha" moments in the middle of math exams?

    I have a very similar phenomenon when working problem sets. I don't get it if I "try hard" but then do when I space out. I agree with what Vanadium 50 and Hurkyl said but I have a couple of things to add.

    After I feel comfortable with the material, I time my myself during problem sets to increase my adrenaline similar to an exam. It's stressful but it works for me and I feel a lot more relaxed during the actual exam. Another thing I do is think of music (or usually drum beast) when I'm jammed completely on a problem. During this time I'll zone out completely and get an "Aha" moment and then dive back into the problem. Music (drums beats) works for me because I'm a musician and it makes me feel relaxed.

    Have you tried analyzing what you think of when you get Aha moments?
     
  11. Jul 3, 2011 #10
    Re: How to get "Aha" moments in the middle of math exams?

    Van has it. The best way to get the Aha moment in an exam is to be totally unprepared for the material. You want to walk in and be seriously bored through the whole exam.
     
  12. Jul 3, 2011 #11
    Re: How to get "Aha" moments in the middle of math exams?

    I think this is less about knowing or not knowing the material, and more about what happens when you have a mental block during an exam. There have been problems where I know exactly what I'm supposed to do in a problem, recognize it's similar to a homework problem... and completely blank. The harder I try to recall what I'm sure I know, the more it slips away from me until I think I'll soon forget how to add. I'm only slightly exaggerating.

    The thing that helps me is to go on to other problems, and then come back to that one later. Or, if your mind is just fatigued and you can't even focus on the other problems, take a small break to meditate, or think of something else.

    This sort of thing happens all the time in chess. I think it was former world champion Mikhail Tal who told the following story about what he does when he gets stuck. He said he thinks about an elephant stuck in a swamp, and of ways to extract the elephant. Maybe you could bring in some cranes? But they might also get stuck in the swamp. Perhaps helicopters could come in with harnesses... etc. By the time he finally got the elephant out of the swamp and looked back at the board, he saw what needed to be done.
     
  13. Jul 3, 2011 #12
    Re: How to get "Aha" moments in the middle of math exams?

    Is it possible that you could be a little burned out? I'm a little burned out this semester and this has been happening to me. Just try to eat well (enough) and get in enough rest as you can. Lots of water helps too.

    I think this is good advice as well.
     
  14. Jul 4, 2011 #13
    Re: How to get "Aha" moments in the middle of math exams?

    Thanks for all the tips!
     
  15. Jul 4, 2011 #14
    Re: How to get "Aha" moments in the middle of math exams?

    Do the easy problems first, that way your confidence is built up, then when you are 'on a roll' tackle the hard questions. Do not waste time and energy on a problem you are not sure of because it will fatigue you and lose your confidence.
     
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