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How important do you value mental calculations

  1. Jun 29, 2008 #1
    Do you think school should integrate classes that promote mental math and mental arithmetic, for example the ability to multiply two digit numbers in your head (say 15x19 or 14x17, etc). These things are critical and many people can't do them with severe brain gyrations! Do you think enough is being done to promote day to day general math that must be done withOUT pencil and paper? What would you say to a proponent of speed math who wants to introduce the trachtenberg speed system or vedic maths as a requirement in the curriculum?
     
  2. jcsd
  3. Jun 29, 2008 #2
    None whatsoever.

    What is so critical about this? My cell phone has a built in calculator, I use it.
     
  4. Jun 29, 2008 #3
    What's 10325890235 x 2345235325 and start the timer.
     
  5. Jun 29, 2008 #4

    lisab

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    I used to work with a guy who could do mental math so fast it would raise eybrows. He was a mediocre scientist, though, because he wasn't a good problem solver. He would use his mental gymnastics to overcompensate, which was kind of annoying.

    Doing mental math is a big time saver, no doubt, but it's not at the core of beign a good scientist - thinking is.
     
  6. Jun 29, 2008 #5
    Was it marlon? He does this thing with his eyebrows......
     
  7. Jun 29, 2008 #6
    I understand what you are getting at. Mental math certainly doesn't hinder you from thinking though, shouldn't one have both? Or do you disagree?
     
  8. Jun 29, 2008 #7

    Chi Meson

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    Some people have the talent, some don't. It's like having perfect pitch: If you have it, then more doors are open for you to pursue. If you don't you bring a tuning fork. Mine's an HP RPN.

    Edit: wow, lots of posting here since I started.
    I think that some have both talents (for fresh analysis and mental math). Our best guy Feynman was there. The combination surely is the sign of a superior scientist, no doubt. If I had to choose between the two talents I'd...

    ...I'd bring my calculator.
     
  9. Jun 29, 2008 #8

    Moonbear

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    I don't think it helps any. In fact, for a scientist, it's better to write it down. That way there's a record of the calculation done in case you made an error somewhere...someone can retrace exactly what you did and where the error was made.
     
  10. Jun 29, 2008 #9

    lisab

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    Well, in terms of an analogy, I'd say...

    clear thinking:mental calculations::writing brilliant litterature:perfect spelling

    It's nice if you can do it, but it's not necessary - especially with computers and calculators.
     
  11. Jun 29, 2008 #10
    I think it's somewhat important. Problem solving and reasoning should definitely be more important, but still. I never really use my mental calculation abilities towards math or science though. Mostly it's just for day to day stuff.
     
  12. Jun 29, 2008 #11
    Thank you. Good salubrious responses. Bows down with eyes closed...falls on a banana peel.
     
  13. Jun 29, 2008 #12
    I think its cool if you can, but I don't think theres any reason to bash people (especially students) that can't and its not bad if you cant..
     
  14. Jun 30, 2008 #13

    BobG

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    About 2.41 x 10^19. The only time consuming thing is counting the zeroes since you didn't use scientific notation.

    I don't think a person needs to be able to do mental calculations to the 26th digit, but he should have some idea of the answer he should get.
     
  15. Jun 30, 2008 #14

    DaveC426913

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    How do you know you have the right answer?

    A calculator = GIGO.
    A human brain can know whether an answer makes sense. But they can only do this if they have some sense to make i.e. mental practice.
     
  16. Jun 30, 2008 #15

    arildno

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    Having automatized the little multiplication table goes a long way to create a mental grid of how "magnitudes" stand in relation to each other, i.e, a rudimentary component of that "mysterious" number sense.

    And there is nothing mysterious about a number sense, or the ability to intuit roughly where some calculation should land you, it is, merely, the condensed outcome of sustained arithmetical PRACTICE.
     
  17. Jun 30, 2008 #16

    loseyourname

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    I kind of feel like quick mental calculations are a good life skill to have, and they're certainly a good test-taking skill to have, but I just tell my students to practice solving problems both with and without a calculator and to do it whichever way is fastest when it comes time to do it for real.

    I don't know what Vedic math is, but for something like 15 x 19, just break it down into (20 x 10) + (20 x 5) - 15, which can be done in under a second (provided you just intuit this and don't actually write it out). At least that's the way I've always done it. Break down any computation into a series of simpler computations. I try to demonstrate doing that, but really, I don't know if they're getting it or not, because the ones who were using calculators before keep using them, and the ones who were not likely already have some technique of their own.

    Really, though, something like 15 x 19 is pretty easy. When you get into much more difficult expressions that require a lot of rearranging, it starts coming down to how many images you can hold in your working memory at one time, which varies from person to person. That's not even computational ability, but just the ability to visualize without missing something.
     
  18. Jun 30, 2008 #17

    DaveC426913

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    The trouble though is that it is only easy for those who have practice at doing it mentally. And no one who starts with a calculator is going to voluntarily do a problem mentally.

    Thus, the need for rote in schools.
     
  19. Jun 30, 2008 #18
    When she was a little tot, my daughter could add 13 digit numbers in her head. I would ask her "What's 2 trillion plus 2 trillion?" and she could work it out without pencil and paper.
     
  20. Jun 30, 2008 #19

    Borek

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    I find mental math important - not necesarilly in terms of getting accurate results of 23567*12365, but in getting correctly order of magnitude of the answer. Saves a lot of time, often I see that the answer is wrong just because it is obvious it should be much smaller/larger.
     
  21. Jun 30, 2008 #20
    Before I write anything down for a homework problem I pretty much solve it in my head first. My friends write down a lot of ideas and work on scratch paper, but I can't write fast and it's a waste of effort, so I do it in my head first.

    Not things like hard integrals, but for example "Okay then I take the integral... which would make A, B, and C go away... alright, that looks doable. Then I'd take that..." etc.

    But arithmetic? Nope. Calculators were invented for a reason.
     
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