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  •  Ha ha! Not all math can be done in your head! (12+ / 0-)

    I fill white boards with the stuff on occasion.

    The most important thing that I would hope the appreciation students would take away is the idea that it is possible to construct logical arguments rigorously relating various notions.  That is, the very idea of how a proof works, and perhaps more importantly, why it is necessary.

    That and the fact that we have had great success quantitatively understanding the natural world with these things!  I.e., it's not all random magic.

    Justice deferred is justice denied. -MLK

    by zephron on Mon Apr 19, 2010 at 10:53:30 AM PDT

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    •  Not all math can be done in your head (10+ / 0-)

      But being able to perform math quickly and easily is key to being able to use it to describe reality. If you cannot manipulate a paintbrush, you can't paint a picture regardless of you native gifts as an artist.

      In theory, there is no difference between theory and practice; but in practice, there always is a difference. - Yogi Berra

      by blue aardvark on Mon Apr 19, 2010 at 10:58:00 AM PDT

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      •  Well, it depends upon your point of view. (5+ / 0-)

        If by math you mean "arithmetic", then should you wish to compute tips, balance your checkbooks, maybe even identify which bag of walnuts is really cheaper, then, yeah, doing it in your head is important.

        However, mathematics is a much larger discipline than that, something that is rarely properly communicated to people outside of the hard sciences.  Ironically, there is a great art to it.  In stark contrast to the cookbook, turn-the-crank formulas we all learned in elementary school, in many cases an almost preternatural intuition is required to make progress.  Something that, as in art, usually comes in equal parts from experience and innate talent.  And like art, there is true beauty in it when all things fall into place, part of a greater whole, each piece a separate face of a deeper truth.  This is rarely done in one's head.

        Justice deferred is justice denied. -MLK

        by zephron on Mon Apr 19, 2010 at 11:11:04 AM PDT

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        •  One of my degrees is in math (6+ / 0-)

          I know precisely whereof you speak about the rush that occurs when you "see" how equations can be used to describe an underlying physical truth.

          I still contend that the ability to speedily do grade school arithmetic in your head is helpful in getting to the epiphany.

          In theory, there is no difference between theory and practice; but in practice, there always is a difference. - Yogi Berra

          by blue aardvark on Mon Apr 19, 2010 at 11:44:40 AM PDT

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          •  Indeed. No argument there. (4+ / 0-)

            I suppose, I would like to see kids also learning more about more complicated concepts that better represent Mathematics and its relationship to the natural world.  All to often ailure to appreciate Mathematics derives from failure to understand its potential.  This can be remedied.

            Also, some of the best mathematicians I know are piss poor at arithmetic!

            Justice deferred is justice denied. -MLK

            by zephron on Mon Apr 19, 2010 at 11:49:25 AM PDT

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          •  one of my inspirations about math and 'rithmetic (4+ / 0-)

            was a local grocer (the 1950s) who did almost all sales in his head. And in those days all the locals would run tabs 'till the end of the month. We'd just put stuff on the counter and he'd say "that'll be $1.32". He'd write the prices on a slip of paper and give it to us to keep, and a copy in his book, but he was never wrong.

            As a consequence I've always sort of kept a reasonableness tally in my head when shopping, and more than a few times the Scanner/Register will say "23.45" and I'll go "Wait, that can't be right...I don't know what the exact answer is, but that isn't it..."

            Without geometry, life is pointless. And blues harmonica players suck.

            by blindcynic on Mon Apr 19, 2010 at 12:59:46 PM PDT

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            •  A real feeling of power, knowing when there is (1+ / 0-)
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              a gross messup and saving $10 and up.

              What is fun is walking up and putting money on the counter, including tax.  The total comes up and the stack gets pushed.   looks on faces are worth the bit of mental stretching

              Laws are like cobwebs, which may catch small flies, but let wasps and hornets break through. Jonathan Swift

              by maybeeso in michigan on Mon Apr 19, 2010 at 05:46:04 PM PDT

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    •  I forget who said it (6+ / 0-)

      but I like the idea that mathematics is only formal philosophy. It is one of the best, longest-lived and most profound metaphors we have for the nature of reality, and the most accurate model to date.

      Government is not instituted for the good of the governor, but of the governed; and power is not an advantage, but a burden. -Algernon Sidney

      by James Robinson on Mon Apr 19, 2010 at 11:06:16 AM PDT

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    •  But basic math - arithmetic - can be done in your (8+ / 0-)

      head.  What's really frightening to me is the number of younger people who literally can't add or subtract (like making change for a purchase) or do simple multiplication or division without a electronic help.  This means they have a rough time estimating things - which means that if they entered things incorrectly, they don't notice that the calculator gave them a very wrong result.  I feel really old every time I think "these kids today.... " but in this one case, I can't help it.

      They only call it Class War when we fight back.

      by lineatus on Mon Apr 19, 2010 at 11:08:25 AM PDT

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    •  Understanding billions (5+ / 0-)

      and how that's different from millions is REALLY important. Being able to understand that qualitative mathematics, as represented by the difference between an analog clock and a digital clock, is really important.

      I get really annoyed when people are off in their estimates by orders of magnitude. Just makes me nuts.

      •  Records! (4+ / 0-)

        More years ago than I'd like to admit I TA'd a course in introductory Calculus.  This was for the math-appreciation crowd, so we started with functions, and in particular, linear functions.  On a problem set they were asked to fit a line to two data points and extrapolate.  Specifically, something like "The world record for the mile run was 5 minutes in 1960 and 4 minutes in 1980.  If it continues to decrease linearly, what will it be in 2000?"  Half the students came up with an answer larger than 4 minutes!  Now, I understood the error they made, but half the students didn't notice that their record was receding!  A stern lecture on checking your answers ensued ...


        Justice deferred is justice denied. -MLK

        by zephron on Mon Apr 19, 2010 at 12:04:17 PM PDT

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    •  I hated those proofs (1+ / 0-)
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      I could solve any math problem, but failed all my math classes because I didn't do it the way I was "taught".

      Repubs - the people in power are not secretly plotting against you. They don't need to. They already beat you in public. (Bill Maher)

      by Sychotic1 on Mon Apr 19, 2010 at 02:09:16 PM PDT

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