Good Math, Bad Math

No Abacus Handy? Use your hands.

Posted by Mark C. Chu-Carroll on October 9, 2006
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Suppose you want to do some math, but you don’t have an abacus handy. Oh, the horror! What do you do?

No problem! Your hands make a *great* two-digit soroban-type abacus. The four beads on the lower deck are your four fingers; the bead on the upper deck is your thumb, as illustrated in this diagram (with apologies for my terrible artwork):

i-8fff8a4227ca8b650be758afc06b1538-hand-abacus.jpg

So the numbers from one to nine look like:

i-55ecfcabcff3cf6b7aa238bb22e7e7b9-finger-numbers.jpg

To get two digits, you use your right hand for the ones, and your left for the tens. So, for example, let’s look at a simple addition:

i-bb114979fd477ca18a884d2969ce4d94-finger-add.jpg

Once you know the abacus, doing this with your hands is pretty simple. It’s definitely a limited technique, since you can’t get past one hundred without using your toes, but it’s a nifty trick, and it’s easy to teach kids to do this for working out math problems. If you’ve got a kid who’s a tactile thinker, it’s amazing how much learning to do this can help them. I’ve seen kids who do paper math with many digits by working out subparts of the problem using this style of finger-abacus.

There’s actually a whole Korean teaching method for math called something like chisan-bop. From what I understand, they build up on this quite a bit, to be able to do much more complicated stuff than just two-digit addition, but I haven’t been able to find an english textbook on chisan-bop. All the english texts basically show what I just did above: the two-digit abacus on the fingers.

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Comments

  1. #1 billb
    October 9, 2006

    I’ve always been a fan of counting in binary on my fingers. It’s not as easy as using your fingers like an abacus, and I wouldn’t want to do any arithmetic, but you can’t count a lot higher (above 1000 with no toes!)! It’s possible to count in ternary on your fingers, too, but it requires significantly more dexterity than I can manage. :)

  2. #2 JYB
    October 9, 2006

    In one of the O’Reilly hacks books it has a section on chisan-bop.

    I think it’s Mind Performance Hacks. I’ll edit when I get home if I’m wrong.

  3. #3 txjak
    October 9, 2006

    Nice demo, but the answer should be 63, not 53. Last step should add 3 not 2.

  4. #4 justawriter
    October 10, 2006

    I remember it as a fad and infomercial fodder back in the late 70s and early 80s. I love abebooks for finding used books and sure enough, here are the two or three books published back then.

  5. #5 Craig Pennington
    October 10, 2006

    I remember the ’80s Korean chisan-bop fad as well (well, not by name.) IIRC, the right hand was the same as hand-abacus, while the left hand went binary. From right to left: Th=10, In=20, Mi=40, Ri=80 and Pi=160; so the max result possible was 319. I don’t remember any specifics beyond that (and don’t even guarantee that I’ve remembered that very well.)

  6. #6 vipstar
    October 10, 2006

    I can’t do 8.. :(

  7. #7 Xanthir, FCD
    October 10, 2006

    I use binary finger-counting a lot. I need to practice more to get my addition better, but it works great for trying to simply count things. Being able to reach 30 on one hand has proven surprisingly useful. And though I don’t usually have a need to count to 1000, the knowledge that I *can* using only my hands is pretty cool.

  8. #8 asinomasimple
    October 11, 2006

    You’re not planning to correct the mistake ?

    Quote:
    Nice demo, but the answer should be 63, not 53. Last step should add 3 not 2.

    Posted by: txjak | October 9, 2006 10:44 PM

  9. #9 Mark C. Chu-Carroll
    October 11, 2006

    asinomasimple:

    Busy with the real job, haven’t had time to get back and edit the post to make the correction. Will do when I have time.

  10. #10 Mark C. Chu-Carroll
    October 11, 2006

    Sorry for the delay in the correction, but the error was in an image file, and editing and uploading a corrected image takes a lot more time than just editing the text in movable type; since I’m up against deadline in my real job, I didn’t have time to get to it until this morning.

  11. #11 Vamsee
    October 11, 2006

    Me neither! :(

  12. #12 Vamsee
    October 11, 2006

    Oops, sorry… I meant I couldn’t do 8 either.

  13. #13 Stephen
    October 12, 2006

    My blog has more detail, but no pictures.
    Counting on your fingers.

    My idea is to teach it to kids. Fear of Math is real. I believe it stems from the idea that if you add 7 + 8 and get 14, it may be off by one, but it is still wrong. Fear of Math comes from the fear of failure. So, if arithmetic can be reduced to a mechanical event which reliably churns out the right answer (IMO, it can), then the whole basis for the Fear of Math vanishes. This should work in kids to prevent the cycle, but it should also work for adults.

    By starting with fingers (which most people carry with them everywhere), and using a technique which is identical on the Japanese abacus (the soroban), it can be extended arbitrarily. My soroban has 27 rods, which is enough for most anything. It can also lead to wicked mental arithmetic. In high school, i used it to compute the sin(23.7) (degrees) to ten digits in my head, in about 35 minutes. You convert to radians, then use the Taylor series formula. I estimate that at one point, there were some 80 digits of intermediate results that needed to be remembered. The answer was then verified on a calculator.

    Far from bragging, i thought the technique was so powerful that anyone could do it. Now, i’m less sure. But certainly, it is powerful, and most everyone can benefit from it.

  14. #14 Nix
    October 13, 2006

    All of this appears to be assuming that the fingers move independently. Unfortunately, they don’t :(

  15. #15 Bart Radzik
    April 18, 2010

    I once reaad that this was first invented by the Sioux Indians, and I’ve been using this method ever since.