A Mental Abacus Lets Math Whizzes Bypass Language

By Veronique Greenwood | August 9, 2011 2:52 pm


What’s the News: Most of us need everyone to stop talking when we perform mental math. But for children trained to do math visually with a “mental abacus,” verbal disturbances roll off their backs, prompting psychologists to posit that unlike the rest of us, they aren’t routing their calculations through words.

What’s the Context:

  • While some of the most brilliant mathematicians have been known for their ability to “think in shapes,” and Einstein said he used “sensations of a kinesthetic or muscular type” to come up with his breakthroughs, math is usually taught much like reading: a system of symbols to be interpreted.
  • It’s been suggest that the mental abacus, a system in which children are taught to use a physical abacus and then learn to manipulate it mentally, uses visual, rather than verbal, brain processes, judging from fMRI studies. And it seems to work phenomenally well: the winner of the 2010 Mental Calculation World Cup was an 11-year-old girl trained in mental abacus.
  • But working memory, the ability to juggle a few things in the front of one’s mind during activities like mental math, is known to have distinct size limitations. Generally, the number of mental objects we can keep up with tops out at three or four. So how are mental abacus users doing it?

How the Heck:

  • To confirm that the mental abacus was indeed not verbal, researchers had subjects trained in mental abacus and subjects without training listen to a recording of a story while performing mental math problems and repeat each of the story’s words as they went. Since mental abacus users often twitch their fingers in the air as though moving abacus beads, which could indicate that motor memory is involved, the researchers also gave some subjects a motor task to perform at the same time or in isolation: drumming their fingers on the table.
  • They found that although untrained subjects found it almost impossible to do calculations while performing the verbal task, it perturbed the mental abacus users only slightly. Turning the tables, the motor task had no effect on untrained subjects, but it did disturb the mental abacus users to a similar, slight extent as the verbal disruption. This confirms that mental abacus users are not using verbal methods in their calculations, and suggests that motor memory might somehow be involved, though more experiments on that point are required.
  • They also found that though there was no clear ceiling on the number of numbers mental abacus users could add, their adding ability declined precipitously when the numbers had more than three digits.
  • This suggests that the limit of their working memory is kicking in not on the number of numbers they add, but on the number of columns on the abacus, where each column corresponds to a decimal place. And maybe that’s why, when we’re stuck in the verbal traffic jam of “three hundred and eight plus seven thousand thirty-four,” they’ve already arrived at the answer.

Reference: Frank MC, Barner D. Representing exact number visually using mental abacus. J Exp Psychol Gen. 2011 Jul 18. Click here for a pdf of the text from the researchers.

Image: mmt2000 / flickr

CATEGORIZED UNDER: Mind & Brain, Top Posts
  • Georg

    Another instance of confusing math and calculation.

    There were some mathemtican genies (eg Gauß) who
    could calculate very well and quick, but that is not
    the general rule.

  • Paul

    Greg Bear, in his two book series “The Forge of God” and “Anvil of Stars”, had human characters using visual/kinetic imagery to do advanced mathematics without the need for manipulation of symbols. Your report reminded me of that.

  • Wynn

    I learned how to use a mental abacus when I was younger and I completely agree that I start having trouble when adding numbers more than 3 digits precisely because that’s how many columns I can keep in my head at one time.

  • AshleyCakes

    Can you learn the mental abacus method when you’re older, say, 25 years old, or would it be more difficult for someone like me to learn it now because I have already learned it the other way? I’d love to sharpen my math skills seeing as how it’s my weakest subject.

  • http://www.ucmas.ca Snehal Karia

    Research suggests that the best age to train a brain is between the formative years of 3 and 14…hence the best age to learn mental abacus is between that age. Abacus can be learned or even mastered but to enhance your visualization skill over the abacus beads, the age bracket becomes critical.

  • 462356

    I wouldn’t worry too much, though, Ashley; you can always wait a bit longer and get a calculator implanted into your brain.

  • Robert Martin, Psy.D.

    The average person can autonomate expertise at any age. 3-14 year olds may have an easier time, but we can all do it with practice, repetition, increasing challenges, and the motivation to keep it up :)

  • tbell

    @ Snehal Karia, I suspect that is an overgeneralization of the critical/sensitive period neuroplasticity findings. There are a great many things that we can learn to do at any age. Vocabulary acquisition for instance, shows lifelong plasticity. There are any number of motor skills that one can learn later in life that also do not seem to be age limited. It’s hard to say, without actually testing it, how easy something is to learn in adulthood (which is where most of us will spend our time).

  • Pippa

    What an interesting article. As a n=1 study, I have always talked about the patterns in numbers and have been able to add numbers on paper faster than most of my peers, who were using a calculator, when we were doing a lot of math – but I was never trained to do this. I did however attend school in my early years in Singapore and remember using an abacus. Although I write down the numbers, I visualize patterns of dots, and rearrange them, now I think about how I do it.

  • Maggie

    Apparently, “some of the most brilliant mathematicians have been known for their ability to ‘think in shapes,’ “. Yes. And so too any good high school geometry student …

    I really wish I could read the referenced article, because I am somewhat surprised that most people perform calculations using language. I do a combination of subvocalizing and visualizing the numbers. I was taught arithmetic with pencil and paper, not through having to recite in front of a teacher, so that may have something to do with it.

  • Cathy

    I suspect this is the method my husband uses to do his fast mental math. I’ve seen him twitch his fingers as he adds up.

    I have a mild case of discalcula, and I have to visualize the numbers as if I’d written them down in order to add anything more than one digit together. Otherwise, the numbers run together and become a big puddle.

  • Jay Warner

    We have been a visually oriented species since before we were Homo Sapiens. Mathematicians talk of ‘building a house, then wandering around in it,” to work on (for them) major problems. Watching an experienced statistician evaluate a problem/project, if you are quick about it, you can follow what he/she says by the imagery used. You can even contribute, if you have a visual sense of the means, standard deviations, and distributions involved. Let’s make ‘visual’ some other things we want to teach/learn.

  • Daniel J. Andrews

    AshleyCakes…the brain is quite a bit more malleable and adaptable than originally thought back in the 60s to even the 90s. You should have no trouble learning a new task if you wish. Math was my weak point too so I learned to do rapid mental math (there are several good books on this in libraries), and now I’m intrigued about the use of an abacus so I’ll look into learning this method (and I’m considerably older than 25, you young ‘un, you).

    I’ll never be a math genius as I struggle to understand concepts that other people grasp right away, but I do eventually grasp the concepts which are all the sweeter because it took so much hard work to understand them. But, people think I am a math genius because I can do basic math calculations (+, -, x, /, sqr rt) in my head before they can find the calculator and enter the numbers themselves, and I understand and can use some fairly high level statistical maths.

    In short, if you want to improve your math, make it fun, and don’t worry about whether or not your brain can adapt to it as an adult. It can. Your biggest limitation will be saying to yourself, “I can’t do math” and eventually you believe it and don’t even try. Avoid that trap, and your brain will eventually take you far beyond what you now think is possible.
    [soapboxing done] :)

  • Bob Hall

    The real question for educators is this: Is learning to add numbers rapidly an essential skill? I think being able to multiply and divide small numbers mentally is important. It’s a skill needed in the grocery store, for just one example. Would abacus training help?

  • http://EPA don bronkema

    we nonagenarians will wait for the implant!

  • http://discovermagazine.com Iain

    Verbal mental math requires adding from the left rather than the right, just like we say it.
    357 + 8791 = 357 + 8000 8357 + 700 9057 + 90 9147 + 1 = 9148. But I don’t use the pluses, it’s a given.
    I can only merge 2 numbers at a time and I find it much easier to reorder by length with the bigger number first. However, if i can name the numbers, I can add them. It really really helps to see them written down (keeps me on track)
    Subtracting I haven’t really tried, hmmm

  • devlyn

    Very cool! I wrote a paper about this in a writing class earlier this year (regarding localized Asian maths skills). ^_^


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