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A Mental Abacus Lets Math Whizzes Bypass Language

By Veronique Greenwood
Aug 9, 2011 11:52 PMNov 20, 2019 3:58 AM


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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

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