How body movements can help with arithmetic

ResearchBlogging.orgClicking on the link below will bring up an image in a new window (you may need to disable pop-up blockers to do this). The picture contains five rows of asterisks. Your job is to count them as quickly as possible. Try using your finger to point and help keep track.

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Now try the same task again, only this time, keep your hands flat on the table while you count.

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If you're like most people, this second task was a little more difficult for you. It's not that you need to use your finger to help you count, it just seems to help things along a bit. When you weren't using your finger to point, you may have found yourself nodding your head to help keep pace with all those asterisks.

A team led by Richard Carlson gave 24 tests like this to 17 students, and verified that pointing to help count asterisks resulted in faster and more accurate counts. But why? Maybe the fact that the items being counted are all asterisks tripped up the students, and they had to use their fingers just to keep their place. Carlson's team repeated the study, only using a variety of different symbols, not just asterisks. They found the same result. Even for a simple counting task, pointing at the things we count makes it easier. But once again the question arises: how is it that simply pointing at things helps us count?

The team repeated the first experiment, but this time they videotaped the students as they completed the task. Once again, half the time the students were allowed to point at the asterisks, and the other half the time they were not.

Two research assistants watched the videos (which were just side-views of the student volunteers' heads) and noted when they saw the heads nodding. The two assistants agreed on what constituted a nod 87 percent of the time. So how does nodding correspond to pointing and accuracy? Here are some results:


When viewers weren't allowed to point, they nearly always nodded as they counted. What's more, non-pointers who nodded were significantly more accurate than non-nodders. It's beginning to look like the body movements themselves are somehow assisting in the counting process.

Carlson's team speculates that when we count, we actually use body movements as placeholders -- memory aids that improve our ability to count.

In a fourth experiment, they extend this reasoning beyond counting to adding numbers. Volunteers were presented with sets of cubes -- real cubes, not images on the computer -- printed with numbers from 2 to 6. Each cube had the same number on all sides (e.g. the "2" cube was always a 2; turning it did not affect its value). A computer told the experimenter how many of each cube to present to the volunteers, and also generated a starting value ranging from 7 to 18.

The task was to add up the values of each cube, plus the starting value. So, for example, a participant might see five cubes, valued at 2, 4, 4, 5, and 6, and be given a starting value of 8. The correct response would be 29. The cubes were presented in a small, open cardboard box, and respondents were encouraged to talk their way through the problem. Half the time, they were allowed to touch and move the cubes, the other half the time, they had to keep their hands flat on the table. Here are the results:


For a small number of cubes, being allowed to touch and move the cubes made no difference in the results, but as the number of cubes increased, the effect became dramatic -- accuracy plummeted and reaction time increased when students were not allowed to touch the cubes. The students who weren't allowed to move the cubes also talked to themselves significantly more often as they tried to work through the problems.

Carlson's team believes that speech may take a similar role to hand movements when doing simple problems like these. Both actions help people keep track of the numbers while they work through the problem. But some of the words used in talking through a problem don't serve this function. When you say "3 and 3 is 6," only the numbers serve to help you keep track. The researchers argue that "and" and "is" in this phrase function more like nodding, to keep rhythm as you work.

So using your body, like using your voice, can help you work through arithmetic problems -- but some parts of your body help more than others.

Related: Children learn best when teaching is out of sync.

Carlson, R.A., Avraamides, M.N., Cary, M., Strasberg, S. (2007). What do the hands externalize in simple arithmetic?. Journal of Experimental Psychology: Learning, Memory, and Cognition, 33(4), 747-756. DOI: 10.1037/0278-7393.33.4.747

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Am I reading that second figure correctly? Participants were able to add up 14 numbers in 1.6 - 1.8 _seconds_ ? That seems awfully fast, were they testing Rainman?

I checked with the article, and that's seconds per item -- so when there were 14 items, it took an average of 22 seconds if you could move the cubes, and 25 seconds if you couldn't.

Hmmmm, this is interesting. In my own personal experience with the task, I felt that the active inhibition of movement was causing some interference in my cognitive abilities.

I would say the act of fidgeting helps relieve some mental stress, freeing up the centers of your brain that would be actively inhibiting the regions used for counting and other cognitive function, along the same lines of removing an epileptic focus in a seizing brain improving the function of the surrounding neural tissues. In the same sense, consciously inhibiting behaviors that would otherwise come naturally can lead to distraction and slowed cognitive function. This can be seen in the chart of timing.

I think the idea behind this project is very plausible as nodding or pointing would work very well to create a motive review/feedback mechanism of temporal and occipital interpretation of vision (especially in the nodding case where the motion directly affects the visual input), but I believe that the results of this data are somewhat skewed by the cognitive tension derived from limiting behaviors.

A good follow up to this study would most likely consist of watching people as they work through cognitive tasks seeing how many employ motive actions or fidget as they work. Also, another study may involve how active movements tracing visual or tactile stimuli helped improve recall of events and their contents.

Maybe the pointing or nodding helps with chunking the data and drawing borders. As you said, 3 and 3 is 6, and pointing or nodding there emphasizes that you are starting anew with adding two different blocks. (I guess what I mean isn't exactly chunking).

On an unrelated note, why is it that every time I open up Cog Daily (I don't use a feed), my Firefox freezes?

I've recently read two studies on some related ideas: the difference between intuitive and symbolic math skills, and the relationship between motor skills and language skills. This study really seems to fill in some of the "space in between" what I've read; given the task complexity, it would appear that the math involved in this study tapped symbolic skills, and the benefit of pointing and nodding certainly support the notion that symbolic representation and manipulation in the brain have some type of feedback relationship with motor control.


I'm guessing the problem is related the the QuickTime movies in two posts below. I'm going to move the movies off the main page; hopefully that will solve your problem. You might also try upgrading to the latest version of QuickTime.

David Pimm in his book: Symbols and Meanings in Mathematics, relates an episode of Japanese school children who were proficient with the soroban (a form of abacus)when asked to perform mental arithmetic with 6 digit numbers mimicked the actions of using the soroban. Is it possible that in order to facilitate the mental abstraction of doing such things as counting it is helpful to use epsodic memory as a reinforcer?

I'm wondering if these results would be different for people who have participated in math competitions such as "Number Sense", which is entirely mental math. When I tried the example, I distracted myself even trying to use my finger; rather, I found it easiest to find the midpoint of each line and use that to count the number of *s, and then use mental math to add them up. If the lines weren't symmetrical, or the *s weren't evenly spaced, then I would have had more problems. With the cubes, though, I don't think I would have needed any physical contact at all.

I actually instinctively force myself not to point or to nod (owing to my old-school manners lessons). I do indeed find it more difficult to keep track that way.

I was diagnosed with a dyslexia-like learning disability when I was young; one of the symptoms the testers looked for was so-called rivers (glowing vertical whitespace between words that form line on which I focus). I find the same effect when counting the stars.

Perhaps I just need to decrease the contrast on my monitor, though...

I just gave this task to my sister and she reacted rather interestingly. She counted with the right hand for the bottom row, then used the mouse cursor for the second to last row, then started counting on her fingers for the top row, and stopped altogether on the last (middle) rows. All the while she only used a pointing mechanism to keep track of the row, but not the individual stars in each row.

Thanks for this post. This is my first time making a comment here, but I do read fairly regularly.

I am a graduate student in Biomedical Engineering. I work mostly with MRI and fMRI for imaging brain function. I have some psychology background, but not a whole lot.

I am also an improviser. I teach and perform improv comedy and I have been doing so for eight years now.

This article inspired me to write an article of my own on my new improv and sketch comedy blog, FuseBox Theatre, about a common phenomenon in improvised theatre: the "talking heads" problem.

Often times beginning improvisers will simply stand on stage and talk, describing the circumstances of their scene rather than truly engaging it. Experienced improvisers tend not to do this, and are generally much more physically active in their scenes. They talk less and do more.

The mention of how when the subjects in this article were not allowed to move they talked more got me thinking about this problem.

If anyone is interested, you can read my article on here.

The site is still relatively new, but we will be adding content regularly if anyone is interested in improvisation and/or the science there-of!

Thanks, and keep up the great work on your site!