fun to talk this week about the rumored ability of babies to do

mathematics. Yes, the concept sounds crazy at first, but every now

and then an article appears in newspapers or on the internet

describing a study that confirms babies have some inherent sense of

basic arithmetic. Is this really true? Are babies born with

fundamental math skills? Let's look at a couple of recent

experiments done on 6-7 month old babies.

One type of study involves presenting a pair of dolls to a baby,

covering them with a screen, and visibly removing one from behind the

screen. Then, when the screen is lifted, there should be one baby

remaining, since 2 minus 1 is 1. However, for half the babies, the

researcher does a little sleight-of-hand so there are still 2 dolls

there when the screen is lifted. They then measure how long the baby

stares at the scene: presumably, if the baby detects the incorrect

math of 2 minus 1 equals 2, it will stare longer. And the results

match the predictions: the babies do stare longer when the two dolls

are there. The researcher concludes that the babies correctly

computed 2 minus 1 equals 1, and wanted the correct answer.

Another type of study has the babies listening to two or three

voices, and then given a choice of looking at two screens, one with

two faces and one with three. If the babies tend to look at the

correct screen, presumably that means that they understand the

abstract concept of numbers, and want the number of visible faces to

correspond to the number of voices. And again, when this study is

done, it is usually found that the babies do spend more time looking

at the screen with the right number of faces.

So, do babies really understand basic concepts of numbers and

subtraction? It's an intriguing idea, but I don't think I'll be

turning over Math Mutation to my daughter any time soon. You can

probably spot some obvious flaws with the designs of these

experiments. With studies on single examples with very small numbers,

it's entirely possible that familiarity bias explains the action of

the babies: it's not too farfetched that the babies have seen one

item subtracted from two, or heard two or three voices, before. If

any of you can recall guessing answers on an elementary school math

quiz when you were young, this is pretty easy to believe.

There are also other factors that could be involved: for example,

in the "2 minus 1" experiment, maybe the babies are just more

interested in greater numbers of items. And like the famous

number-counting horses, it's hard to be sure if subtle cues from the

experimenter were not involved, since I doubt they are even allowed to

leave a baby totally free of adult supervision for very long. I would

be much more convinced by these studies if the articles specified that

had used randomized sets of one-digit numbers and blind

supervisors, unaware of the experiment, that were different for each

baby.

I should qualify this by mentioning that I haven't done a

comprehensive review of the journal literature on the topic, so maybe

the issue is just that the news articles I've seen were

oversimplified. But I have found an interesting skeptical article on

the topic by Leslie Cohen from the University of Texas, linked in the

show notes. Among other things, she attempted the baby-subtraction

experiment with a slightly wider range of numbers. In the end she was

not convinced that the claims of baby mathematical skills were

genuine. She makes the excellent point that before attributing a

complex cognitive process to a baby, you should very carefully

consider simpler explanations for what you are observing.

Babies are cute. Shouldn't that be good enough for us? Do we

have to require mathematical skills too?

And this has been your math mutation for today.

I'd first like to say I was so excited to hear this podcast.

ReplyDeleteI'd also like topoint out that Leslie Cohen is a he and is now Professor Emeritus at UT-Austin. He was my graduate adviser in the late 90s. The study you reference and the corresponding debate with Karen Wynn were based on my masters thesis. In the original paper, we conducted a control experiment where babies were shown either 1, 2, 3, or 4 dolls and tended to look longer the more dolls shown. I encourage you to read the entire paper which is on his lab site.

http://homepage.psy.utexas.edu/homepage/group/CohenLAB/pubs/Cohen_and_Marks_final.pdf

Wow, thanks for the comment! I think this is the first time someone whose work I discuss in the podcast has actually contacted me. I'm honored. That reference is nice, I'll have to read it in more detail.

ReplyDelete(BTW-- next time you see Leslie, tell him I apologize for getting his gender wrong. :-) )