Tuesday, December 27, 2011

37: Baby Math

    In honor of my daughter's first birthday, I thought it would be
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
    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.

  • Article on study of 6-month-olds recognizing subtraction
  • Article on study where 7-month olds match voices to images
  • A skeptical paper on Baby Math studies

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

      I'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.


    2. 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.

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