On Wed, Oct 31, 2012 at 9:21 AM, Robert Hansen <bob@rsccore.com> wrote:

Irregardless of the title of his book and his intent, Dehaene doesn't show "number sense" in animals, he shows "quantitive sense". It would be as if I said that animals and humans share the innate sense of speech because we both are capable of making sounds. I opined then that this was a deliberate slight of hand by Dehaene. Talk about something that would catch the reader's attention (number sense), establish something else (quantitive sense), continue on as if you had established the other (number sense). I suppose that since this work is meant for popular appeal rather than science, Dehaene can use any plot device he wishes.

"Quantitive", or, the already existing word "quantitative" is fine with me for what Dehaene calls "number". I think, though, that you're conflating what Dehaene calls "number sense" with what is more commonly called "number sense"---and the two are indeed different. And your use of the phrase in a sense other than Dehaene's doesn't contradict his hypotheses. It simply points out that they're about something you refuse to deal with.

I think Dehaene makes a good *experimental* case for an innate quantitative sense, to use a phrase you prefer, in all higher animals and many lower ones. And the hypothesis that "mathy" kids are the ones who manage to connect that innate sense with the algorithms of arithmetic, while one cause of non-mathiness is failure to do so, offers some explanation of things I've seen in the classroom.

There are kids who don't know when addition is appropriate or when multiplication is. That seems to me to be well explained by such a failure to connect.  This is exactly what one would expect of a kid who learns algorithms because required to do so instead of as something connected to the real world.

The issue then becomes one of devising *experiments* to follow up on this hypothesis---not, as you seem to think, offering rationalizations for not believing it. Most of those rationalizations can be easily defeated by noting that humans have bigger, more versatile brains---which are capable of extending innate qualities in ways that animal brains aren't.

What couldn't be so defeated is evidence from well-defined experiments.

--Louis A. Talman
  Department of Mathematical and Computer Sciences
  Metropolitan State College of Denver