Obviously, that answer is wrong.  The traditional answer to this "real world" problem is, "If it takes 4 hours for one boy to do a job and 3 hours for another boy to do the job, the two boys working together never will get done.


At 08:01 AM 11/1/2012, Louis Talman wrote:

On Wed, Oct 31, 2012 at 9:39 PM, Robert Hansen <bob@rsccore.com> wrote:

My hypothesis is that quantitative sense and number sense are two very different things. One is concrete and physical while the other is imagined and abstract yet can be applied to the first.

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.

Well, I have devised the experiment, and solved the riddle, without even having to perform the experiment. There is the line between quantitative sense and number sense.

You've devised a thought experiment that demonstrates that you use the phrase "number sense" in a different way than Dehaene uses. It demonstrates nothing about humans' failure to connect what you call "quantitative sense" with the algorithms of arithmetic.

And any teacher knows that the lesson you think you taught is often quite different from the lesson the students learned. So your "$$$ for books" offer is irrelevant.

It's pretty easy to show that many kids don't know what addition is for. Tell them that it takes Lou 4 hours to wash all the windows, but that Bob can do the same chore in 3 hours. Then ask them how long it will take them it they both work on the together. You'd be surprised at the number of college students who will tell you 7 hours or 3.5 hours.

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

  < http://rowdy.mscd.edu/%7Etalmanl>