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