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Topic: Algebra drill versus intuition
Replies: 0

 Jerry Uhl Posts: 1,267 Registered: 12/3/04
Algebra drill versus intuition
Posted: Jun 9, 1997 11:42 PM

There is a very powerful article on numerical sense in the July Discover
magazine. It summarizes a ten year research project ron the human brain
by Stanlislas Dehaene in France. Dehaene was originally led into this
project by working with a brain damaged fellow who lost all ability to
calculate but retained the ability to estimate.

From the article:
After getting his masters [in mathematics] Dehaene gave up doing
mathematics in favor of trying to understand how the brain does it.
One conclusion he has reached after a decade of research is that the brain
has a very hard time. Dehaene writes:"Rigorous calculations do not come
easily to Homo Sapiens. Like so many other animals, it is born with a fuzzy
and approximate concept of number.... While our culture invented logic and
arithmetic,our brain remained unchanged and restive to even the simplest of
alogorithms."...."the brain isn't capable of doing long division without
concentrating on the mechanics. It takes extreme concentration and when you
see the brain activity, it's enormous. It's really hard work. And meanwhile
it's not concentrating on the meaning of what it's doing and when it makes
a mistake, it's an monstrous one. I think it's better that children do
their calculations with calculators. At least then they have the result
right away. They don't spend a minute thinking about how they got the
result, and they can confront the size of the result with the number they
statrted with and develop their intuition that way."

Dehaene's book "Number Sense" will be published in the US this fall.

-Jerry Uhl

----------------------------------------------------------------------
Jerry Uhl juhl@ncsa.uiuc.edu
Professor of Mathematics 1409 West Green Street
University of Illinois Urbana,Illinois 61801
Calculus&Mathematica Development Team
http://www-cm.math.uiuc.edu
http://www-cm.math.uiuc.edu/dep

[If] logic is the hygiene of the mathematician, it is not his source of food.
---Andre Weil

Only professional mathematicians learn anything from proofs. Other people
learn from explanations.
---R. P. Boas

+++++++++++End forwarded message+++++++++++

I repeat: We simply don't have enough evidence about the role of
computational skill in algebra, especially at the calculus entry-level, to
decide what its place in (to paraphrase Mark Van Doren) the natural history of
a mathematical mind might be.

I can't help but note that Klein has responded to just one of the issues I
raised...

--Lou Talman