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Re: Why Dehaene is Wrong
Posted:
Nov 4, 2012 12:57 AM
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At 11:06 PM 11/1/2012, Louis Talman wrote:
>Those who succeed in mathematics today generally did well at
>arithmetic as kids. But when I grew up, great numbers of children
>did well at arithmetic. They had to, because calculators didn't
>exist. Very few of those people succeeded at algebra, let alone
>mathematics. There is a serious disconnect here.
Are you sure of that? That's not the experience I had in my
small-town Iowa high school. My recollection is that everybody took
it (Algebra I, I mean) as freshman and most of the students were at
least borderline successful. It was proof-based geometry in the
sophomore year where lots of students, including college-intending
students, "hit the wall".
>And the ancient Greeks---who invented modern mathematics---are
>certainly a counterexample to your "natural progression". They
>accomplished a great deal without beginning with the algorithms we
>ask kids to study today. Indeed, it's likely that they weren't very
>good at arithmetic at all. So their "progression", if there was such
>a thing, was entirely different from the one you think you've identified.
And what percentage of the general population ancient Greeks are
you talking about here? I do believe that select subset would eat
modern mathematics for lunch but the ancient Greek equivalent of an
ordinary engineering student at your campus?
>This last example suggests very strongly that arithmetic, while it
>may be *an* entry into mathematics, is not the *only* entry. Your
>"natural progression" completely ignores a significant possibility:
>The primacy of arithmetic is simply an artifact of a curriculum that
>denies entry to those who haven't acquired proficiency at
>arithmetic. (A curriculum, moreover, that's now strongly distorted
>by the effects of fifty years of standardized, multiple-guess,
>truth-or-consequences, mis-matching tests.)
One of my old favorites for denying reality: Need
improvement? Change the curriculum and pedagogy. Need to prove that
you have achieved your goal? Change the assessments.
My old mandate remains appropriate, "Dance with the guy what brung ya."
Wayne
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