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Re: Why Dehaene is Wrong
Posted:
Nov 4, 2012 4:54 PM
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On Sat, Nov 3, 2012 at 10:57 PM, Wayne Bishop <wbishop@calstatela.edu>wrote:
> 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".
Quite sure. My high school was fed by two junior highs. There were two
ninth-grade first-year algebra sections (and none for eighth-grade) in my
junior high school, and the other was about the same size. The high school
didn't offer that course.
There were just two sections of tenth-grade geometry in high school.
There was considerable attrition between ninth grade and my senior year.
Only 121 were graduated. Of those, only 15 took trigonometry--the highest
level of mathematics the school offered.
>
>
> 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?
>
The percentage was high enough to support the famous line above the door to
Plato's academy.
>
> 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.
>
That's hardly relevant to the points I raised. Especially in view of the
fact that the assessments have changed the curriculum.
>
> My old mandate remains appropriate, "Dance with the guy what brung ya."
>
> On the other hand, what's sauce for the goose is sauce for the gander.
--
--Louis A. Talman
Department of Mathematical and Computer Sciences
Metropolitan State College of Denver
<http://rowdy.mscd.edu/%7Etalmanl>
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