[Squeakland] Panel discussion: Can the American Mind be Opened?
Alan Kay
alan.kay at vpri.org
Sat Nov 24 06:37:10 PST 2007
Thanks Bill --
I think you make the central point about all this.
Cheers,
Alan
----------
At 05:53 AM 11/24/2007, Bill Kerr wrote:
>David:
>>Further, but perhaps drifting off topic for squeakland, is it provable
>>that 'back to basics' and 'progressivism' are equally as inadequate?
>Alan:
>I said above that the simplistic versions of both are quite
>wrongheaded in my opinion. If you don't understand mathematics, then
>it doesn't matter what your educational persuasion might be -- the
>odds are greatly in favor that it will be quite misinterpreted.
>
>
>David,
>
>I read the original maths history
><http://www.csun.edu/~vcmth00m/AHistory.html>http://www.csun.edu/~vcmth00m/AHistory.html
>that prompted your initial questions about constructivism and agree
>that it critiques the cluster of overlapping outlooks that go under
>the names of progressivism / discovery learning / constructivism -
>fuzzy descriptors
>
>But more importantly IMO it also takes the position that the
>dichotomy b/w "back to basics" and "conceptual understandings" is a
>bogus one. ie. that you need a solid foundation to build conceptual
>understandings. The problem here is that some people in the name of
>constructivism have argued that some basics are not accessible to
>children. (refer to the H Wu paper cited at the bottom of this post)
>
>I think the issue is that real mathematicians who also understand
>children development ought to be the ones working out the curriculum
>guidelines. This would exclude those who understand children
>development in some other field but who are not real mathematicians
>and would also exclude those who understand maths deeply but not
>children development.
>
>This has not been our experience in Australia. I cited a book in an
>earlier discussion by 2 outstanding maths educators documenting how
>their input into curriculum development was sidelined. National
>Curriculum Debacle by Clements and Ellerton
><http://squeakland.org/pipermail/squeakland/2007-August/003741.html>http://squeakland.org/pipermail/squeakland/2007-August/003741.html
>For some reason the way curriculum is written excludes the people
>who would be able to write a good curriculum -> those with both
>subject and child development expertise
>
>For me the key section of the history was this:
>"Sifting through the claims and counterclaims, journalists of the
>1990s tended to portray the math wars as an extended disagreement
>between those who wanted basic skills versus those who favored
>conceptual understanding of mathematics. The parents and
>mathematicians who criticized the NCTM aligned curricula were
>portrayed as proponents of basic skills, while educational
>administrators, professors of education, and other defenders of
>these programs, were portrayed as proponents of conceptual
>understanding, and sometimes even "higher order thinking." This
>dichotomy is implausible. The parents leading the opposition to the
>NCTM Standards, as discussed below, had considerable expertise in
>mathematics, generally exceeding that of the education
>professionals. This was even more the case of the large number of
>mathematicians who criticized these programs. Among them were some
>of the world's most distinguished mathematicians, in some cases with
>mathematical capabilities near the very limits of human ability. By
>contrast, many of the education professionals who spoke of
>"conceptual understanding" lacked even a rudimentary knowledge of mathematics.
>
>More fundamentally, the separation of conceptual understanding from
>basic skills in mathematics is misguided. It is not possible to
>teach conceptual understanding in mathematics without the supporting
>basic skills, and basic skills are weakened by a lack of
>understanding. The essential connection between basic skills and
>understanding of concepts in mathematics was perhaps most eloquently
>explained by U.C. Berkeley mathematician Hung-Hsi Wu in his paper,
>Basic Skills Versus Conceptual Understanding: A Bogus Dichotomy in
>Mathematics Education.75"
>
>Papert is also critical of NCTM but is clearly both a good
>mathematician and someone who understands child development - and
>has put himself into the constructivist / constructionist group
>
>I followed that link in the history to this paper which is a more
>direct and concrete critique of discovery learning taken too far,
>with well explained examples of different approaches:
>
><http://www.aft.org/pubs-reports/american_educator/fall99/wu.pdf>http://www.aft.org/pubs-reports/american_educator/fall99/wu.pdf
>
>BASIC SKILLS VERSUS CONCEPTUAL UNDERSTANDING
>A Bogus Dichotomy in Mathematics Education
>BY H. WU
>
>cheers,
>--
>Bill Kerr
><http://billkerr2.blogspot.com/>http://billkerr2.blogspot.com/
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