Posted by Alan Kay-4 on Nov 24, 2007; 2:37pm
URL: https://forum.world.st/Panel-discussion-Can-the-American-Mind-be-Opened-tp114756p114773.html

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
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
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

BASIC SKILLS VERSUS CONCEPTUAL UNDERSTANDING
A Bogus Dichotomy in Mathematics Education
BY H. WU

cheers,
--
Bill Kerr
http://billkerr2.blogspot.com/

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