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/