[Squeakland] Panel discussion: Can the American Mind be Opened?

Bill Kerr billkerr at gmail.com
Sat Nov 24 05:53:31 PST 2007


Further, but perhaps drifting off topic for squeakland, is it provable
that 'back to basics' and 'progressivism' are equally as inadequate?

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.


I read the original maths history
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
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:


A Bogus Dichotomy in Mathematics Education

-- =

Bill Kerr
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