[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.




At 05:53 AM 11/24/2007, Bill Kerr wrote:
>>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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