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Re: Too Little, Too Late? WSJ on the NCTM
Posted:
Sep 13, 2006 9:12 AM
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At 07:20 PM 9/12/2006, Ralph A. Raimi wrote:
>On Tue, 12 Sep 2006, Wayne Bishop wrote:
>
>>>In this class, the students didn't use the lettered variables that are so
>>prevalent in standard algebraic equations. Instead, they arrived at
>>answers using Cuisenaire rods, sticks of varying colors and lengths
>>that they manipulate into patterns on the tops of their desks. The
>>children use the rods to learn about the relationship between
>>multiplication and geometry.
>
>The author is confused, or got his information from an inarticulate
>source. Singapore uses "bar diagrams", which sort of resemble
>pictures of rods, whether of wood or of stone. NO; Singapore does
>not use Cuisinaire rods, which are a European invention certainly
>unknown to Singapore when they were invented around 1950, and have
>nothing really to do with geometry anyhow.
Thanks, Ralph, and belated congratulations on being quoted in the
story, but the detail herein looks more like the author being
deliberately confused by misinformation from an articulate
source. Probably from among the usual culprits but complete
mathematical ignorance on the part of the school cannot be completely
ruled out.
That appears to have been a Cuisinaire exercise, not something from
the Singapore curriculum; neither in letter nor in spirit. My guess
is that the (ubiquitous) Singapore unitary bars were being conflated
with standard manipulative exercises with Cuisinaire rods. You know,
"That's what we're already doing!" And have been doing for a couple
of decades. At the expense of PUFM, not to its enhancement. Haim
mentioned that some of the Singapore bar problems can made physical
by using Cuisinaire rods if they happened to be available. It's true
and I have seen a couple of cases where that approach had been taken
to meet the needs of the kinesthetic learners, you know. My
conviction was that the approach had introduced a problem not present
in the Singapore approach of sketches of the unitary bars. Useful,
maybe, for a teacher's presentation of the Singapore approach but
that the rods, rather than helping, were getting in the road and were
creating an artificial dependency on a physical situation instead of
focusing on the underlying conceptual ideas.
One of the Math-Teach respondents picked up on my preliminary
conclusion that the Curriculum Focal Points are "still far too vague
to control curricular and *pedagogical* decision making" and bent it
into something I had not intended. I was only objecting to there
being enough fuzziness in the NCTM Focal Points that such an
amorphous Cuisinaire rod activity at Garfield Elementary School in
Revere, Mass could pass as an example of - as *the* example of -
Singapore Math. On Page 1 of such an important national newspaper no
less. Does anybody know what the school's actual student performance
is? Here's all I was able to get:
<http://profiles.doe.mass.edu/mcas/mcascharts.asp?mode=so&view=tst&ot=5&o=1417&so=12982-6&school=248056&mcasyear=2004>MCAS
Annual Comparisons for Garfield Elementary School
"Fewer than 10 students were tested in the Garfield Elementary School in 2005."
"Fewer than 10 students were tested in the Garfield Elementary School in 2004."
"Fewer than 10 students were tested in the Garfield Elementary School in 2003."
I am not convinced that the school is really a Singapore Math
school. Maybe it is but maybe it isn't. For all I yet know, it may
just be another of those that has a leader with a knack for pushing
buttons to get lots of oohs and aahs in well-structured visitations
by external observers. Somehow that seems to be more important in
education circles than stellar - or even just competent - objectively
assessed student performance. It certainly worked effectively to
spread the gospel throughout the "reform math" era or it never would
have gotten off the ground. People adopt real change very slowly in
education - even with clear evidence of failure or of success - so
the lack of inclusion of student performance data in the article,
along with its lack at the Massachusetts site, is not encouraging.
The article itself was *very* encouraging, of course, the Singapore
Mathematics curriculum is great. It just doesn't need such "improvements".
Wayne
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