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Topic: Re: "by type" and Problem solving
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Michael Paul Goldenberg

Posts: 7,041
From: Ann Arbor, MI
Registered: 12/3/04
Re: "by type" and Problem solving
Posted: Dec 9, 1995 7:52 PM
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At 5:07 PM 12/9/95, Andrei TOOM wrote:
>Regretfully, I have to abbreviate Botula's message, although all of
>it is very interesting. Note that Botula understands that `teaching
>these strategies is not inherently opposed to teaching through
>problem solving'. I completely agree. Some VIPs among educators
>scornfully bashed making tables and other ways to organize data
>and even word problems in general. (See e.g. Usiskin's paper.)
>All this does not mean that I completely agree with Botula.
>Botula naively shares the common illusion that the Standards
>have some `true' meaning which is often `misunderstood'.
>My opinion is that authors of Standards had no more clear ideas
>than those teachers to whom they addressed and who now alledgedly
>`misunderstand' their confused and confusing documents.
>Also Botula seems to think that is is sufficient to `explain' to
>teachers several rules and principles, and they will teach better.
>I think that the greatest problem with most teachers is that they
>know too little mathematics, and while they know so little of it,
>any `explanations' of `how to teach' are largely useless.
>Andrei Toom

I, too, have done some clipping. I should add that I agree with a good deal
of the part of Andrei's post which I have deleted (yes, you read that
correctly; occasionally, he makes a sensible point, and I'd be
intellectually dishonest if I failed to acknowledge it when I think he's
made one).

But I think he once again goes way too far with another empty assault on
the Standards, documents I believe he understands quite poorly. I think M.
Botula is very much on point in his previous couple of posts and is not in
need of correction by Andrei. I certainly can't accept his interpretation
of Mr.Usiskin (or anyone else who Andrei perceives as pro-Standards)
without seeing the particular references; unfortunately, these are not
provided in his latest post.

So while I concur with the general notion that far too many teachers, FOR
WHATEVER REASON, are likely to take only the trappings of reform ideas in
mathematics education (e.g., believing that there's magic in manipulatives
or in Polya's heuristic), I think Andrei's 'analysis' is strictly
seat-of-his-pants: he BELIEVES rather strongly that American education is
poor; that Americans are lazy; that reform educators are ignorant and/or
deluded. He makes a rather dramatic claim in his last sentence: that MOST
teachers know TOO LITTLE MATHEMATICS and that such lack of knowledge
hamstrings efforts at reforming pedagogy. While this claim is glaringly
overstated and lacks any evidence, it may indeed have some merit. But as
long as Andrei simply makes assertions, rather than presents either
evidence (and I'm not talking about statistical 'proof') or argument, it is
difficult to take such claims seriously.

I continue to request that Andrei provide us with some specific cases,
drawn from his own practice if need be, along with his take on what such
cases imply. Then, perhaps, we'll have something to discuss that will go

|Michael Paul Goldenberg
|University of Michigan 310 E. Cross St.
|School of Education 4002 Ypsilanti, MI 48198
|Ann Arbor, MI 48109-1259 (313) 482-9585
|(313) 747-2244
|"Truth is a mobile army of metaphors."
|Friedrich Nietzsche

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