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Topic: Allen's critique of NCTM Standards
Replies: 7   Last Post: Jan 3, 1996 11:17 PM

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Chi-Tien Hsu

Posts: 144
Registered: 12/6/04
Re: Allen's critique of NCTM Standards
Posted: Dec 26, 1995 11:59 PM
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> >Just want to ask a simple question: how the new assessment standards will treat
> >students who like to make precise, short, mathemtically suuficient "two columns
> >proof"? One of my Russian colleague once told me, a lot of the US-made 10 pages
> >research papers will become 2 pages in Russian standard. Are we lacking in this
> >area or have we already gotten too much? Just a question.
> >
> >Howard Wrote:

> >>>The Standards also suggest
> >de-emphasizing the two-column form of proof and putting greater emphasis on
> >paragraph, sentence and oral forms.

> >>>
> >
> >Chi-Tien
> >
> >---- a Physicist who does teach K-12 math.
> >
> >
> >

> Initial reaction--Huh? So, two-column proofs are inherently "precise,
> short, and mathematically sufficient"? I think not. The form has little to
> do with it. I have yet to see any advanced mathematics text which uses the
> two-column proof. It has been argued that this form makes it easier for
> students to learn proof. I don't agree and think perhaps flow-charts are
> better for learning.
> On a more personal, certainly chauvinistic note--Russians make a lot of
> claims, most of them as empty as the Steppes. For pity sakes the Russians
> can't even build a decent tractor.
> H^2

I did not mean it is inherently "precise ....", what I meant was the two-column
proofs which are "precise ...". A lengthy proof full of human language can still
be mathematically insufficient. What my question was simply whether if the
standards "require" students to put in a lot of human language which is very
often unnecessary. Mathematics is an artistic language, like poem, the shorter
the better, provided it is precise and sufficient. If the integration of
human language can help students obtain better mathematics understanding during
the learning process, I have no trouble with. But my feeling is this approach
should not be universal because many students might feel uncomfortable with it.
Secondly, this should not be included as "required" knowledge in math assessment
since it is not mathematics. It is certainly not fair to students who can learn
good math without it.

Text book should be written to help students learn from "not understanding" to
"understanding" using whatever way possible. Many explanations through lengthy
human language may sometimes be necessary. Most of the time we do not read the
whole text but able to get the complete knowledge.
When one "does" mathematics,
it is not necessary to waste so much time in translating back and forth between
mathematical language and human language..

About Russian papers, just for your information, many of those 2 pages Russian
papers are also highly respected in the Physics community in US. It is only the
culture here that we, including myself, are trained to put in more explanations
in the form of human language. I did not say which way is better or worse. I
only question whether if it is the "shortage" in this country.

Since you mentioned yourself, I would ask another question: how much the
Superpower Chauvinism contributes to the lost of competitiveness of this
great nation in today's world?


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