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Re: Allen's critique of NCTM Standards
Posted:
Dec 26, 1995 11:59 PM


> > >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 USmade 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 > >deemphasizing the twocolumn form of proof and putting greater emphasis on > >paragraph, sentence and oral forms. > >>> > > > >ChiTien > > > > a Physicist who does teach K12 math. > > > > > > > > Initial reactionHuh? So, twocolumn 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 > twocolumn proof. It has been argued that this form makes it easier for > students to learn proof. I don't agree and think perhaps flowcharts are > better for learning. > On a more personal, certainly chauvinistic noteRussians 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 twocolumn 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?
ChiTien



