Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Topic: Inclusion research
Replies: 88   Last Post: May 12, 2010 11:40 AM

 Messages: [ Previous | Next ]
 Herman Rubin Posts: 968 Registered: 12/6/04
Re: Inclusion research
Posted: Feb 12, 1997 9:13 PM

In article <33024F7D.167@flash.net>, sara lehman <sllehman@flash.net> wrote:
>Marc Whitaker wrote:

>> Nicole Budiselich wrote:

>> > gino crocetti wrote:
>> > students helping the other children in the classroom. All of the
>> > students will be able get a better understanding of the topic that is
>> > being covered in the class.

>> As a parent, I would resent my daughter taking time away from her
>> studies to help those who couldn't or wouldn't keep up. Rather than
>> spending half her class time assisting others, she could be progresing
>> at a faster rate, and should.

>> I mean the word proof not in the sense of the lawyers, who set
>> two half proofs equal to a whole one, but in the sense of a
>> mathematician, where half proof = 0, and it is demanded for
>> proof that every doubt becomes impossible.

>> Karl Friedrich Gauss (1777-1855)
>> In G. Simmons Calculus Gems, New York: McGraw Hill inc., 1992.

>A true test of students' learning is to ask them to explain what they
>have learned to others.

This is very definitely not the case. There are things which can be
explained, and things which cannot. Also, it is quite possible to
understand to some extent, or even fully, and not to be able to
explain.

The real test if understanding is the ability to use the material in
new situations. This cannot be explained, but merely presented, and
hopefully evoked. Ask a good writer how thoughts are put into words,
and a useful answer will not result. Teachers fool themselves when
they claim to be teaching writing; mechanics and some criticism can
be taught, but that does not help getting the thoughts onto the paper.

A mathematician can prove theorems, but cannot explain how the proofs
are found. When an artist tries to just daub, it still comes out
looking artistic.

At the time of Gauss, one could come close to explaining what a full
proof was, but not quite. A century later, it could be taught in the
schools. This can be very helpful in learning how to prove theorems,
as it does allow mechanical checking of a formal proof, rarely done.
When my son learned how to find proofs himself, he could not have
explained even the checking process to anyone; he just knew it.

Also, being able to explain something to someone might depend on the
learner being receptive. Often this reduces to the problem of being
able to unlearn; it is better not to be in this position. It seems
that about half of the children taught to read by the whole word
method never could learn to decode words not taught in this manner.

--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558

Date Subject Author
2/1/97 neubert@mentor.cup.edu
2/1/97 catherine
2/1/97 Marc Whitaker
2/4/97 kristin michelle snyder
2/4/97 Marc Whitaker
2/4/97 David Hole
2/5/97 W.P. Fleischmann
2/6/97 tom dean
2/10/97 Lynne
2/10/97 David M. Childers
2/13/97 catherine
2/13/97 Marc
2/15/97 Donna Mettler
2/15/97 C. Graham
2/15/97 mikevano@ix.netcom.com
2/16/97 RW
2/18/97 Bellew Family
2/18/97 Marc
2/23/97 Ken Laha
2/23/97 Herman Rubin
2/23/97 Gmlyle@scvnet.com
2/26/97 andrewto
2/27/97 George Huczek
7/19/99 Sabrina
2/27/97 catherine
2/16/97 Herman Rubin
2/22/97 ne@nb.net
2/22/97 Herman Rubin
2/22/97 ne@nb.net
2/22/97 David L. Hanson
2/23/97 Frank A. Bouchard
2/22/97 Herman Rubin
2/25/97 Robert Bacal
2/27/97 Herman Rubin
2/27/97 Rich Washabaugh
2/27/97 mikevano@ix.netcom.com
2/28/97 Brian M. Scott
3/3/97 mikevano@ix.netcom.com
3/4/97 Brian M. Scott
3/4/97 garscosi@pipeline.com
3/1/97 Philip Cain
3/1/97 Robert Bacal
3/4/97 Albert Yang
3/4/97 Robert Bacal
3/6/97 Herman Rubin
3/8/97 Robert Bacal
3/13/97 Brian M. Scott
3/13/97 sockeye
3/14/97 Albert Yang
3/4/97 Rich Washabaugh
2/22/97 garscosi@pipeline.com
3/3/97 Melvin Billik
3/8/97 catherine
2/13/97 nospam@geocities.com
2/15/97 Herman Rubin
2/18/97 catherine
2/13/97 Herman Rubin
2/14/97 TRM
2/19/97 LOOKER
2/19/97 Marc
2/20/97 catherine
2/20/97 catherine
2/21/97 Rod Beaumont
2/4/97 Carri Mueller
2/4/97 nospam@geocities.com
2/4/97 Herman Rubin
2/4/97 jodee foell
2/8/97 gino crocetti
2/8/97 Chris
5/12/10 David D. Sullivan
2/9/97 Rogan
2/9/97 nskrenes
2/9/97 Carolyn Jean Fairman
2/10/97 horvath
2/11/97 Nicole Budiselich
2/11/97 Marc Whitaker
2/12/97 sara lehman
2/12/97 Marc
2/12/97 nospam@geocities.com
2/15/97 Michael D. Neller
2/12/97 Herman Rubin
2/12/97 Shannon M. Seigfried
2/7/97 Fred W. Bach, TRIUMF Operations
2/16/97 hdbiker@mhtc.net