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Topic: Failing Linear Algebra:
Replies: 91   Last Post: Jan 10, 2007 12:56 PM

 Messages: [ Previous | Next ]
 Marc Olschok Posts: 409 Registered: 12/6/04
Re: Failing Linear Algebra:
Posted: Apr 24, 2004 2:10 PM

Daniel Grubb <grubb@lola.math.niu.edu> wrote:
>
>>> No, for proof classes, which linear algebra is in many places,
>>> it is crucial to *memorize* the definitions. This holds for
>>> all the proof classes at higher levels also. There is simply no
>>> way of giving rigorous proofs if you don't know the actual
>>> definitions. All too often, students have some very vague ideas
>>> of what is going on and then can't even get started on a proof
>>> because they don't know the *exact* definiton used in the course.

>
>>No disagreement here. Perhaps Thomas only meant to warn against
>>blind memorization without understanding. This way a student would
>>end up with the ability to repeat the memorized definition but
>>nothing else. This danger is even greater, when those definitions
>>are memorized as isolated entities, without checking them against
>>examplex, counterexamples and proofs.

>
> I agree. After you have those definitions memorized, you have to
> get understanding of those definitions through theorems and examples,
> which show unforseen consequences of those definitions.

Actually, (simple) examples and theorems already help in the process
of learning the definitions. Of course a student needs to be willing
to look up the definitions in the text while going through these
examples.

The analogy with learning a foreign language has already been stressed:
although it is desirable that the vocabulary eventually "sinks in",
you would use new words in simple sentences early on in order to
foster memorization.

Marc

Date Subject Author
4/24/04 Daniel Grubb
4/24/04 Marc Olschok
4/24/04 Daniel Grubb
4/24/04 Marc Olschok
4/24/04 Daniel Grubb
4/24/04 Thomas Nordhaus
4/24/04 Dave Rusin
4/25/04 Jonathan Miller
4/25/04 Felix Goldberg
4/24/04 Daniel Grubb
4/28/04 Tim Mellor
4/28/04 James Dolan
4/28/04 Daniel Grubb
4/28/04 James Dolan
4/28/04 Daniel Grubb
4/28/04 gersh@bialer.com
4/29/04 Daniel Grubb
4/29/04 Dave Rusin
4/28/04 Guest
4/29/04 Guest
4/28/04 Guest
1/10/07 David C. Ullrich
4/29/04 Dave Rusin
4/28/04 Guest
1/10/07 Law Hiu Chung
1/10/07 Dave Seaman
1/10/07 Marc Olschok
1/10/07 George Cox
4/28/04 Guest
1/10/07 Dave Rusin
4/28/04 Lee Rudolph
4/28/04 Guest
4/28/04 Guest
1/10/07 Marc Olschok
1/10/07 Toni Lassila
4/29/04 Guest
1/10/07 M L
1/10/07 Thomas Nordhaus
4/30/04 Guest
1/10/07 David C. Ullrich
1/10/07 Toni Lassila
4/30/04 Guest
1/10/07 George Cox
1/10/07 Marc Olschok
4/30/04 Guest
4/30/04 Guest
4/27/04 Guest
1/10/07 Thomas Nordhaus
1/10/07 David C. Ullrich
1/10/07 Dave Rusin
1/10/07 David C. Ullrich
5/9/04 James Dolan
5/10/04 David C. Ullrich
5/10/04 James Dolan
5/10/04 David C. Ullrich
5/10/04 Marc Olschok
5/10/04 David C. Ullrich
4/27/04 Guest
1/10/07 Thomas Nordhaus
4/27/04 Guest
1/10/07 magidin@math.berkeley.edu
1/10/07 David C. Ullrich
1/10/07 Marc Olschok
1/10/07 David C. Ullrich
1/10/07 Tim Mellor
4/28/04 Daniel Grubb
4/28/04 Daniel Grubb
4/27/04 Guest
1/10/07 David C. Ullrich
4/28/04 Dave Rusin
4/28/04 Daniel Grubb
4/27/04 Guest
1/10/07 Marc Olschok
4/24/04 Wayne Brown
4/24/04 Thomas Nordhaus
4/24/04 David Ames