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

 Messages: [ Previous | Next ]
 Thomas Nordhaus Posts: 433 Registered: 12/13/04
Re: Failing Linear Algebra:
Posted: Apr 24, 2004 11:02 AM

grubb@lola.math.niu.edu (Daniel Grubb) schrieb:

>
>>When I'm not sure, I go back to my book and look it up (Happened
>>recently, when I wasn't sure what the exact definition of a refinement
>>is (in the context of paracompact top. spaces)). You forget, of
>>course, unless you solve problems or apply in a regular way.

>
>Yes, we all forget things over time. But if you are taking a course
>in topology that covers paracompactness, I would certainly hope
>you have the definition of 'refinement' memorized (by whatever
>method) come time for the exam. Or even time to read the next theorem.
>If you don't, the definition of paracompactness will be very hard to
>understand.

textbook, looked through the section on partition of unity and so on.
I wouldn't have time in an exam, so I would have missed the points. In
an examination situation the material would have been a lot closer,
timewise, and I could have reconstructed the definition by reflecting
on the problems that I solved before. Like: "What has to be subset of
what?... Ah, of course!"

Ok, this may not be practical sound advice. If the exam is just
designed for the students to dump factual knowledge in contrast to
solving problems you'll have to memorize because of the sheer
quantity. You have to become a "definition robot". Like - (maybe)
medical doctors, who'll have to recite all the bones in the human body
in alphabetical order.

>
>>>The student should be able to give a rendition that is at least
>>>equivalent to the one given in the book and that uses precise language.

>
>>Absolutely right. But it should go above Parroting, that's what I
>>meant.

>
>Of course it should. But I am lucky to get anything close to an
>equivalent statement of the definition from my students. Simply
>getting them to understand the difference between 'if...then'
>and 'and' has been a struggle.

Hmm, maybe the student should have a minimum amount of talent, maybe
it is as simple as that?

Thomas

>
>--Dan Grubb

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