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

 Messages: [ Previous | Next ]
 Dave Rusin Posts: 3,118 Registered: 12/6/04
Re: Failing Linear Algebra:
Posted: Apr 28, 2004 1:02 PM

Several of us have argued that a good measure of a student's progress
in Linear Algebra is his or her ability to define things accurately.

Others have responded that memorization per se is useless, that
strict memorization is unnecessary, or that learning the definitions
is not getting at the heart of the subject; and I agree that, taken by
themselves, these statements are correct. Still, I hold to the stance
in my first paragraph because, for the average student at my institution,
memorizing the definitions is the way to begin this course.

Anonymous wrote:

>>>> So you can do a little self-assessment here to figure out whether
>>>> what you're missing is bits of topics or the core idea: can you,
>>>> right this minute, define what a vector space is?

>>
>>> Hopefully not just as a one-to-one rendition of phrases from a
>>> textbook...

>>
>> 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.

>
> Let me try that one...independence means a group of vectors (in
> homogenous form???) such that if they all equal the zero vector, then
> the only possible way for that is the each coefficient of every vector
> has to equal 0 too.

OK, now, jdolan and others who pooh-poohed the idea of memorizing
definitions: what say you to this student? Seems to me he has
made my point for me ...

dave

PS -- This student's definition is no worse than the average that I
would get here from a student preparing for our final exam. Not
surprisingly, there are not many A's and B's when I give semester grades.

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