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

 Messages: [ Previous | Next ]
 David C. Ullrich Posts: 21,553 Registered: 12/6/04
Re: Failing Linear Algebra:
Posted: Apr 29, 2004 7:39 AM

On 28 Apr 2004 17:02:40 GMT, rusin@vesuvius.math.niu.edu (Dave Rusin)
wrote:

>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.

Precisely. This may be a reasonable place to say something that
I've been meaning to say in all this:

Some of us are saying that memorizing the definitions by rote
is stupid, instead the student should learn the definitions by
using them, the way we do when we learn a new topic. This
is missing the point: _regardless_ of _how_ one learns those
definitions, "we" all agree that one _does_ need to _know_
the definitions eventually in order to be able to do the
things one is supposed to be able to do. The problem is
that the students _don't_ believe that they need to know
the definitions.

(It could even be that they would agree that "I need to
know the definitions" is true, but it doesn't follow that
they actually believe they need to _know_ the definitions,
because, as we've seen here, their definition of "know

>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.

************************

David C. Ullrich

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