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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: May 1, 2004 5:45 AM

On 01 May 2004 00:28:02 GMT, Anonymous wrote:

>Ullrich:
>

>>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.

>
>Right. But I still think it's possible to know the definition of something
>*without* being able to state or explain the definition clearly.

I've already acknowledged this, at least twice, in reference to
your garbled attempt at a definition of "independent". If we're
talking about being able to prove things (which by the way
_is_ what we're talking about) then this sort of understanding
is useless - to be able to give a coherent proof of something
involving independence you need to be able to state things
clearly.

continue to insist that the advice people are giving is
wrong. You wanted to know why you're flunking linear
algebra. Several people conjectured is was because you
simply don't know the material, probably starting with
the definitions. When you gave a "definition" of
"independent" that _confirmed_ people's conjectures
about the fact that you simply don't know the definitions.

If you had any sense you'd stop insisting that you do
know the definitions in some sense, and instead
simply go back and _learn_ the definitions, in the
sense that's _required_. ("Required" in the sense
that it's necessary in order to succeed in what you're
trying to do, whether or not explicitly required by
the instructor.) Because the advice you've been
given by many people is _correct_, whether you
believe it or not. (The advice has been essentially
unanimous - essentially nobody disputed the fact
that you needed to know the definitions precisely,
the quibbles were over whether you should memorize
them by rote or learn them through using them.
When you showed us your incoherent version of
the definition of "independent" people stopped

You're reminding me of the student who asked
me yesterday for help getting some graphics
from Mathematica into Word. I had a plan for
how to do that. It took a little while because
instead of doing what I suggested first he wanted
to try this and then try that - I really didn't understand
why he wasn't willing to just try what I wanted to
suggest, given that the things he'd been trying
had not been giving satisfactory results, and he'd
asked me to help. When I finally got him to try
the things I wanted to try it worked out just fine.

>For example,
>the word "the". We all know what it means and when it can and can't be used.
>But, can any of us actually define it? Probably not. In fact, I'd be willing
>to argue that we actually understand things *better* when we know what they're
>used for and how to use them, and we can do that without defining them.

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

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