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

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 David C. Ullrich Posts: 21,553 Registered: 12/6/04
Re: Failing Linear Algebra:
Posted: May 10, 2004 5:24 PM

On Mon, 10 May 2004 16:44:17 +0000 (UTC), Marc Olschok
<sa796ol@l1-hrz.uni-duisburg.de> wrote:

>David C. Ullrich <ullrich@math.okstate.edu> wrote:
>>[...]
>> (i) the ability to engage in precise reasoning is very important.
>> (ii) the ability to memorize definitions is relatively unimportant.
>> (iii) someone whose notion of a certain definition is as above
>> will not be able to engage in precise reasoning.
>>
>> Those three statements seem mutually inconsistent.

>
>As far as I have understood from following this thread, James' main
>point was, that (iii) is compatible with (ii). While it is certainly
>useful to have the precise definitions available _in_memory_ the
>actual prerequisite from (iii) is, that they are available _at_all_.
>
>In fact, in my opinion the initial problems of the OP arose, because
>after having read the text and memorizing some item in a distorted
>version, he _never_again_ consulted the original texts with the definitions
>to check what had sunk in his memory.
>
>So in a nutshell: it is nice to have it in memory but if not, one should
>face it and grab for the reference again.
>
>I admit that it must be painfull to look up the definition of a vector space
>more than once or twice. But after tackling a couple of problems and
>exercises and after having looked it up and used it e.g. 5 or 6 times,
>it sinks into memory. This is far better than trying to memorize in
>isolation before one starts to tackle any problems.

Oh. Well all that's perfectly reasonable. As I think I've said at
least once, "the problem" is that "they" don't believe that they
need to _know_ the definitions (or what amounts to the same
thing, they think they know the definitions when they're able
to give garbled versions like the one a few posts up.)

>Marc

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

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