
Re: Failing Linear Algebra:
Posted:
May 10, 2004 12:07 PM


On Mon, 10 May 2004 15:56:10 +0000 (UTC), jdolan@mathrsn03.math.ucr.edu (James Dolan) wrote:
>in article <rsku90pc4s1omkhee2sd1vdpt17eicehut@4ax.com>, >david c. ullrich <ullrich@math.okstate.edu> wrote: > >On Sun, 9 May 2004 20:43:01 +0000 (UTC), >jdolan@mathcln01.math.ucr.edu (James Dolan) wrote: > >>in article <c6oo3g$nd0$1@news.math.niu.edu>, >>dave rusin <rusin@vesuvius.math.niu.edu> wrote: >> >>>> 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 poohpoohed the idea of memorizing >>definitions: what say you to this student? Seems to me he has >>made my point for me ... >> >> >>hi dave. i've been too busy to keep up with this thread lately, but i >>happened to glance at the new "linear algebra definitions" thread that >>the student in question started a couple of days ago, and it looks >>like he has unmade your point for you. >> >>anyway, i think it does students a great disservice to conflate the >>very important ability to engage in precise reasoning with the >>completely unimportant ability to memorize definitions. > >And you _really_ think that if he's saying things like "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" he's >going to be able to engage in precise reasoning about independence? > >presumably if i thought that then i would have said something remotely >like it. i'll take the fact that you're spewing nonsense like this >now as your concession that you've lost the argument.
Uh, you don't seem to be making much sense  from your last two posts it appears that you agree that each of the following statements is correct:
(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.
I imagine I'm missing something. Which part of what you've said am I misinterpreting?
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David C. Ullrich

