On Sun, 9 May 2004 20:43:01 +0000 (UTC), email@example.com (James Dolan) wrote:
>in article <firstname.lastname@example.org>, >dave rusin <email@example.com> 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 pooh-poohed 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?
(Where the definition of "engage in precise reasoning" of course includes the ability to _express_ one's precise reasoning in a way that can be unambiguously interpreted by others.)
>i think another problem in this thread is the conflation of the >question of what are good strategies for students and teachers to use >in a reasonable learning and teaching environment with the question of >what are allegedly tolerable survival strategies for dealing with the >typical u.s. college or university environment.