in article <email@example.com>, dave rusin <firstname.lastname@example.org> 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.
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.