On 28 Apr 2004 17:02:40 GMT, email@example.com (Dave Rusin) wrote:
>Several of us have argued that a good measure of a student's progress >in Linear Algebra is his or her ability to define things accurately. > >Others have responded that memorization per se is useless, that >strict memorization is unnecessary, or that learning the definitions >is not getting at the heart of the subject; and I agree that, taken by >themselves, these statements are correct. Still, I hold to the stance >in my first paragraph because, for the average student at my institution, >memorizing the definitions is the way to begin this course.
Precisely. This may be a reasonable place to say something that I've been meaning to say in all this:
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. The problem is that the students _don't_ believe that they need to know the definitions.
(It could even be that they would agree that "I need to know the definitions" is true, but it doesn't follow that they actually believe they need to _know_ the definitions, because, as we've seen here, their definition of "know the definitions" is totally inadequate.)
>Now, in article <firstname.lastname@example.org>, >Anonymous wrote: > >>>>> So you can do a little self-assessment here to figure out whether >>>>> what you're missing is bits of topics or the core idea: can you, >>>>> right this minute, define what a vector space is? >>> >>>> Hopefully not just as a one-to-one rendition of phrases from a >>>> textbook... >>> >>> 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 ... > >dave > >PS -- This student's definition is no worse than the average that I >would get here from a student preparing for our final exam. Not >surprisingly, there are not many A's and B's when I give semester grades.