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.
Now, in article <email@example.com>, 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 ...
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.