
Re: Failing Linear Algebra:
Posted:
Apr 28, 2004 8:33 AM


On Tue, 27 Apr 2004 22:41:50 +0000 (UTC), magidin@math.berkeley.edu (Arturo Magidin) wrote:
>In article <20040427182710.15274.00000430@mbm18.aol.com>, >Anonymous wrote: >>David: >> >>>Actually from what you say here it seems pretty likely that >>>you do know what linear independence _is_, but the >>>way you're stating the definition is totally wrong. >> >>Right. That's my point. I *do* know the definition, but the phrasing always >>gets me. > >That tells me that you do not really "know" the definition. You >>think< you know it, you >think< you understand it, but you >actually do not. If you did, the phrasing would not be a problem.
Or, as seems quite possible from the definition he gave, he does understand what independence means, but he doesn't understand how to state things coherently. (Which of course is equally fatal  one of many reasons for memorizing these definitions vergatim is to give us a stock of examples to use in learning _how_ to say _exactly_ what we mean.)
>> It's like this, probably, for a bunch of the main terms. Still, you >>say the number one problem is that students don't understand all the >>definitions. Is my understanding of "independence" then not good enough? Or >>is it? > >If your understanding is not sufficient to lead you to a coherent and >correct statement of the term, then it is not good enough. Unless you >can state coherently and correctly what the definition is, then it >will cause you problems when you try to use it.
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David C. Ullrich

