>In article <firstname.lastname@example.org>, Thomas >Nordhaus <email@example.com> wrote: > >> firstname.lastname@example.org (Dave Rusin) schrieb: >> >> >a significant role. They often stumble because (among other problems) >> >they don't realize they need to _memorize_ definitions _precisely_. >> >> Memorize? I can't remember ever memorizing anything. Better just to >> practice until you understand. Discuss, ask questions, apply. That way >> you memorize, of course, but that's just a side-effect. >> > >It's nice to think that all the students are going to go home and >follow your advice and "discuss, ask questions, apply", but they're >not. Most will not, even the better ones. > >Failing a class sucks. Dave's advice to memorize the definitions >precisely is good, because a large part of the points for a beginning >linear algebra course is based on reciting the definitions. The way >the typical service course is rigged is to weed out the people who >can't memorize or do the rote computation.
OK. My comment came from my own experience during my study (70s, Germany, 80s USA). The situation then / there was probably very much different from the situation you're talking about. The time was anti-authoritative. We were protesting and boycotting all the time (or so I seem to remember). Professors wore long hair and were members of exotic communist parties. It was *very* liberal. We hadn't any exams (had to do assignments of course). Classes were small...
Later at graduate school in USA, work was very hard. You could barely finish the assignments, had to teach Calculus-courses and such things. But you could simply not do it by way of memorizing. You just had to solve problems and apply theory all the time. So memorizing came just along the way.
Fact is, that I (fortunately) never *had* to study by way of memorizing, "cramming".
> >We're talking about someone who probably doesn't even remember enough >to discuss anything about vector spaces. You may not have ever >memorized a definition (seems remarkable, but possible),