Path: utzoo!utgpu!watmath!clyde!att!osu-cis!tut.cis.ohio-state.edu!rutgers!mit-eddie!killer!elg From: elg@killer.DALLAS.TX.US (Eric Green) Newsgroups: comp.edu Subject: Re: Student preparedness Message-ID: <6579@killer.DALLAS.TX.US> Date: 29 Dec 88 05:27:31 GMT References: <2141@faline.bellcore.com> Organization: The Unix(R) Connection, Dallas, Texas Lines: 64 in article <2141@faline.bellcore.com>, dph@faline.bellcore.com (Daniel P. Heyman) says: >> In article <1077@l.cc.purdue.edu> cik@l.cc.purdue.edu (Herman Rubin) writes: >> > >> >Teaching means presenting the WHY, not the HOW. It is very difficult to teach >> >the why to students who are not research caliber who already know the how. > The results were about the same. My theory is that students got > used to taking notes, got good grades by doing so, and won't change > something they don't regard as broke. Another aspect is: copying is > easy, thinking about what's going on is hard, and one takes the path > of least resistance. More probably, the students didn't trust the instructor to keep to his word (about the "why" part, that is). The majority of instructors at the freshman and sophomore levels in college give tests that are basically fancy games of Trivial Pursuit. If you understand the principles, but don't memorize the correct trivia (equations, etc.), you don't get the grade. So students get in the habit of taking notes, basically an aid for memorizing the trivia. Even when you give out lecture notes, they'll still scribble in their notebook... after all, they're not doing it for informational purposes, they're doing it as a method of rote memorization of trivia. It has nothing to do with whether or not the student wants to think about the subject matter of the course. In practice, I've found that the people who DON'T think about the subject matter get lousy grades no matter what they do on the memorization front (because they don't have a framework for applying their aquired trivia). On the other hand, the converse sometimes occurs... people not memorizing the right trivia for an exam, and getting lousy grades... which is why many students are fanatical about memorizing trivia, because it seems to be the only way to make a good grade in college (maybe Mr. Rubin et. al. dispute that, but possibly that's because they're rather exceptional individuals... some people remember important trivia rather easily, without making any heroic efforts, but most don't). > My way of taking notes was to write down the theorem and key steps > in the proof, with comments on the why of certain steps. For homework > I would fill in the manipulations; I usually felt that I understood > the proof because I did it myself with hints from class. Looking back at my college career, I have a number of regrets, a major one among them that I never did reach critical mass in mathematics. It was always a rather difficult subject for me, mostly because for the most part I was thrashing about in murky waters with no idea of the relevance of what was on the test to mathematics as a whole. I wish I'd had a class that dealt with the fundamentals of mathematics, with the "why" of how the whole thing works... a possible format would be as a sort of "math history" course, about how the various branches of modern mathematics came into existence, e.g. how XYZ was trying to solve ABC problems mathematically and came up with branch I of mathematics, by saying "gee, what if I did this?"... Again, it's Mr. Rubin's "why" vs "how" dichotomy. Such a course would concentrate on principles, and in future courses you'd cover the "how" of various branches in depth. Instead, the first course the typical college student takes is Algebra (for non-engineers) or Calculus (for engineers), both of which are almost entirely "how" oriented, concentrating upon the mechanical manipulation of symbols with little attention to the "why". -- Eric Lee Green ..!{ames,decwrl,mit-eddie,osu-cis}!killer!elg Snail Mail P.O. Box 92191 Lafayette, LA 70509 Netter A: In Hell they run VMS. Netter B: No. In Hell, they run MS-DOS. And you only get 256k.