Comments on: And then, on sixth down, the Eagles gained 4 yards

By: billy-jay

billy-jay — Sun, 29 May 2005 09:30:13 +0000

The situation stipulated in the problem could be an actual case if penalties weren't included (and they wouldn't be, if the object was to compile stats on the offense).

That in no way negates your points, though, which are spot on. (Spot on? Maybe I've been reading too much Billy Beck.)

Rock on,

Bill

By: Curt

Curt — Sat, 28 May 2005 18:42:06 +0000

I don’t dispute your premise that instruction should be more problem-oriented but I do question your assertion that: “No matter which branch of mathematics we look at, from the purely theoretical to the applied, the mathematicians or scientists working in that branch are, fundamentally, taking what they know and trying to synthesize it in some original and creative way to produce some new theorem or formula that better describes the situation.” I don’t think that that’s true in large swaths of engineering or science, let alone more remidal uses of math like accounting, where it seems to me that I lot of the work does consist of plugging in formulas. I’m not really sure if you are criticizing university math departments or middle- and high schools, but if the former the standarized-test example doesn’t seem particularly apposite, and if the later I’m not sure if the point of those classes is, or need be, to teach people to think like mathematicians.

By: Curt

Curt — Sat, 28 May 2005 17:17:58 +0000

But isn’t that, i.e. university classes, pretty much by definition then (or at least the way you’ve defined it) different in kind from the situation facing middle and high school teachers who are dealing with students who don’t necessarily have any common ground or interests?

By: shonk

shonk — Fri, 27 May 2005 05:36:17 +0000

Nevertheless, one would have to interpret “actual, conceivable problems that might arise in the student’s experience” pretty loosely to include (correct me if I’m wrong) what I imagine to be the bulk of problem-solving in university mathematics departments.

Well, maybe I should have said "actual, conceivable problems" without the qualifier to include those liberal arts majors taking Calc. I. Aside from that particular case, though, most students taking university math classes are either math majors or people that will (or at least could) use math in their fields (engineers, pre-med students, students in the hard sciences, etc.), so my stipulation isn't entirely unreasonable.

By: Curt

Curt — Thu, 26 May 2005 09:16:46 +0000

By: Andy Stedman

Andy Stedman — Wed, 25 May 2005 20:32:03 +0000

Semi-off-topic comment: I took a course on probability and statistics in college, and the texbook writer definitely had a well-developed sense of the macabre, which made its way into his story problems:

“A bus crash kills, on average, 32% of the occupants…” “A disease, which kills on average 10% of those who contract it…” “An ax-murderer picks houses at random from a phone book…”

(okay, I made up the examples as the book isn’t in front of me, but I’m not far off.)