On Sat, Nov 3, 2012 at 10:57 PM, Wayne Bishop <firstname.lastname@example.org>wrote:
> At 11:06 PM 11/1/2012, Louis Talman wrote: > > Those who succeed in mathematics today generally did well at arithmetic >> as kids. But when I grew up, great numbers of children did well at >> arithmetic. They had to, because calculators didn't exist. Very few of >> those people succeeded at algebra, let alone mathematics. There is a >> serious disconnect here. >> > > Are you sure of that? That's not the experience I had in my small-town > Iowa high school. My recollection is that everybody took it (Algebra I, I > mean) as freshman and most of the students were at least borderline > successful. It was proof-based geometry in the sophomore year where lots > of students, including college-intending students, "hit the wall".
Quite sure. My high school was fed by two junior highs. There were two ninth-grade first-year algebra sections (and none for eighth-grade) in my junior high school, and the other was about the same size. The high school didn't offer that course.
There were just two sections of tenth-grade geometry in high school.
There was considerable attrition between ninth grade and my senior year. Only 121 were graduated. Of those, only 15 took trigonometry--the highest level of mathematics the school offered.
> > > And the ancient Greeks---who invented modern mathematics---are certainly >> a counterexample to your "natural progression". They accomplished a great >> deal without beginning with the algorithms we ask kids to study today. >> Indeed, it's likely that they weren't very good at arithmetic at all. So >> their "progression", if there was such a thing, was entirely different from >> the one you think you've identified. >> > > And what percentage of the general population ancient Greeks are you > talking about here? I do believe that select subset would eat modern > mathematics for lunch but the ancient Greek equivalent of an ordinary > engineering student at your campus? >
The percentage was high enough to support the famous line above the door to Plato's academy.
> > This last example suggests very strongly that arithmetic, while it may be >> *an* entry into mathematics, is not the *only* entry. Your "natural >> progression" completely ignores a significant possibility: The primacy of >> arithmetic is simply an artifact of a curriculum that denies entry to those >> who haven't acquired proficiency at arithmetic. (A curriculum, moreover, >> that's now strongly distorted by the effects of fifty years of >> standardized, multiple-guess, truth-or-consequences, mis-matching tests.) >> > > One of my old favorites for denying reality: Need improvement? Change > the curriculum and pedagogy. Need to prove that you have achieved your > goal? Change the assessments. >
That's hardly relevant to the points I raised. Especially in view of the fact that the assessments have changed the curriculum.
> > My old mandate remains appropriate, "Dance with the guy what brung ya." > > On the other hand, what's sauce for the goose is sauce for the gander.
-- --Louis A. Talman Department of Mathematical and Computer Sciences Metropolitan State College of Denver