Just to clear something up, it is not my contention that everyone that is successful at arithmetic is successful at algebra. My contention is, and what my analysis of millions of exams proved, is that everyone successful at algebra is successful at arithmetic.
On Nov 4, 2012, at 4:54 PM, Louis Talman <firstname.lastname@example.org> wrote:
> > > On Sat, Nov 3, 2012 at 10:57 PM, Wayne Bishop <email@example.com> 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 > > <http://rowdy.mscd.edu/%7Etalmanl>