>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".
>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?
>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.
My old mandate remains appropriate, "Dance with the guy what brung ya."