On Thu, Oct 7, 2010 at 12:43 PM, Jonathan Groves <JGroves@kaplan.edu> wrote: > Wayne, > > So any form of inquiry-based learning is not honest? Just because some > teachers botch it by either taking it way too far or using it > inappropriately or otherwise not using such learning techniques skillfully > proves that inquiry-based learning does not work, that such learning must > be fake? If we do try to teach inquiry-based learning without guiding > students or insisting that they discover ideas or mathematical or scientific > truths way beyond their level, then we do not go anywhere. And unfortunately > I have seen others distort what discovery learning means by appealing to > textbooks that take this approach or perhaps appealing to something else.
Whereas Wayne was coming off as more ignorant than he really is, about Dr. Sage -- how poetic, to be having that name for a token constructivist -- I'm coming off (above) as more knowing than I really am (putting a bold face on my ignorance).
Although I've read some constructivism, I'm no Piaget expert. I'm more familiar with that guy who studied imprinting in geese, as a geek I looked up to (Charlie Thomforde) went and worked with that guy in Switzerland or someplace. No, not Pavlov. Then I've looked into Caleb Gattegno some. In physics, it's Karplus.
And then my story picks up with *constructionists* (note spelling difference), as Seymour Papert (Logo) and fellow travelers (Alan Kay) weren't necessarily wanting to share the same brand, even if still Euro-centric in a lot of ways (more of an East Coast thing maybe, a difference twixt Boston / Cambridge and Portland: fewer Yanks out here, not as WASPy, more Chinesey).
So when Wayne talks about "inquiry based learning", I really have not that much of a clue (I haven't been waging Math Wars in California for the last half-century).
I didn't attend much of K-12 here in the USA. Just K-2, first have of 9th, and that's pretty much it. Which is why I'm always hearkening back to those international schools in my writing, aiming to catch diplomats-to-be before they lose any ability to remain cosmopolitan in their thinking, descend into some parochial soap opera, some Scopes Trial (at the St. Sensible where I taught, in Jersey City, they all watched General Hospital -- an OK place to start, when teaching World History, which was also on my plate (not just Geometry thru Calculus)).
Coming from my GNU Math angle, I just begin with the premise (conclusion) that these older text books are just grist for the mill, raw material, check-outable from libraries.
But in having no computer programming, not even pseudo-code (unless you go back to the 1980s, where we had a quick flirt with a Math Makeover - -- me at McGraw-Hill at the time), I just have to throw up my hands and say "wait a minute, this can't be pre-college material!"
The college profs disagree, by and large, because they know what they get away with, and it ain't just computer science. But then I never said "just computer science". I dare any math teacher to say the RSA public key crypto algorithm is devoid of real (as in pure) math. And if you accept that it's real math, and within range, then why make "physics based calculus" your only "royal road"?
I'm suggesting a minimum of two mainstream pipelines, and many a design pattern would show that to be wise, competition against monopoly, a tug against complacency. For this reason, we need to lay track for a spanking new Digital Math right alongside the old Analog Math (precalc and calc).
That's really not so far-fetched. I simply assume it's what the international schools will be doing. I think of Phillips / Andover as 2nd tier but closer to prototypical.
Now I'm back to sounding like I know a lot. But hey, I never went to ed school... No wait, I did: St. Peter's College in Jersey City, Dr. Caulfield a good teacher and the guy who placed me at the academy. Only a few courses there, before I got the full time position.
The way it was taught at St. Peter's was very philosophical, so I felt right at home. What was more noticeable was how so many math teachers were running the other way, trying to get out of school teaching and into IT jobs. I'd had a lot of computer science at Princeton, but wanted to teach high school. Seemed kinda backwards.
But then I got into IT work later, think going back and forth is actually an OK way to go. But it's all very discrete, so that even though I get to work with the AAPT folks, Dr. Bob Fuller in particular, I'm always chawing at biochemisty, talking about the IT-like nature of the "central dogma" (about DNA/RNA).
Digital Math doesn't entirely eschew Calculus, but if you don't wanna spend hours learning Integration by Parts, we understand. That may not be your chosen profession, plus Mathematica will do it for you.