I think it's worth looking over the shoulders of computer science professors, when it comes to tracking the Math Wars. They have their own perspective, of course. I encourage posters here to poke around, get familiar.
Maria Droujkova is a role model in this respect (when it comes to poking around on many lists), as her Math 2.0 website indeed works at pulling a lot of these threads together, including looking at the future role of computers, which hardly anyone is doing on math-teach besides me (take the bait anyone?).
If you dig further into February and March on this math-thinking-l, you'll see they're squabbling about whether to use functional or imperative paradigms (or do we call these "paradigms"?), a debate that goes completely over the heads of most laymen, yet creates the appearance of a logjam that may scare away funders.
I allude to this debate in speaking of Great Lambda worshipers (part of our cyber-space geography might be to identify their holiest web sites). Python's "little lambda" borrows from the LISP / Scheme family but was little more than a twinkle in Guido's eye (hence "little lambda").
I've blogged more about this logjam, trying to get more philosophers to serve as referees:
I realize we're not used to philosophers having much of a constructive role in the Math Wars, so this attempt to recruit a few sounds rather off beat and alien. Putting these debates on the shoulders of politicians and bureaucrats makes even less sense however. We need more polymaths to weigh in, pronto.
On this list (math-teach), GS comes off as a philosopher, being into management theory. In fact, lots of manager-engineers are also philosophers, either in or out of the closet as such. Terry Bristol, president of ISEPP (that Linus Pauling House group I mention) is out of the closet as a philosopher, as are Glenn and myself.
That doesn't put us all on the same page, but at least we're willing to read outside any one specialized area -- very important if wanting to venture into policy-making.
"Read widely or perish" might be the better enjoinder than "publish or perish", although when you post to the Internet, that's an opportunity to show you've been doing some homework, reading outside just one narrow field.
On Tue, Mar 16, 2010 at 12:33 PM, David Gries <dgries at twcny.rr.com> wrote:
<< snip >>
> Any high-school or college level course that teaches recursive functions should be teaching such a model of execution. However, knowing how to execute a function call is entirely different from knowing how to understand (prove correct) a function based on its specification; the latter is really dependent on mathematical induction. > > David Gries > gries at cs.cornell.edu >
Mathematics versus Computer Science =============================
This is somewhat encouraging to read, as Gary is pointing to a K-12 math standards site, no mention of CS anywhere I don't think. The governors don't care about CS that much, an elective in high school, not a requirement.
What's encouraging is that a CS specialist would still look for (and maybe find) a toe hold in K-12.
Standards Crafting in Oregon =====================
Is Oregon's governor consulting with our Linus Pauling House group regarding where math teaching might go? Terry organized a Math Summit for the whole state in 1997, featuring Sir Roger Penrose, Keith Devlin and several other luminaries.
I was a workshop leader and mic runner, wrote up the event, made the ideas public.
Ever since then, I've been traveling around the world (OK, a couple trips), thanks to sponsors (Swedish), touting something more up to date and technologically informed (something more like the Litvins text, though I've not been especially anti the Great Lambda worshipers (Python has "little lambda")).
Goals for Computational Math ======================
Any computer programming at all would be a big step in the right direction, as it means freedom to use more powerful technology in a math class setting, getting free from just calculators (still the norm in most venues). We need a mathematics for the digital age, call it discrete, call it computational, call it whatever you like. We needed it 10 years ago.
The use of GIS (geographic information systems) to spread information relevant to policy-making (a fond goal of Ecotrust, one of our flagship NGOs) is more likely in proportion to getting students used to working with the likes of Google Earth.
If you're used to flying over zip codes, picking up characteristic statistics, you're going to be a whole lot more effective in public debates, won't just be a "mindless voter" who hits a lever every six months or so (very not participatory, that image of democracy).
Geometry and geography should be intimately conjoined, as one of the deepest criticisms leveled at USA kids especially is they have no concept of where things are or of what the world looks like. This extends to lack of knowledge of one's own city and how to get around.
Math class should help with this, shedding the stereotype about never being about the real world.
The Oregon Curriculum Network has been on-line for well over a decade, providing plenty of free resources to both charter and home schools (all public and private schools have a charter of some kind, so I tend to lump them as such).
We've also been tapped by Saturday Academy to offer what Silicon Foresters consider cutting edge math. Both Glenn Stockton and I are in the batters' box. Saturday Academy is sponsored by IBM, Xerox and such players and aims to provide what the governors seem to not care about: a relevant education.
No, to the best of my knowledge, our bevy of scientists and engineers has not been consulted, nor has ONAMI been approached (our nanotechnology hub, state funded, interested in education, has a Zome buckyball in the conference room).
So if the process in Oregon is any indication of what the process is like in other states, I'd say it's probably shallow and the result of a lot of unimaginative memo writing (we should exhume the paper trail to get a sense of it).
I don't expect much will come of it, as serious-minded professionals such as we find here will blow the whistle, register their disdain.
What I suspect is going on is a lot of cutting and pasting across state lines at the middle management level, a mediocretizing process often confused with democratizing.
It'd be convenient for mass publishers to have this "one size fits all" set of standards to write to, another way to combat localization, place based curricula, schools that emphasize faculty control mixed with strong town-gown relations etc.
We know from biology that mono-culture is dangerous, leads to ecosystem fragility. In the USA we have 50 states for a reason, i.e. to retain some strategic level of diversity associated with continued viability. Congratulations to Alaska and Texas for so far refusing to toe the party line.
> On Mar 16, 2010, at 3:05 PM, Litvin wrote: > > Have people looked at the draft released a few days ago by the national panel? http://www.corestandards.org/. They say 48 states agreed to adopt it (Texas and Alaska are the holdouts.) It does mention discrete mathematics... in exactly one sentence: "Other forms of advanced work are possible (for example in discrete mathematics or advanced statistics) and can be eventually added to the standards." If not for this sentence, one might think this draft was written before Turing was born. This is a step back from NCTM standards of a dozen years ago, where discsrete math merited a whole paragraph. This standards draft also mentions computational, in exactly one sentence: "A graphing utility or a CAS can be used to experiment with properties of the functions and their graphs and to build computational models of functions, including recursively defined functions." > > Seems like one more missed opportunity... > > BTW, can someone tell me what they mean by "building computational models of functions"? > > Gary Litvin > www.skylit.com >