On Mon, Dec 21, 2009 at 4:11 PM, Michael Paul Goldenberg <email@example.com> wrote: > Quoting Jerry Becker <jbecker@SIU.EDU>: > >> ***************************** >> From INSIDE HIGHER ED, Monday, December 21, 2009. See >> http://www.insidehighered.com/news/2009/12/21/math >> ***************************** >> Boosting Math Standards
STANDARDS: WHO SETS THEM?
HP in Corvallis, Oregon was a HQS for the famous scientific calculators of the 1970s. Privileged school kids like me were thrilled to get access to those HP 35s and 45s. My high school friend's dad had an HP65, one of the first programmables. I'd go over to his house after school especially to play with it. We were such geeks.
Some campus facilities from that era have been converted to a nanotechnology lab. ONAMI is the nonprofit guiding some of that research (onami.us).
Should ONAMI, other coalitions of academic and industrial institutions, set curriculum standards?
They already provide lots of STEM content, but don't claim to be setting standards themselves. Why not though? Must we bottleneck through the states all the time? MPG has pointed us to that talk by Dylan. Google is likewise in the curriculum writing these days.
The Jason Project is an excellent example of how it works today in that the web site claims to align with state and national science standards (which I don't doubt). But then it's also helping to *set* those standards in the sense that these are the scientists who know how to do science.
Does Congress teach the National Geographic Society what geography is all about, or vice versa? OK, it's a bit of a two way street, but lets admit that standards and laws are not the same thing. You need more than state governments to have some real standards in this picture You need professions, guilds, other standards-concerned bodies.
During our recent field trip to ONAMI (we being ISEPP, isepp.org, meets in the Linus Pauling House in zip code 97214), I noticed the PR materials included a Zome kit that assembles a Buckyball (no, there's no gift shop on the premises).
Zome, or Zometool, for those who don't know, has long been on the market as one of the stronger spatial geometry kits. The plastic hubs and their intricate sets of holes anchor a small vocabulary of edge lengths, color coded. They're popular with home scholars (home schoolers), as will as with some academic geometers and assorted polyhedralists.
The edge lengths are not arbitrary, because the objective (standard) with this kit is to accommodate the building of some well known shapes, polyhedra, lattices. Students of Zome become familiar with these lengths and angles, acquiring more or less facility with trigonometry, perhaps even some linear algebra (vector operations in a spatial context).
George Hart, creator of Pavilion of Polyhedreality on the web, a valuable resource, has published a book on Zome and it's applications as a learning tool (curriculum artifact).
An interesting wrinkle: Scott Vorthmann has developed a valuable yet free Java program, installable over the Internet, which allows students to build Zome structures on screen. This virtual Zome or vZome saves in a variety of formats, including .wrl files, viewable in free browser plug-ins as rotatable, fly throughable (see links below).
The curriculum writing I've been sharing recently on Wikieducator, sprinkled with various objectives (Wikieducator comes with templates for flagging these), likewise includes sharing about these polyhedra and their lattices (honeycombs). We've all seen Kirby yakking (sometimes ranting) about this content in this archive over the years, playing it up, making a big deal out of a specific volumes table, on which included are those A&B modules.
My school of thought, cliquish yet influential (in some niches), likes to recommend using what we call a "concentric hierarchy" of said polyhedra as a kind of curriculum switchboard, as a grand central station, a way of cramming lots of useful information into a minimal and memorable package that crops up in multiple lesson plans.
I'm appending a quote, from Siobhan Robert's book 'King of Infinite Space', about the great geometer Donald Coxeter, giving a sense of the motivation here. She quotes some thoughtful individuals with impressive job title, helping us look over their shoulders regarding their heartfelt curriculum concerns. **
I note that Zome (or vZome) might be used to model said hierarchy, routinely cite other artifacts as well (e.g. CubeIT by Huntar), as there's a hands-on component to spatial geometrics. Not everyone has a budget for such things, so there's also the option to use less commercial supplies.
So does this mean ISEPP is a source of curriculum standards and lesson plans, or ONAMI?
In this case, the Oregon Curriculum Network is taking the credit (blame), letting these other players off the hook. I'm not consulting with either Skip or Terry before posting this stuff, just want to weave together some of the picture on the ground.
ISEPP gives me outlets for field testing, outreach to teachers. Saturday Academy has likewise permitted field testing, piloting, directly with the high school aged. I've been sharing my results for some years in this archive.
The standards have to do with spatial geometry, computer skills. Some of the lesson plans have to do with Zome and/or vZome. Some plans feature Python.
What's important here is this distinction between the standards and the plans. The standards needn't be pegged to specific kits or computer languages.
The plans using these products may cite the relevant standards and objectives, but other plans using different products may cite the very same standards.
How does a set of standards coming from a coalition or network, a citizen group, impact what's taught in an everyday high school? This is an interesting nexus to explore. The citizen group may actually include teachers as members. The NCTM is a good example.
Probably the easiest answer is the processes and politics vary by region, so it's of limited relevance to dissect my situation in Oregon in too much gory detail. We might still look at some common patterns. That should be for some other post though, as this one is already plenty long.
I conclude this case study with some recent exemplary screen shots of vZome. These are by an accomplished teacher in our group (D. Koski) and is the kind of thing I share with teachers who might come to our meetings or simply send email.
The thing about standards and lesson plans is they sometimes spread with little regard for political boundaries. This kind of geometry we're doing has fans and practitioners in Japan for example (e.g. Yasushi Kajikawa, whom I've met on at least two occasions, both times in North America -- he's published in Scientific American, though in the Japanese edition -- did you know of such a thing?).
We're already familiar with the international spread of standards and practices from Waldorf, Montesorri and other such custom curricula. The religious schools have their own way of developing and propagating standards (the Jesuits, the Quakers...).
These case histories should remind us of the diversity and multiplicity of curriculum sources. I'm not seeing where "national standards" could ever gel from this, but then I left out ETS and the college placement tests. These latter have been influential in promoting a kind of mono-culture, which from my point of view has slowed adoption of some necessary upgrades.
That's partly why I look for the propagation of these upgrades outside of Oregon, in Canada for example. The inertia behind vast bureaucracies, of any description, is such that innovation occurs only in pockets, in niches. Saxon spread by a similar process, through self schoolers and charters.
There's typically a kind of "underground" consisting of early adopters of something, which to outsiders may appear like some kind of conspiracy. New Math was no exception.
It behooves us, as curriculum reformers, to be aware of these patterns and incorporate them into our thinking. Begin planning for the backlash even before you're done with the early pilots chapter. Our goal is to empower teachers already on the front lines, by giving them better material (material that takes some getting used to, but since when has the world stood still?).
** embedded in my blog:
Returning to King of Infinite Space, I notice Walter Whiteley, director of applied mathematics at York University in Toronto, may have views similar to Alan Kay's, regarding our descent into idiocracy. Quoting from Roberts again:
For Whitely, it all comes down to underlining how visual perception builds into reasoning in the brain... "Failure to do and teach mathematics visually is excluding numerous people and making mathematics harder," Whitely concluded. And he conjectured that the dearth of the visual, the decline in classical geometry over the last hundred years, has had a regressive effect, resulting in "the geometry gap." This is much like "the ingenuity gap," a concept raised in the book of the same name -- by Thomas Homer-Dixon, director of the University of Toronto's Trudeau Centre for Peace and Conflict Studies -- chronicling examples of people and societies facing a crisis of ingenuity or know-how, which leaves them unable to solve problems of their own creation. Whitely's thesis holds that in the realm of science, the sedentary, mathematical areas of our brains, and the consequent lack of ingenuity - -- the inability to solve problems and make discoveries - -- results from an ignorance of visual and geometrical tools.
That sounds a lot like a passage from Jared Diamond's book Collapse: How Societies Choose to Fail or Succeed.