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Topic: Boosting Math Standards
Replies: 19   Last Post: Dec 25, 2009 11:45 PM

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Kirby Urner

Posts: 4,713
Registered: 12/6/04
Re: Boosting Math Standards
Posted: Dec 23, 2009 4:57 PM
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On Mon, Dec 21, 2009 at 4:11 PM, Michael Paul Goldenberg <> wrote:
> Quoting Jerry Becker <jbecker@SIU.EDU>:

>> *****************************
>> From INSIDE HIGHER ED, Monday, December 21, 2009. See
>> *****************************
>> Boosting Math Standards


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 (

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

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,, 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

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).

Peter Pearce developed a different node and
connector system with 26 spokes, per pg. 67 of
his classic 'Structure in Nature Is a Strategy
for Design' (1978, 1990).

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

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

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.

Some vZomes by DAve Koski:


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

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

That sounds a lot like a passage from Jared Diamond's
book Collapse: How Societies Choose to Fail or Succeed.

[ ]

- --
>>> from mars import math

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