[Edu-sig] Summary/Overview re Math Reform (my agenda -- Urner)

[Kirby Urner]

So I just started this thread on 'Calculus Mountain' on math-learn:
http://www.mathforum.com/epigone/math-learn/slingsamwang

Basically, I'm arguing that we should evolve the computer science track into
an alternative numeracy track, skirting calculus mountain yet providing
plenty of useful mathematics.  

This track will co-exist with, and compete with, the current precalc-calc
track, which today monopolizes K-12 as the only gateway into college level
technology tracks and careers.

"""
Let kids electing a discrete math and computer science track excel in
their own direction, according to alternative criteria.  College and
corporate admissions officers should be open to this alternative mix
of skills, which are on target for so many real world positions (I
know this first hand).
"""
[ http://www.mathforum.com/epigone/math-learn/slingsamwang ] 

This isn't a new approach for me.  I've long push a three-pronged agenda
along these lines:

I. Math through Programming -- use a computer language, esp one w/ an
interactive shell, to explore concepts and help make them concrete [1]

II. Math through Storytelling -- integrate better with the historical
record, e.g. talk about the role of cryptography in warfare and commerce, or
about the importance of 'ciphers' (Arabic algorithms) to the European
Renaissance [2]

III. Beyond Flatland -- integrate better with spatial geometry via computer
graphics, especially around polyhedra and polyhedral numbers [3]

The excerpt below is from a background paper I prepared in advance of my
presentation at Pycon 2004 -- a presentation I was unable to make owing to
family illness and an abortive sojourn in DC (I'm trying Pycon again this
year, but I'm not formally presenting anything):

"""
And so I see the encroachment of computer science into the high schools as
at least initially somewhat competetive with the traditional curriculum. For
the first time in a very long time, the pre-college mathematics curriculum
is getting a makeover from a neighboring discipline. The ecology is being
disrupted. For example, there's potential here for computer science to be
cast as an underdog, recruiting students (and teachers) who are dissatisfied
with a mathematics track that seems to lack immediate relevance. Whereas the
calculus will remain important, it's somewhat debatable whether a high
degree of proficiency in integration by parts by the end of high school, is
any more worthy a goal than mastery of regular expressions (both technical
skills), especially if a conceptual grasp of the calculus is an element in
both scenarios.
"""
[  http://www.python.org/pycon/dc2004/papers/15/ ]

I consider all of this groundwork essentially complete and ready to
withstand real world testing.  

I think the open source community is well positioned to assist with this
agenda, and thanks to these links to the Fuller School, has a lot of
leverage for raising living standards more generally, i.e. by focusing
attention on an artifacts-and-technology based approach to social change.  

There're no political strings attached to this agenda, or if you find some,
feel free to snip them, or attach others.

We just want to improve the math-science-humanities curriculum all around.  

If that's seen as "liberal" (OK by me), then it's liberal in the sense of
"liberal arts" i.e. it's about keeping an open mind, which in turn means
keeping the vital shared knowledge base free and open source (a long term
goal of serious scholarship -- not new to this era).

Kirby
Adjunct Faculty
Portland State University

[1] the ISETL curriculum was consciously developed along these lines (thanks
to Tim Peters for alerting me to this).  APL/J have always been promulgated
with an eye towards math pedagogy (Iverson himself helped me with my 'Jiving
in J' paper: http://www.4dsolutions.net/ocn/Jlang.html ).  Scheme and Python
have likewise made forays in this direction (thanks to Danny Yoo for
pointing me to that RSA-in-Scheme web page).

[2] Here's an interesting quote from Bucky Fuller.  He's speaking off the
top of his head, i.e. this is the transcript of an audio recording:

===========
034   The word cipher has secret connotations for this reason. Because
people used it, they needed to use it, you understand "I've got to do my own
calculations" but if I get caught so I must be very secretive. Gradually the
significance of the cipher permeates society, particularly the young student
world that was literate. So the students of Northern Italy and Southern
Germany began to realize more and more the significance of the cipher, and
the positioning of numbers to do their own calculations. Young peoples'
faces are less familiar than the older peoples' faces, and so the young
people could get away with what the older people couldn't, so approximately
the year 1200, 500 years after the Arabic numerals came into the
Mediterranean world, that the treatise was written, that's 1200, and 300
years later it was impossible to ever again enforce the prohibition against
use of the cipher. And this is a wonderful date we're talking about 1500,
five hundred years ago. And this is exactly when Copernicus comes in. Here
was Copernicus, suddenly, with the capability to calculate; and calculating
the positions and some of the interrelationships of these, what we call the
planets, he came to the conclusion that our earth was also a planet, and
behaving in relationship to the sun the way the other planets were.

035  	And this opened up a completely new excitation of humanity.
===========
>From 'Everything I Know' transcript of the audio tracks, 1997 (the actual
recording was made in the 1975).

[3] To the polyhedral numbers thread (which connects to Pascal's Triangle
ala the 'Book of Numbers' by Conway and Guy), I add Bucky Fuller's
concentric hierarchy in the CCP sphere packing context.  

Basically, 12 balls around a nuclear ball in the CCP conformation define a 
* cuboctahedron (volume 20)
the voronoi cells of which are 
* rhombic dodecahedra (volume 6)
embedded in which sphere-embracing cells are 
* an octahedron as long face diagonals (volume 4)
and 
* its dual cube as short face diagonals (volume 3)
in which cube are embedded 
* two tetrahedra as face diagonals (each of volume 1)

Animated GIF:  http://www.grunch.net/synergetics