As I've posted before to this listserv, my hankering
is to trailblaze a path thru the maths that provides
some serious vista views for the non math major, is
geared towards the liberal arts, but yet is most
definitely not a "for dummies" warming over of some
leftover pablum.
So for those not planning to go the pre-calc/calc
route, we should have some alternative curriculum
which encourages math type ratiocination, but
maybe strays into areas deemed "off limits" by
die-hard old school scholaists -- into Java for
example, and the object-oriented view of life.
Phase One is to rehabilitate the visual imagination,
and/or the tactile for those who want to feel their
way along. This means hands-on model making, with
serious supplies, commercial stuff, not just pipe
cleaners and sipping straws, although that works
too for some applications. Euler's V+F=E+2 is
there right from the get go, along with the Archi-
Platonic polyhedra, colorful and bright.[1]
Students get right away that this is a Renaissance
style approach, with lots of art project potential.
Coffee table books like the Hargittai's re 'Symmetry:
A Unifying Concept' will be old friends by courses'
end.[2] And of course the one by Williams.[3]
Phase Two is to set ourselves apart, to learn some-
thing new and different, so we don't feel like we're
simply imitating what the others our doing, but at
a lower level. To this end, I've pioneered (in
collaboration with others) a kind of vector math-
ematics that's both familiar and unfamiliar at the
same time. I call it NeoCartesian, even though its
four basis vectors go from the center of a tetra-
hedron to it's four vertices, and have 4-tuple (vs.
XYZ 3-tuple) coordinates: (1,0,0,0)(0,1,0,0)(0,0,1,0)
and (0,0,0,1). Call those A,B,C,D. By a process of
negation (e.g. E=-A, F=-B...) and vector addition
(e.g. I = A+B), we get whole number 4-tuples for
the vertices of the tetrahedron, inverted tetrahedron,
cube, octahedron, rhombic dodecahedron, cuboctahedron.
We also have whole number volumes for these critters
-- again, something the mainstreamer math people
don't get (because they're using the cube for a
unit of volume, but we're being snobby, looking
down our noses at such a dark ages convention --
heh heh):
Tetrahedron: 1
Cube: 3
Octahedron: 4
Rh Dodeca: 6
Cubocta: 20
Which brings me to my 'Teaching OOP and Coordinate
Geometry Using Polyhedra', now online at the Oregon
Curriculum Network website.[4] So I won't repeat all
that content here, but merely assert that students
will end up with a sure grasp of vector addition,
plus have some confidance with symbolic manipulation
using a math notation -- which includes an implementation
in some computer language, probably Java. The results
will be some of that art project stuff I mentioned,
as you can see here for example:
http://www.inetarena.com/~pdx4d/ocn/graphics/script.gif
http://www.inetarena.com/~pdx4d/ocn/graphics/javasamp.jpg
http://www.inetarena.com/~pdx4d/ocn/graphics/fancy.gif
So far, all of this is Linux compatible i.e. you don't
have to spend big bucks for an entry level machine
any more, and if you're lucky, your school will provide
adequate facilities (which you may optionally supplement
with personal devices purchased from your own accounts).
Mexico higher ed is standardizing on Linux. Perhaps
this curriculum will go NAFTA (catch on south of the
border and trickle back to USAers down the road a
piece).
This is a barest briefing of the direction in which
I'm moving, with some test markets in tow (lots of
listserv activity, as my students, some in the USA,
some not, grok and respond, and sometimes protest too
much!). From the looks of things, this is gonna fly,
and teachers will be lining up to master the requisite
methods and skills, as the enrollment potential is
huge. We have lots of students very eager for
opportunities to access the high tech world, with
skills a little deeper than word processing or running
a spreadsheet. Programming gives them that confidance,
while the content will include borrowings from topology,
analytic geometry, matrix algebra, dynamical systems
theory and more (I've even got a section on quaternions).
If anyone on this list wants to explore this alternative
curriculum in more depth, feel free to give me a holler
and/or anonymously explore the aforementioned web pages.
This is a time to get in on the ground floor and master
some new skills. Your peers might look to you as a
willing guinea pig. Test the waters on behalf of your
faculty and report back your findings.
Kirby Urner
Curriculum writer
Oregon Curriculum Network[5]
PS: for more info re the "Math Makeover in the Silicon
Forest" see the March 1999 issue of FoxPro Advisor
(computer mag), my article starting on page 48.
[1] http://www.inetarena.com/~pdx4d/ocn/outline1.html
[2] http://www.amazon.com/exec/obidos/ASIN/0679769455/
See also:
http://www.amazon.com/exec/obidos/ASIN/0070342512/
http://www.amazon.com/exec/obidos/ASIN/9810206003/
(follow links for more of a similar breed)
[3] http://www.amazon.com/exec/obidos/ASIN/048623729X
[4] http://www.inetarena.com/~pdx4d/ocn/oop.html
[5] http://www.inetarena.com/~pdx4d/
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