This was a most useful outline, John, and thanks for the URLs (below).
You've performed a valuable service by contextualizing STRUCK within
a very generic and relevant grab bag of connected topics (kind of
like "design science" does).
Just to add a little from my perspective, as a curriculum writer
wanting to give kids better access, preparation, skills, conceptual
mastery over these CAD-related computer tools earlier in their
careers...
What's so useful about VRML and Povray is they take something very
close to Cartesian input (just a tiny hop, notation-wise, from any
standard text book) and take care of all the perspective and view-
point overhead automatically.
Drawing perspective on a chalkboard is something teachers usually do
pretty well, and some kids, but I think a lot of what keeps so much
of the curriculum confined to "flatland" (XY grids, but not so many
XYZ grids) is until recently only the textbook companies had access
to the really good 3D graphics.
With VRML and Povray, children can dive into the world of 3D without
having to learn a Renaissance drawing system (horizon point and all
that). They can feed their shapes in notation (like a musical score)
and get very high quality renderings from multiple angles, and/or
change the viewpoint in real time using VRML (e.g. Cosmo 2.0).
These "graphing calculators" are far less adept at doing anything
3D plus VRML and Povray are both free, once you have a decent computer.
So I'd like to see curriculum which focuses on very simple renderings
(even just the XYZ axes floating in space) and then takes kids through
the steps of building software methods to output whatever function or
network of connected edges (e.g. a polyhedral wireframe) to Povray.
Even "flat" graphs, e.g. of COS(X), will show up on an XYZ apparatus
in 3D, as I show at http://www.inetarena.com/~pdx4d/ocn/calculus1.html
for example (towards the bottom, on the left).
Once these "nuts and bolts" are understood, then zooming back to a
more comprehensive package, such as STRUCK, builds outward from an
understanding of how Povray and VRML are "scored" (what kinds of scripts
they expect). This takes the "black box" sense out of it -- I regard
education as a process of showing the insides of as many "black boxes"
as kids sense they need to see, in order to become competent enough
to innovate and improve upon whatever existing designs.
Of course Mathematica and other "graphing packages" will connect math
to 3D visuals. But I really think there are serious advantages to
going with Povray in particular, simply because (as your outline
points out) it is also the entryway freeware into a whole world of
art-related powers and concerns -- shading, textures, lighting,
reflectivity... a whole world which "straight math" tries not to
concern itself with, but which _should_ be a part of the early
grade curriculum, because bridging geometry and art is core.
Any curriculum which ignores the geometric bridge between art and
science is doing grave disservice and should be dropped or upgraded
with all possible speed.
Not that I'm against Mathematica in any way, but it's an expensive
package and I think too many teachers are unaware of the leverage
they have using downloadable freeware for multiple platforms (both
Cosmo and Povray run on many species of capable machine).
[outline snipped]
>40. and... There are many places to look
> i. Here are some of my favorites:
>a. Cadalog: http://cadalog.com/
>b. POV-Ray Homepage: http://www.povray.org/
>c. POV-Ray Stuff: http://www.wakingdream.com/dale/
>d. Beautiful Code: http://www.xs4all.nl/~gdj/
>e. Springspace: http://www.wolfe.net:/~setebos/springspace.html
>f. Keith Rule: http://www.europa.com/~keithr/
>g. Richard Hawkins: http://www.newciv.org/Synergetic_Geometry/
>h. Hypertoons:http://www.rt66.com/~charhawk/mods.html
>i. Design Science Central: http://www.inetarena.com/~pdx4d/
>j. Virtual Synergetics: http://www.cris.com/~rjbono/html/struckvrml.html
Kirby
Curriculum writer
4D Solutions
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