[Edu-sig] Summarizing some threads (KIrby again)...
kirby.urner at gmail.com
Sat Oct 24 01:11:59 CEST 2009
Those of you frequenting this list for some years will recognize most
of these themes. From time to time I like to archive a summary.
I. Math Objects (an approach to learning math)
II. Objects First (an approach to learning programming)
These two go hand-in-hand.
Math Objects are traditional concepts such as polynomials, polyhedra,
vectors, integers, treated as Types of Thing, i.e. we're making math
concepts concrete by distilling the "things" or "types" people have
invented over the centuries. One place to begin, familiar to computer
science, is to differentiate alpha from numeric types.
Objects First means taking the object-oriented philosophy seriously,
meaning we're mining everyday (ordinary) human language semantics,
wherein we already think in terms of named things (nouns) having
behaviors (verbs) and attributes (adjectives).
My curriculum anchors Objects (things) in the biological world of
biota, animals, creatures, flora and fauna. Then we move to the more
abstract types of object of interest in mathematics, polyhedra
especially because these are also visible and tangible, forming a
bridge to that biological world.
Python is especially cool as an OO language because when building a
biological creature as a template, one has these special names that
look somewhat like __ribs__. The methods stack up providing a
backbone or rack of ribs i.e. there's a visual analogy to a creature,
a snake in particular, right in the language itself.
The Objects First approach doesn't buy into the "ontogeny
recapitulated phylogeny" ideology, by which I mean: just because
programming languages evolved a certain way doesn't mean newcomers
have to traverse the discipline in that same order. Regions new to
telephony don't need to install land lines before they go with cell
phones -- go straight to cell (straight to OO).
III. streamlining the teaching of spatial geometry
I've separated this last theme out of the mix because it's what sets
me apart more than the above and makes me a marginal figure,
apparently off my rocker in some way.
I passionately believe that we should be taking greater advantage of
the streamlining done by the geodesic dome guy, Bucky Fuller,
regarding how to compact a lot of geometric information into a
compressed data structure he named the concentric hierarchy of
polyhedra (meaning you include them inside each other, sort of like
Russian dolls -- not a new idea, but the devil is in the details).
I won't go into some verbose presentation of III in this post.
However I do think when you move from calculators to full fledged
computers, then it's time to get off the plane and start taking
advantage of those much bigger and more colorful screens. So even if
you're highly skeptical of the Bucky Fuller bit, you might stay with
me on this notion the polyhedra and spatial geometry will naturally
come into vogue as we move beyond calculators and start taking more
advantage of computers.
I've invested many years developing these ideas and presenting them in
cogent form. The materials are open source and on the Internet.
Again, it's III that makes me moves me into the "esoteric" category,
where I start questioning only using a Euclidean set of axioms, start
taking up a "geometry of lumps" and making all sorts of high level
connections to Karl Menger (dimension theorist) and Ludwig
I also tend to get polemical, as a lot of positive futurism attaches
here, and to the extent the world seems unnecessarily hellish, I get
exercised about wasting already stockpiled assets that might make a
big positive difference. I inherited this long-running campaign from
an earlier generation and have a lot of loyalty to some of my mentors
in this area, including but not limited to Bucky Fuller himself.
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