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More of Urner's ET stuff (or maybe it's just French?)
Posted:
Aug 11, 2006 8:54 PM


OK, so Mark Shuttleworth should get primary credit for coming up with the basic pipeline: Logo  Smalltalk  Python, where these three are delegates for particular modes of humanmachine engagement.
In Logo mode, we're piloting fish or turtles, developing motor skills in a first person context, recapitulating early childhood, except now with a 3rd person keyboardists view (ala LOGO by Seymour Papert and celebrities). Nowadays, it's MindStorms if you can afford high end toy stores. Looking forward to more freebie avatars on screen, ala Panda3D, if high end unaffordable (and/or unnecessary).
In Smalltalk mode, we're getting our feet wet in new concepts, relating to the OO paradigm in particular (Smalltalk was the language that put OO on the map). The Smalltalk legacy is towards immersive worlds, completely engaging environments, prestocked with many wonders (musical instruments especially). There's a paradise fantasyland aspect, and that's not unintended. Children should see their relationship to their tools as one of creator and author. We develop worlds, as a means to share our joys with others. This is not a bad thing.
Finally, in Python mode, we start to get under the surface to figure out in some depth how it all works. They take us back stage, into the basement, or wherever the figurative "programmers" of this stuff hang out. That's a move into archetypes and metaclasses, and synchronizes with a more adult consciousness, a coming of age.
As for whether Richard Stallman approves of my absconding with Gnu, I'm not sure. I'm leaving it as a pun, plus am committed to populating with animals (consider myself an ally of O'Reilly in this respect). The original New Math might here be cited (as a source of the pun), and Tom Lehrer's excellent contribution to American (and world) music on 'That Was the Year that Was'.
However, unlike New Math, gnu math is not focused on sets as the beallendall data structure. They don't permit duplicates, and that's already reason enough to have 'multisets'  except I call them lists (lists of lists make arrays (here feel free to dive in to the whole discussion of dimension and ranking, studied in J and APL)). Anyway, we have lots of data structures. Dictionaries are really cool, really necessary. Cardinality before ordinality (pairing before ranking).
And how shall we impart "data structures" to these media savvy youngsters? Dot notation. Think of these as toyz (what I say instead of eToys sometimes). You've got all these precoded, alreadyuseful objects, gifts from your Cprogrammer ancestors, who saw to it that these were as fast and efficient, and reliable, as they could make them (doesn't mean there aren't bugs). C is very close to the metal, like assembler. In chemistry, we'll talk more about that metal (the electronics behind the code).
>From dot notation and data structures, we go to functions (intersection with standard algebra), and especially to sequences, which we classify as convergent, divergent, periodic and aperiodic (not rejecting other schemes). Convergence takes us to Limits, ala L'Hopital. Aperiodic takes us to Chaos, ala Poincaré. So that's calculus and fractals  stuff to come back to. But it's the divergent I want to look at: the figurate and polyhedral number sequences. And in particular: 1, 12, 42, 92, 162... That's an important computer graphic. More mathcasts in the works.
And from functions (for sequences especially), we go to classes, class definitions. Among the first to be defined: Vectors and Polyhedra. Why? Because with that leap, we'll connect the polyhedra in our sequences, with the polyhedra of XYZ coordinates. This will provide strong connectivity for further explorations (e.g. back to fractals, for complex plane coordinates  not the same as XYZ).
Obviously I've expanded the Python piece of this triad rather extensively, hardly mentioning the Logo or Smalltalk phases by comparison. That's because I'm specialized towards the upper end of the 818 age range, and handle that far end of the pipeline. I'm one of the Python teachers, a snake charmer. Teachers of my ilk come last, before we turn you over to the upper division people (the pipeline continues, for most engineering professions anyway).
To recapitulate:
Logo  Smalltalk  Python
Logo: simple coordinates (xy, preview xyz) Smalltalk: immersive, lots of toys (multimedia) Python: more starkly lexical, more of the math
Breaking down the Python piece: dot notation and the OO paradigm (history and design) types of objects (primitives and other builtins) coding functions (algorithms for generating sequences) coding classes (vectors and polyhedra, divergence)
I thank many here unnamed teachers (gnu math and otherwise) for much of the above. I couldn't have done it without you. Let's keep the ideas flowing, via the usual circuits.
[apologies from the crosspost from mathteach but I wanted to fix a typo and thank some more peers, so this'll be the one that I link to  KU] **************************************************************************** * To post to the list: email mathedcc@mathforum.org * * To unsubscribe, email the message "unsubscribe mathedcc" to majordomo@mathforum.org * * Archives at http://mathforum.org/kb/forum.jspa?forumID=184 * ****************************************************************************



