On Tue, Mar 9, 2010 at 11:11 AM, Daniel Ajoy <da.a...@gmail.com> wrote: > Comparison between TurtleArt, Etoys, Scratch, and GameMaker, on how they > represent basic math concepts: > > * Negative Numbers (the number line) > * Equality > * Assignment > * Binary arithmetic operator, addition > * Decimal Numbers > > http://tonyforster.blogspot.com/2010/03/programming-and-mathematics.html >
Thanks for posting to edu-sig Daniel. We could use a lot more of this kind of literature. This guy in Austrailia is lightyears ahead of most bloggers I've read. I note MariaD has already posted her appreciative comments. That's Maria Droujkova, salonstress for our Elluminate session the other evening, twixt the functional programmers and a couple imperative types. http://mybizmo.blogspot.com/2010/02/learning-on-line.html ( Maria reminds me of Romany Marie, Queen of Greenwich Village: http://coffeeshopsnet.blogspot.com/2009/03/serving-buzz.html ) On the topic of turtles, I'm using them to draw plane-nets in this post: http://mathforum.org/kb/message.jspa?messageID=7007687&tstart=0 They also come forward as illustrative of the object (instance) versus type distinction, which is just a hair's breadth different from the old philosophical distinction between ideal forms and their temporal expression.** If you scan the above post to math-teach, you'll see this passage, especially apropos to threads here on edu-sig: """ > [b] Note that [2] is a discrete concept more or less, [3] is continuous MOL. > OK to play it this way. Length may be developed more discretely if we need to. The literal pixels and voxels are discrete. Digital computers, implementing these turtles, use discrete math. This was one of my beefs with calling it Discrete Math instead of Digital Math originally (talking about Track 2): they might keep us from working with polyhedra if we called it discrete, because polyhedra used to be considered "perfectly continuous solids". Giving them a purely digital treatment, on the other hand, such as by rendering them with a ray tracer (POV-Ray), would not bring us into conflict with those protecting Discrete Math from "alien" topics. Digital Math would embrace Polyhedra. As it turns out, you're able to get Polyhedra into discrete math via graph theory (polyhedra (as wireframes) are simply graphs). Litvins Math for the Digital Age has V + F == E + 2 in one section, though most of its graphs are planar, like plane-nets. In other words, my fears we're ill-founded and we'll be able to make do with a Discrete Math labeling for Track 2. YMMV. """ Autobio: For those of you just joining us, I'm a long-time activist on edu-sig with my own quirky agenda: 0. to advance more computer programming in the context of high school math learning especially (I used to be a high school math teacher, after working under Dr. Rorty on the Wittgenstein stuff (he coined the term "linguistic turn"), later at McGraw-Hill in computer literacy, more recently a trainer with Saturday Academy (saturdayacademy.org), attending that luncheon tomorrow @ Oregon Zoo (no kidding)); 1. to advance a streamlining approach to polyhedra based on what I sometimes call "tetrahedral mensuration" inheriting from the work of an American Transcendentalist philosopher some of you may have heard of, but thought he was an architect. To this end, I've been using Python + VPython, and Python + Povray especially. I've been a controversial figure in the Python community, consider myself lucky and privileged to be with PSF. Chairman Steve and I did some great work during Pycon 2009, however I missed Pycon 2010 entirely, needing to mind the fort in my zip code area (97214). My company, 4D Solutions, sponsors the Oregon Curriculum Network, which has championed Python for some decades. Check: http://www.4dsolutions.net/ocn/cp4e.html Kirby > _______________________________________________ > Edu-sig mailing list > Edu-sig@python.org > http://mail.python.org/mailman/listinfo/edu-sig > ** Do I think the object oriented shoptalk "just happens" to sound philosophical by accident? Does anyone I wonder? On the contrary, isn't it obvious that OO was deeply embedded in ordinary language to begin with? We already think in terms of "things" with behaviors and attributes. We already think in terms of the generic dog or horse (as a concept), versus the individual manifestations of this animal, each in its own time and place. Since the so-called "linguistic turn" in philosophy, we're respectful of the "ordinary language" roots of anything -- a pretty radical change from the old days, when "meta-physicians" ruled the roost. ( I should reintroduce myself as some guy who studied Wittgenstein's stuff at Princeton. Gregor, our resident turtle-meister (Standard Library) has sent me some links about that, such as to pictures of the house Wittgenstein designed in Vienna, for his sister I think it was. Very austere and simple, not unlike his writing in some ways. ) _______________________________________________ Edu-sig mailing list Edu-sig@python.org http://mail.python.org/mailman/listinfo/edu-sig
