[Edu-sig] More preaching to the choir...
Edward Cherlin
echerlin at gmail.com
Sat Nov 1 07:54:57 CET 2008
On Sun, Oct 19, 2008 at 4:41 PM, kirby urner <kirby.urner at gmail.com> wrote:
>
> Yes, not that hard, agreed. I think we're in the right headspace, here on
> edu-sig, re teaching physics / math and so on with all this well known
> content, plus adding more experimental fun around the edges, ala programming
> just for the fun of it (ab attitude we highly encourage).
>
> Given how OO makes "objects" so concrete (per Concrete Mathematics) it's not
> so unrealistic to suggest adding some quaternions to the mix, just one more
> animal in our zoomorphic kingdom (or queendom, not pretending to know).
Well, once you get to that point, you can easily add octonions,
spinors, tensors, operators, crystallographic groups, and quantum
groups. ^_^
However, I have started a project at EduForge.org that I call
Kindergarten Calculus, to approach the issues from the opposite
direction. The question is how to demonstrate the fundamental concepts
of calculus visually to preschool children with no numbers and no
symbols. Limits, tangents, maxima and minima, definite integrals (area
under a curve), and other materials. I know how to start, but not how
far we can go. I can certainly show the Fundamental Theorem of
Calculus and the Mean Value Theorems. There are some simple cases of
Calculus of Variations that have physics equivalents. We have to think
about what has an algorithmic equivalent that we can program visually.
Anyone interested is welcome to join the project.
> Given XO is hardware with access to the cloud (by design) it's unnecessary
> to map curriculum to it or any other hardware device, as this isn't about
> hardware in the first place, but curriculum, and there's so much already out
> there, much of it very pre-computer in flavor, yet nevertheless relevant,
> Hamilton's brief included, Kepler's and so on.
I would like to factor each of those lessons into concepts that can be
taught at different ages, and to introduce them in sequence at the
appropriate ages. This should produce much deeper understanding than
waiting until students are supposed to be able to do it all at once.
Thus Galilean gravity in a uniform field can be demonstrated via
programming to third graders, while full Newtonian gravity requires
calculus.
> That being said, I like the idea of equipment especially designed with the
> needs of young children in mind. I was gleeful that so many adults found
> the XO frustrating to use because of the tiny keys. That's the whole point
> -- it's for them, not you. Of course in this sense there's a need for Sugar
> friendly apps, and/or new kinds of Sugar. I'm eager to find out more.
>
> All that's really needed, in terms of equipment, is a decent browser and
> Python itself (if teaching Python). In addition to writing stuff for
> laptops (multiple platform), I'm aiming at the LCD (or "flatscreen") market,
> piping directly to coffee shops (e.g. booths), so an intimate group might
> study together without bringing any hardware whatsoever. The same LCD plays
> music and does Apple style visualizations i.e. isn't just for "study hall"
> activities (these might be small screens, between HD and iPod, XO a source
> of ideas).
>
> So now that we know what the future looks like, I'm wondering how geeks will
> spontaneously self-organize to deliver a quality product. I imagine more
> Rich Data Structures will be a part of it, as in canned Periodic Table
> modules, with XML i/o if not natively XML -- I'm somewhat influenced by
> Ruby's anti-XMLism, GIS data re cities (example @ my site), insectavora and
> so on.
>
> However, I'm not expected all the stress of development to fall on open
> source developers. Much of this stuff will be kept under wraps and niche
> marketed under more restrictive licensing, simply because there's a market
> for it and open source isn't the answer to every prayer, even if it is to so
> many. Several of us here wear multiple hats in that regard e.g. contribute
> to open source yet support clients who don't choose to compete in that arena
> -- describes my situation at least.
>
> I'll be interested to hear more about what develops in those projects I
> learned about at the most recent OSCON, as many of those *were* open source,
> just not based anywhere close to Portland. As you might imagine, I have a
> hard time keeping up even just with what goes on in my home town.
>
> Kirby Urner
> Fine Grind Productions
>
>
> On Sun, Oct 19, 2008 at 3:30 PM, Edward Cherlin <echerlin at gmail.com> wrote:
>>
>> 2008/10/19 kirby urner <kirby.urner at gmail.com>:
>> >
>> >
>> > Here's a pointer to some related writings @ Math Forum, which I used to
>> > tell
>> > Arthur S. (this archive) was more like "center ring" in my circus, i.e.
>> > where math teachers meet irrespective of caring about geek subculture,
>> > computers etc.:
>> >
>> > http://mathforum.org/kb/thread.jspa?threadID=1845616&tstart=0
>> >
>> > Re planets in orbit, another interesting implementation, already field
>> > tested, multiplies complex numbers of unit radius, begetting rotation,
>> > then
>> > scales appropriately. Of course these orbits are merely circular, so
>> > not
>> > that realistic, so apply some field distortion if wanting elliptic (not
>> > something we tried).
>>
>> I did a simulation of elliptical orbits in TutSim on the Apple II in
>> 1982. It isn't that hard. I know of several different ways of
>> programming it, using inverse-square gravity, Kepler's law of equal
>> areas, and other equivalent mathematical representations. I set up a
>> three-body simulation in which one object was thrown out and the other
>> two settled into elliptical orbits around their barycenter, after a
>> chaotic early period. There are such simulations in a number of
>> languages, including Python and Smalltalk, where students can vary
>> parameters and watch the results. Some of this is in the Sugar
>> software for the OLPC XO.
>>
>> A. K. Dewdney's book The Planiverse describes simulations of inverse
>> linear gravity in 2D, and others have done inverse cube gravity in 4D.
>> You can get weird weather, seasons, and climate effects on planets in
>> 4D with two independent axes of rotation, depending in particular on
>> whether the rotation periods and the revolution period are close to or
>> far from simple integer ratios.
>>
>> > Here's some code:
>> > http://www.4dsolutions.net/ocn/python/orbits.py
>> >
>> > Kirby
>> > 4D
--
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