[Edu-sig] More preaching to the choir...

[kirby urner]

On Fri, Oct 31, 2008 at 11:54 PM, Edward Cherlin <echerlin at gmail.com> wrote:
> 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. ^_^

Some could maybe.  Quaternions predate Gibbs-Heaviside vectors as we learn
'em in school these days, have strong application in the gaming industry, as
faster than rotation matrices in a lot of ways.  I've published some
work on this
already e.g.

http://www.4dsolutions.net/ocn/oopalgebra.html
http://www.4dsolutions.net/ocn/numeracy1.html

> 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.
>

So like Sourceforge then, but for lesson programming.  Cool.

>> 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.

Yes, my goal as well, to develop a spiraling sequence of topics.  However
I tend to de-emphasize calculus as a standalone topic, merge it back into
the physics from whence it derives, freeing up more of the math curriculum
for the group and number theory topics we need to explain RSA pre-college.

This will be a focus of a Pycon 2009 tutorial, if it gets approved.

Kirby