[Edu-sig] number-line graphics for teaching arithmetic

[Fred Yankowski]

Kirby,

Thank you for the reply.  I've read through some of your "Numeracy"
writings in the past and have run some of the Python/PovRay programs
as well.  I'll try running the examples you included in your note.

On Thu, Dec 28, 2000 at 11:34:06PM -0800, Kirby Urner wrote:
> Your number line program sounds like fun -- especially for
> the person learning a programming language.  For a 7 year 
> old, it might be just as instructive to use felt pens or 
> colored pencils though.

My primary goal is to teach useful visual models for arithmetic.
Doing some fun programming (myself and/or with my son) is a bonus, but
secondary.

> As mentioned at my "Getting Inventive with Vectors" at 
> http://www.inetarena.com/~pdx4d/numeracy1.html ,

... I think that URL should be
<http://www.inetarena.com/~pdx4d/ocn/numeracy1.html> ...

> I like to go for a more complete vector concept, and not make the
> number line too front and center initially.  Space first, planes and
> lines second, is my approach (take freedoms away later, but start
> with what's most familiar and real i.e. volume).

That sounds cool, but I'm not convinced about how well it actually
plays out.  Worth a try though.

> So to kids, it seems like real numbers start out acting like 
> vectors, but then vectors come along and start doing the 
> number line thing like they've already been doing -- but 
> now using this new terminology.  Confusing.  Recapitulates 
> the historical sequence (Euclid -> Grassmann) more than 
> presents a coherent conceptual logic.[1]

I followed your references about Grassmann and I'm interested in
learning more.  Can you refer me to some good books on the subject?
I took many Math classes in college (too many years ago) so I can
handle an in-depth presentation.  I've meant to learn differential
geometry for many years, ever since picking up Wheeler's "Gravitation"
book, but have never taken the time to do so.  Maybe this study will
edge me into it.  While browsing in the bookstore I encountered a book
called "Geometric Transformations" by Mortenson.  Is that a good
reference for this subject?

-- 
Fred Yankowski           fred@OntoSys.com      tel: +1.630.879.1312
Principal Consultant     www.OntoSys.com       fax: +1.630.879.1370
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