René Descartes <http://en.wikipedia.org/wiki/Ren%C3%A9_Descartes> would ask
you to put the sliders on his coordinate system,
http://en.wikipedia.org/wiki/Cartesian_coordinate_system, probably now on
the left and bottom.  They would then suggest or represent number scales and
 their motion would be related geometrically with the objects number
changes.
This would help hand-eye coordination and recruit muscle memory into the
learning process.

Nice idea to use the XO figures.  I can imagine also using a gray-to-colored
transition as an alternate way to reveal the product and sums against a
constant field of figures as subtle way to show what "could be" or "what
was" before and after a change.

When it comes time to show fractions, for example, the figures could fill
with "ink" on continuous scale rather than discrete  sliders.

Great start!     --Fred


2009/3/19 Jason Rock <[email protected]>

> Here is an alpha version of the idea as well as a mock up for anyone
> interested.  I appreciate any comments.
>
> --Jason
>
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