WebMath: using online math tools

[June Lester]

Given that we now have a number of nice tools for teaching online math,
what can/should we now be doing differently?  Example: there is a web-based
grapher that does zooming (or the MathView/LiveMath plug-in will).  This
means, for example, that instead of doing the standard "secant-line -->
tangent-line" motivation for derivatives, I can easily do a "local linear
approximation" motivation: keep zooming in on a point, the curve gets
closer to a line, find the slope of the line (equivalent, but a slightly
different point of view).

What other things can we do differently with existing online tools?  Our
treatment of graphing should definitely be changed, for example - requiring
students to use calculus to graph a function is pointless in these days of
online graphers (at least it certainly seems to to the students) - but then
how do we use the tools to get the students to understand the relations
between the calculus and the graphs? Or is it important to understand them
anyway?

I'd like to bring some fresh ideas to the Calculus I course I'm designing,
but I'm interested in all innovative ways to use interactivity to teach
mathematics online.  If you have any concrete examples you'd like to share,
so much the better.

Thanks.

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