>
> Some may say I should persevere until the students "snap out" of their
> old passive way of doing things.  If I was sure this was the silver
> bullet of math teaching, I would be confident enough to fight this
> battle. I'm not sure this is the holy grail yet.
>
>

This is certainly pedagogical, not really computer or math per se.
But (at least in the US) nearly every math class is more or less
formula-driven, so it can extremely intimidating for a student to have
to do something like this - and then to add to it a non-click way of
interacting with computers, where one has to precisely word what one
wants the computer to do, adds an additional layer of difficulty.

That doesn't mean you shouldn't try it!  But having students have to
learn both math and to program (understanding lists and defining
functions is definitely real programming to someone who has only used
GUIs, especially ones that mimic "natural" motion) at the same time
introduces a number of challenges, and certainly isn't a 'magic
bullet'.  However, if you have the energy and support of
administrators and parents to continue getting students to really
interact and learn the material in this way, I think it could be quite
successful - especially if you are able to get the same students for a
couple years.  It takes a long time to unlearn how to learn math, if
you know what I mean; even weak students are far more comfortable
doing it the 'traditional' way (which is not necessarily a 'bad' way),
because it's familiar, than trying something new which might help
those particular students internalize it better.

As a final suggestion, you might want to make the transition to the
typing a little more gradually - perhaps using Sage @interacts that
are completely click or drag, then ones where you have to type in
numbers, then ones where you have to type in functions or symbolic
expressions, then ones where depending on several controls different
things happen, then what you are doing.  The Scratch project at MIT
(http://scratch.mit.edu/) is also an excellent way to think about
programming in a different way, though I don't know how usable it
would be for a math class.

Oh, and I missed the fact that this is online below.  Yup, another
layer of pedagogical challenge, since you aren't 'right there' over
the shoulder.  Sort of like the discussions on sage-support :)

Good luck!

- kcrisman

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