Hiya Jason,
It really depends and certainly I am no expert. And probably most of
this is boring so feel free to ignore.

As I said above, I use a combination of GeoGebra and Scratch and Sage
and I am just starting with sage.
I would say that MY most important use of the worksheets in SAGE has
been to help ME understand the material and find an understandable way
to teach it. A friend in mathfuture forum quoted somebody saying
something like "If I can explain it to a computer, then I understand
it". That is EXACTLY how I feel.

With respect to students: Mostly classroom demonstration via an LCD
projector.
My rule 1: Build the applet/worksheet in class so they don't think its
magic. I rarely show "ready-to-use" stuff unless I have built the
basic model first.
My rule 2: Make sure they understand the stuff that no computer will
do for you. Then if the curriculum requires that we solve the
"computer part" by hand, show them how to check it using the applet/
worksheet.

Given this:
The 3D Line and Surface Integrals, Vector Calculus stuff is for my son
and daughter-in-law. Neither of them does the sage. They watch me do
it :)
He is studying chemical engineering and hates this math because he
sees no use for it (and like many boys and men refuses to learn
something he doesn't understand). He likes the visuals and it connects
to understanding.
But even my daughter-in-law (who is a very dedicated electrical
engineering student) was horribly frustrated by this material. She got
A's on the tests and said she didn't know what she was doing. The sage
demos helped.
---
I have been doing this for them for awhile. Usually, I try to make a
combination of short youtube videos, worksheets with lots of graphic
explanations, solvers, applets/ interactivities.
Once I make them, I tend to post them online and usually get decent
feedback and views (nothing like khan of course...). I try to do some
in english and macedonian so there is often an odd combination of
resources :)

In my math undergraduate courses, I tend to just do in-class demos. (I
currently teach Calc1 and Calc2, so e.g. I show them how do calculate
Taylor polynomials and then draw both functions so they see if, where,
how approximation works.)
I tried integrating IT into the grading, but I have huge class sizes
and that wasn't working.
They love to look at the 3d stuff so I do show the sage stuff in class
as reward for good behavior :)

In my math modelling courses (smaller), I hold online classes (in
macedonian) and my kids have to create a variety of (usually geogebra)
worksheets and then make little videos about what they learn. It
usually takes twice as long as you think it will :)
In my graduate courses, I do in-class demos and then assign "similar"
problems where they create worksheets themselves.  (This is mostly
probability and statistics to IT engineers and we use scratch.)
and on and on i go.... Linda

On Feb 7, 2:22 pm, Jason Grout <jason-s...@creativetrax.com> wrote:
> On 2/7/12 5:13 AM, LFS wrote:
>
> > I have this dream too; I get so annoyed when mathematicians (myself
> > totally included) spend time forcing our students to learn techniques
> > that a computer can do, but don't spend time teaching them carefully
> > and with understanding the techniques a computer cannot do. With
> > respect to this, I have gotten a bit stuck trying to explain
> > parameterization and so have slowed down with the sage videos. I will
> > be back :)
>
> I am really curious how you use these worksheets in your teaching.
> Classroom demonstrations in a lab?  Student work outside of class?
>
> I ask because I am always looking for better ways to use computer tools
> to enhance learning.
>
> Thanks,
>
> Jason

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