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 Subject: Projects Author: Cathi Date: Mar 18 2003
Hi Alice,

I'm intrigued by your use of projects in Geometry. I?d like to hear more about
the projects that you do.

My students have worked on projects, also, of two types. One type of project is
an in-class hands-on exploration (using GSP) and the other type of project
is "extra credit" which may or may not involve technology. Sometimes I ask them
to go on the internet and research a certain topic, and explain it in their own
words, like finding and explaining alternate proofs of the Pythagorean
theorem.

The in-class projects are usually explorations on a certain topic, and include
writing about their results. Some involve technology and some don?t. One of my
favorites, involving technology, (besides the Center of a Triangle) is one I
call "Quads into Circles".  I have some GSP files on this, but don?t know if we
can attach files to a posting. So I?ll try to describe this project, below:

I?ve constructed some quadrilaterals in GSP, a parallelogram, a rectangle, and
a rhombus. In one GSP file, there?s a "random" parallelogram and a circle next
to it. The question is asked "Can you fit this parallelogram into the circle, so
that it is inscribed? The students experiment by dragging the figure into the
circle; they drag sides and vertices until the quad appears to be inscribed.
They discover that to be inscribed, a parallelogram needs to be have right
angles; that is, it needs to be a rectangle. They are then asked to explain
why/prove this. And so forth for the other quads.

This is the kind of project that I really like ? exploration, conjecture,
proof/explanation.
My students write reflections on their work, and keep a portfolio. More than one
student has written "I felt like this was MY theorem, like I had discovered it
myself, and showed that it was true." This is owning the mathematics!

Can you describe a few of the projects that your students do? Thanks!