### Walking, Folding, and Computing to Visualize Geometric Concepts

James Morrow
I will describe several laboratories used in Explorations in Geometry, an
introductory mathematics course that is an alternative to calculus at Mount
Holyoke College. Most students who take the course have had bad experiences in
at least one of their high school mathematics classes: getting a bad grade,
having a poor teacher, or just disliking mathematics (despite, for many, having
received good grades). Evaluations indicate that most students now have a
greater appreciation for how mathematics is connected to artistic activity and
to other systems of knowledge and for mathematics as a creative endeavor.

Each class in Explorations consists primarily of laboratory activities. These
labs include a geometry walk; origami constructions; paper-folding for
geometric constructions, such as equilateral triangles folded from squares and
angle trisection; use of dynamic geometry software to simulate such processes
as paper folding and sliding ladders; and comparison of Euclidean to hyperbolic
triangles also using dynamic geometry software.

In this paper I will focus
on a few of the labs from the list above. For each lab, I'll discuss the lab
instructions and my experience using them, and describe the educational
benefits of each and the issues I try to consider as I design a lab.