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.