### Spherical Geometry Project for Elementary Education Students

Jeff Johannes
My students begin my geometry for elementary education course by thinking about
the geometry of the Earth's surface. Each group of students gets their own
beach ball or tennis ball for hands-on experimentation.

Students create
definitions of shortest distance, straight lines, parallel lines and triangles
on the sphere, and then explore the consequences of those definitions. Further
experiments explore the properties of intersections of lines, sums of angles on
triangles, congruence theorems for triangles, and parallel properties in
spherical geometry.\par Pedagogically, this project encourages students to work
with each other and with the instructor at the beginning of the semester.
Furthermore, it demonstrates to them the power of their own intuition and that
their ideas can be more important than those of an authority.