Geometry Papers that Count
Paul
J. Karafiol,
The author describes a
series of short writing assignments for students that nurture geometric
reasoning while requiring only basic numerical familiarity. The results
are that students become comfortable discussing symmetries, congruence, and the
use of systematic reasoning without being overwhelmed with the demand for a
rigorous, axiom-based proof. While the author has used these writing assignments
most extensively in high school geometry classes, they could also be used as
non-frightening introductory writing assignments in upper-level courses.
The same assignments are also open to extensions and generalizations that spark
a student's interest in self-motivated mathematical research.