Geometry Papers that Count

 

Paul J. Karafiol,

Walter Payton College Prep High School, Chicago, Illinois

 

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.