PROCEEDINGS OF THE 15TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION (Vol 1)
2012
Portland, Oregon
For Educational Color Work: Diagrams in Geometry Proofs
Page: 1-458
Historically grounded in Oliver Byrne's reworking of Euclid's Elements, and based on a student- generated proof, we investigate the use of coloring to enhance geometry proofs. Charlotte Knight, an undergraduate mathematics major enrolled in a modern geometry course, regularly employed coloring techniques as a tool in her proof-writing. We met for a single semi-structured, task-based interview to discuss Charlotte’s use of coloring in her organization and understanding of geometry proofs. Results indicate that Charlotte’s use of diagrams is closely related to her construction of a proof. In particular, her use of color serves several purposes: (1) as an organizational tool to connect her diagrams to the content of her proofs, (2) to enhance her understanding of the proof she is writing, and (3) to illustrate relationships within her diagrams and proofs. We believe this small study has particularly interesting pedagogical implications at the post-secondary level as well as for K-12 mathematics instruction.