229 Avery Hall
University of Nebraska -- Lincoln
Lincoln, Nebraska 68588
cgiusti2 "at" standard university e-mail suffix
When I internalize a piece of mathematics, I fit it into a larger conceptual web in which collections of ideas flows naturally toward their conclusions. When teaching I try to focus not just on communicating facts and theorems but also on imparting my "feel" for this web.
To this end, I am interested in using the concept of formal ontologies (as introduced to me by David Spivak) as a classroom learning tool. In particular, I suspect that this framework is suited for use in regular lecture courses as a medium for student-directed review and in IBL classrooms as a "blank" to suggest directions for student thinking.
I am deeply interested in the future of technology in mathematics education and in the migration from textbook reliance to open courseware. I am particularly fond of WeBWorK and Sage as examples of excellent free learning tools.