Visual Mathematics via Computer-based Guided Active Discovery

Jerry Uhl and Debra Woods
Department of Mathematics
University of Illinois at Urbana-Champaign
Urbana, IL 61801, USA

Abstract. Conventional wisdom has it that effective use of Mathematica and the internet involves copying standard text materials into Mathematica notebooks and distributing them on the internet. The main result of this approach is to freeze the current mathematics curriculum and bog it down with all the other ineffective baggage commonly found in conventional mathematics teaching.

This talk will survey ways currently in use at Illinois of using Mathematica notebooks and the internet to modernize the content and the style of mathematics teaching chiefly by replacing blackboard (or PowerPoint) with student generated interactive visualizations that are used to cement ideas before the words go on. Instead of memorizations, students get to play with a concept thus forming their personal view of the issue at hand through guided active discovery.

One important aspect to this approach is the idea of student internet mentors who take new students under their wings and nurture their mathematical awakening.

This talk will also look at some of the interactive computer-based lessons and will look at the way the program is currently administered.