In an attempt to specify in some canonical terms what many heuristic programs known as "expert systems" do, an analysis was made of ten rule-based systems. It was found that these programs proceed through easily identifiable phases of data abstraction, heuristic mapping onto a hierarchy of pre-enumerated solutions, and refinement within this…

Explores the role of proof in mathematics education and provides justification for its importance in the curriculum. Discusses three applications of dynamic geometry software--heuristics, exploration, and visualization--as tools in the teaching of proof and as potential challenges to the importance of proof. (Author/MM)