The Geometric Supposer: Promoting Thinking and Learning

Traditionally, the teaching of high school geometry has emphasized the principles of deductive systems. This approach often forces students to learn how to manipulate mathematical systems while it denies them an equal opportunity to create geometry. Geometry teachers have always faced the dilemma of having to instil in their students an appreciation of deductive mathematical systems while at the same time offering them an opportunity to create mathematics. This article describes our approach in dealing with this dilemma.