Background

The early Greeks thought abstractly in pictures. Historical proofs of the Pythagorean theorem are entirely geometric, devoid of the algebraic symbols that 8th-graders worldwide struggle to memorize. The original version of Isaac Newton's Principia, in which he lays out the foundations of the calculus, also uses geometry instead of mathematical symbols to make the famous points. Principia was later "translated" into algebraic notation so that it could be understood by a symbol-oriented audience.

As we enter the digital age, we find ourselves returning to the pictoral values of our intellectual forebearers. Not only mathematical abstractions, but also intellectual collaboration and self-expression can be performed and communicated via interactive multi-media instead of static text. Today, for example, the Pythagorean Theorem is animated and interactive. Click here, here, or here for multi-media expressions of Pythagoras's famous deduction.

As a result, we are called upon to develop a new set of skills for abstract thinking and the sharing of ideas.

VizAbility is an educational CD-ROM designed to address this emerging need. Its goal is to teach visual thinking to all age levels. What follows is a critical review of VizAbility from an educational standpoint.