Nick Jackiw
Friday 16th November 2007
3:30-5pm
Abstract:
In considering the geometric figure, Kant distinguishes between image—the traditional visual
diagram—and schemata, the generalized concept of that diagram that “can never exist anywhere
except in thought.” Dynamic Geometry figures produced by recent software such as The
Geometer’s Sketchpad have bridged this conceptual divide, through the introduction of flexible,
rubbery diagrams that (under manipulation) can transform into all valid realizations of their
defining geometric constraints, while at every instant retaining the immediacy and tangibility of
specific images.
In turn, they have spawned a (slow) revolution in schools: over the past decade,
Sketchpad has become the most widely-used school mathematics in the United States, and
possibly the world. But the series of transitions involved in that movement—from propositional
to image-based forms of mathematical argument, from paper-and-pencil to digital definitions of
image, and most importantly from static to dynamic conceptions of mathematics—have hardly
occurred without hiccough.
Some of these transitions are only weakly understood theoretically;
and some have encountered strong pedagogic and political opposition. In this talk, Sketchpad’s
author explores the implications of Dynamic Geometry visualization on mathematical inquiry
and pedagogic practice in the context of school (6-12) mathematics, and surveys a variety of
responses to the Dynamic Geometry phenomenon from mathematical, epistemological and
historical perspectives.
