A Black Box in a dynamic geometry environment is a figure whose construction is unknown, or a tool whose function is unknown to the user. Trying to determine how the figure was created or what the tool does reverses the usual direction of dynamic geometry activities. Instead of using familiar tools to construct a figure with certain properties, the student begins with a figure or by constructing a figure and then has to determine the properties of the figure in order to understand what the construction involved.
Black boxes can be created by adding new buttons to the tool bar (in Cabri), using scripts (in Geometer's Sketchpad) or by using prepared figures.
For example, the figure to the right is a Black Box created with CabriJava. You can move the red point labeled “A” and observe what the blue point “X” does. How could you construct a point that would behave the way the blue point behaves as you move the red point? Are there other ways to achieve the same effect?
Supported by a research grant from the Social Sciences and Humanities Research Council of Canada
Page last updated May 2005 by David Reid