Technologically Embodied
Geometric Functions

With Technologically Embodied Geometric Functions, students develop conceptual metaphors that directly relate computer-based sensory motor experiences of abstract function concepts. This approach relies on four foundations:

Use the Materials, Support the Work

We’re working hard to create the sketches, worksheets, and support materials for these Web Sketchpad activities. Ours is a volunteer effort on the part of everyone involved, both curriculum developers and field testers, and we make these activities freely available for you to download and use with your own students.

As we develop, revise and expand the activities, we need your help. Email your commentary (What worked well? What didn’t?) and your suggested improvements to the webmaster.

Function Dance Presentation

In a function dance, the independent variable leads and the dependent variable follows. A Geometric Function can be thought of as a function dance, with the point variables as the dancers, the screen as the dance floor and a geometric transformation determining the way the dancers move.

Students can also perform such Geometric Function dances physically in the classroom, with the two dancers moving according to a chosen transformation. In the Function Dance activity, students use the same transformations to perform both traditional (physical) dances in the classroom and virtual dances on the computer.

This workshop has three parts, all from the viewpoint of functions as dances:

1. We survey a collection of Sketchpad-based Geometric Function activities.
2. In small groups we use computers to do virtual versions of several activities.
3. In small groups we perform physical dances using several transformations.

Try the Online Dances

You can try out eight virtual dances online. The independent (lead) dancer moves at a constant speed around a polygon, and your job is to dance the dependent role, following the independent dancer according to the rules of the function. Try one of the Translation dances first, to warm up before trying the more challenging Reflection, Rotation, and Dilation dances. Before you begin each dance you can set the difficulty level, making the dance slower (to practice your moves) or faster (to challenge yourself).