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:
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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:
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).
You can download the sketches, worksheets, and teacher notes for many of the activities from the Dynamic Number site. (Downloads in bold are the ones used in the workshop itself.)
Finally, you can download two experimental activities and three dynagraph activities:
These activities are designed for use with The Geometer's Sketchpad. All are compatible with the Mac and Windows versions of Sketchpad, and many are compatible with Sketchpad Explorer, a free app for the iPad.Update History: