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.

Pedagogical Foundation of Geometric Functions

A critical pedagogical goal of Geometric Functions activities is to enable conceptual metaphors that connect students’ concrete experiences to their developing conceptual understanding of functions. One support for such metaphors is that computers, like functions, accept input (a moving finger or mouse) and produce output (an image on the screen).

These activities create another support by exploiting the two-dimensional window that the mouse and screen provide on the Euclidean plane to embody geometric point variables and functions in two dimensions. With the concrete and abstract poles of the metaphor sharing structure (input determines output) and geometry (of two dimensions), the activities achieve a very short “metaphorical distance.”

The pedagogical design of the Geometric Function activities also emphasizes tasks of high cognitive demand, cooperative learning, high-level questioning techniques, and formative assessment. The activities are intended to promote instrumental genesis—the level of skill and comfort in which the student’s conceptual understanding both influences and is influenced by the use of the tool.

Finally, for these activities to fulfill their promise, for them to be effective and engaging in developing students’ understanding of function concepts, we need your help. Use the activities with your students, and then send us feedback and suggestions and encourage your students to do the same.

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