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:
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.
Related pages: Mathematical Foundation Cognitive Science Foundation Technology Foundation
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.
Update History:02 January 2014: Created this page.
This web site is based in part upon work supported by the National Science Foundation under NCSU IUSE award 1712280 (July 2017 through June 2019) and KCP Technologies DRK-12 award ID 0918733 (September 2009 through August 2013). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
We are deeply grateful to McGraw-Hill Education for making Web Sketchpad available for these activities.
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