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.
This unit, featured in the February 2016 issue of Mathematics Teacher, provides a transition from functions in geometry to functions in algebra. (Readers of the online version of the article will note that all figures after the first are live websketches: figures that can be directly manipulated on the article’s web page.)
In this unit students transfer their understanding of geometric functions that take a point in the plane as input and produce another point as output—reflection, rotation, dilation, and translation in “Flatland”— to linear functions that take a real number as input and produce another real number as output. Students restrict the domains of the geometric functions to number lines (“Lineland”), measure the values of the variables, and discover that composing and restricting just two geometric functions enables them to create any linear function geometrically. In the culminating activities students represent these geometrically-constructed functions in both Dynagraph* and Cartesian graph forms.
The video below shows and describes the activities of this unit in less than 7 minutes.
These activities are drafts. They all include student worksheets and websketches, and a number of them include performance-based assessment games. None of them yet incorporate teacher-support materials, though we hope to be able to provide those soon. We are revising the worksheets, websketches, and assessment materials as we we continue using them with students and observing students' successes and challenges. Please contact the webmaster with your questions, comments, and suggestions for improvements, or for information about our field-test program.
Each activity below is expected to require one or two class periods. The first activity is a review activity from the introductory unit to prepare students for the rest of the activities. Click any blue header below to go to that activity's web page.
These activities are designed to accomplish a number of objectives. In doing them, students will:
▹︎︎ The Fine Print
* Dynagraphs were invented by Paul Goldenberg, Philip Lewis, and James O’Keefe. See their classic 1992 article “Dynamic representation and the development of a process understanding of function.” In G. Harel and E. Dubinsky (Eds.), The Concept of Function: Aspects of Epistemology and Pedagogy. MAA Notes V. 25 (1992), Mathematical Association of America.