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.

Two Birds, One Stone: Functions & Transformations

Scott Steketee presented this workshop at the 2013 ATMOPAV fall meeting.

Description

In grades 7-12, CCSSM emphasizes functions and geometric transformations, and states that students should understand transformations as functions. By thinking of these topics as two sides of the same mathematical coin, students gain a deeper understanding of both. Examine the mathematical connections, and use the Sketchpad activities provided here.

Note to Attendees

Thanks for your interest, and I look forward to receiving your comments and suggestions on the activities. I have not yet had time to write the teacher notes to accompany the Graph Dancer sketches; I hope to do those soon.

Presentation Sketch

Download the presentation sketch I used during the session itself. The resources provided here reflect and support the three themes of the presentation (the fact that function and transformation are synonyms, the integration of algebra and geometry, and the value of incorporating motion and feeling into students' experiences of mathematics).

Activity Sketches You can download all of the activity sketches in this zip file.

Geometric Functions Activities

These five activities (ID the Suspects, Family Resemblances, Reflection Challenges, Dance the Dependent Variable, and Animated Special Effects) come from the collection of Geometric Functions activities developed in the course of the Dynamic Number NSF Project.

Shaky Golden Gate

I created this special effect for my presentation on Functions and Pictures at the 2013 Baltimore Regional NCTM Conference.

Dynagraph Dilation and Translation

This page from my presentation sketch is brand new. I've been thinking for a while now about how to structure an activity in which students come to realize that multiplication and dilation are equivalent operations (in one and two dimensions respectively), and that addition and translation are similarly equivalent operations. I have not yet turned the idea into a full-fledged activity, but someday it will leave the nest. (Sorry; could not resist the pun.)

The Graph Dancer Games

These games now have their own page.

Parabolas in Factored Form and Cartesian Graphs and Polar Graphs

These two activities are among the Sample Activities that are included with every copy of Sketchpad. You can find them by choosing Help | Teaching with Sketchpad | Sample Activities, or you can download them from these links: Parabolas in Factored Form and Cartesian Graphs and Polar Graphs.

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