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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Scott Steketee and Daniel Scher presented this session at the 2013 NCTM Regional Meeting in Baltimore.
Graphics special effects are everywhere: TV, the Internet, the movies, games—everywhere. But kids seldom think about the functions that create these images. We’ll distort pictures with Sketchpad’s custom transformations, create fractal plants from iterated functions, and define a function by drawing its graph on the screen. Classroom-ready activities provided.
Note to Attendees
Thanks for your enthusiasm and your active participation! I really enjoyed working with you, and I look forward to receiving your comments and suggestions on the activities. I have made several corrections in the Graph Dancer sketches since my original post on Friday after the end of the conference. I have not yet had time to write the teacher notes to accompany the sketches; I hope to do those soon.
Blog Post and Movie Trailer
In advance of the presentation, I blogged on the Sine of the Times blog, and recorded the movie trailer below for our session in order to incorporate some of the special effects that I showed in the session. You can also download the sketch I used to make the movie. (This sketch contains the credits for the images used in the movie; any uncredited images come from the Picture Gallery linked on Sketchpad's Help menu.)
Download the presentation materials used during the session itself. The resources provided here reflect and support the three themes of the presentation (the connection between functions and pictures, the integration of algebra and geometry, and the value of putting motion and feeling into students' experiences of function).
Graph Dancer Games
In these games you are challenged to drag a y-value character to make it dance, either along the y axis or in the Cartesian plane, in coordination with the x-value's movement along the x-axis. Each game has a variety of levels, and uses a particular function as the choreography rule. Fortunately, you have some hints to help you. (Go to the Graph Dancer Games activity 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.
The swirling effect (shown in the movie trailer and on the title page of the presentation sketch) is developed in a pair of activities from the Geometric Functions collection on the Dynamic Number website.
Pictures from Functions
In this activity you will produce several striking fractal images. To make each of these images, you create a single function that takes a point on the plane (the "seed" point) to another point (the "image" point). Next, you iterate this process, at each step generating a new image point by applying the function to the output of the previous step. You will introduce an element of unpredictability into the function, with the result that each example produces a striking picture. (Download the Fractal Fern activity.)
These activities are based on The Geometer's Sketchpad. and were developed in conjunction with the Dynamic Number Project. All are compatible with the Mac and Windows versions of Sketchpad, and many are compatible with Sketchpad Explorer, a free app for the iPad.