I am a graduate student in Mathematics Education at the University of Illinois at Urbana-Champaign. My advisor is Kenneth J. Travers. (Ken's advisees generally think he walks on water, and we're a pretty perceptive bunch.)
I am particularly interested in using appropriate technology to find better ways to teach calculus to undergraduate students majoring in engineering and physics. I have written a few papers, which are available on the web. These papers are mostly about calculus instruction in one way or another, with a lot of attention to the use of technology to increase understanding.
My dissertation is a comparison of two ways of using technology to introduce the derivative in a first-semester calculus course. This is the part of my site that should be changing most rapidly this semester--but hasn't been. I'll try to do better. Really, Mom, I'm working on it.
One of the instructional methods in my study uses a computer and an ultrasonic motion detector, produced by Vernier Software. As the student walks back and forth in front of the detector, the computer displays a graph of the student's motion. Motion detectors have been used successfully to teach graphing concepts to students from middle school through college. I am using the motion detector to help the students see how the speed of the motion is represented by the slope of the distance graph and the height of the velocity graph. Once this conceptual link between the slope of one graph and the magnitude of another is established, it forms a foundation for understanding the derivative.
The other instructional method is similar, but uses a Java applet I wrote to simulate the motion detector. One of the advantages of this applet is that it can be used by anyone with a computer and internet access, without any need for special equipment such as a motion sensor. It remains to be seen whether the students will develop the same understanding of the concept without the physical motion involved in using the motion sensor.
You can check out the Java applet, but be warned that Java appears to be a bit buggy. The applet will run on some browsers but not others. So far, I have been able to get it to work only on newer PC browsers and on Internet Explorer for the Mac. It hates old browsers and Netscape on Macs. The portal page tells you how to get around the quirks and then takes you to the applet itself. If you can get it started, it is pretty cool.
I am also working on a collection of Java applets to help students learn about Ohm's Law and other basic concepts in electric circuits. I start by considering the flow of water, and then use that as a model for the flow of electricity.
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This page last revised January 15, 2003.