I did my doctoral work in Mathematics Education at the University of Illinois at Urbana-Champaign. My advisor was 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. They could use better formatting, including printer-friendly versions. I hope to get to that soon, so check back if you're interested.
My dissertation is a comparison of two ways of using technology to introduce the derivative in a first-semester calculus course.
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 use 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. One of hte main questions of my study was whether the students would develop the same understanding of the concept without the physical motion involved in using the motion sensor. They did. In fact, the Java group did slightly better than the motion sensor group, although the difference was not statistically significant.
You can check out the Java applet. It seems to have improved with age. The old version of this page warned that the applet would not run on all browsers, but with recent improvements in browsers it runs very well. The portal page tells you a little bit about it and then takes you to the applet itself.
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 June 19, 2009.