## Using Computer-Based Laboratories to Teach Graphing and the Derivative at the College Level

Lisa Denise Murphy

Welcome to the home page for my dissertation study. This site will provide information about my study as it progresses. The first thing to check out is the report on the pilot study. I wrote this report in preparation for my oral preliminary exam, which I passed in August of 1999. In consultation with my committee, I have changed a few of the plans for my main study from what they were in the prelim paper, but the major stuff is still the same.

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 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.

In September of 1999, 47 first-semester calculus students participated in my study by taking the pre-test. Thirty-two of these came to the first instructional session, and thirty also attended the second session, which included the post-test. The students who took the post-test were evenly divided; 15 had received one form of instruction and the other 15 had received the other form. I would like to say I planned it that way, but partly it was luck; I didn't know which of the original 47 would fail to appear for the instruction. (Had I been alert, I would have paid the 17 who skipped the instruction to take the post-test, so that I could compare their results to those of the subjects who received the instruction, but I missed my chance there.)

In late January and early February of 2000, I will be repeating this process with a new class of first-semester calculus students. This time I will interview some of them, and if there is a substantial group of students who participate only as far as the pre-test I may try to bribe them to take the post-test. I am giving the subjects the address of a web page designed to answer their questions about the study.

In the end I hope to be able to make and defend some conclusions about the relative effectiveness of the two forms of instruction. From the results so far, it appears that there is little or no difference in performance due to form of instruction. Thant's nifty, because the Java applet is quite a bit cheaper and more convenient than the motion sensors. If it is equally effective then it should turn out to be very useful. [I want to emphasize that I am working with university undergraduates. I would expect to find more of a difference between the two forms of technology if I were working with children.]

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