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Abstract
Scientists have frequently been able to do physical demonstrations in class, while mathematicians have rarely had the opportunity. Manipulate provides mathematicians with a tool where we can now easily do classroom experiments. This is particularly effective if combined with a classroom voting technology often called "clickers."
Classroom voting (using clickers) is a significant new educational technology of the last 10 years and is rapidly growing in popularity. How does it work? Using the classroom computer projector, the teacher shows students a multiple choice or true/false question in a Mathematica window. Each student has an assigned "clicker" to use to answer the question. Their individual responses, anonymous to the rest of the class, appear collectively on a bar graph after a certain time period. (Software that comes with the clickers handles the administration of timing, collecting, and displaying student responses.) This gives both the students and teacher immediate feedback. Ideally some questions are sufficiently challenging that about half the class answers correctly. Then the teacher tells the students "Convince your neighbor why your answer is right," and the class is polled again. Frequently the proportion of correct student responses increases dramatically. This makes for an engaged class where students are thinking and having fun.
Mathematica has always been a useful companion to clickers. Frequently I have made a plot or done a computation in class while discussing the answer to a clicker question. With Manipulate, the marriage of clickers and Mathematica has opened up new ways to enhance student learning. For example, ask the students "What will be the effect on A by moving the slider to change B?" This can then be followed up with another conceptual question: "Why did that happen?" Calculus examples will be presented showing concept questions based on classroom experiments made possible with Mathematica's dynamic interactivity. The Wolfram Demonstrations Project is a great source for materials that can be turned into classroom experiments.
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