Lead by Example


Abstract:
From Dr. Z.

Body:
Doron Zeilberger always has good opinions. His 65th is no exception, where he discusses two of his favorite pedagogical techniques, introduction by example and programming for understanding. I've seen my teachers use the first plenty of times. As Zeilberger notes, though, the goal isn't just to show an example, but the simplest nontrivial example. For example, in graph theory we find the smallest nontrivial graph that has a certain property (since the empty graph often has the property simply because it has no edges), or we provide a slightly larger example and leave it as an exercise for students to find a smaller one, since finding such an example forces you to really understand what it is you're looking for. Using programming to understand is something both Zeilberger and I have advocated before, but I'll add that recently I had to program the RSA algorithm because I couldn't find an implementation in Scheme (I'll post the code sometime soon). As I wrote the algorithm, I had to build my understanding of the underlying concepts in order to be sure it worked right. When I finished, I understood how RSA worked a lot better than I did before. So listen to Zeilberger: introduce by example and program for understanding.

Posted: Sun - May 8, 2005 at 02:23 AM         |    

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