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Commentary: Problem Solving Seminar -- Three-Level Pyramid Test
This is the only time I’ve done a three level pyramid test, where students work first individually, then in groups, then as the whole class. I’m not sure why I haven’t done it again; I think this is a great test, and as I remember (it’s been six years), it went well. I think students ended up needing a lot more time than was allotted, which was OK, as the class was a seminar. We spent a long time after the test generalizing the last problem, ultimately to a continuous model. The first problem contains variations of Cuisinaire Rod Train Problems (see here for an activity on this topic); these are generally hard for students. The second problem concerns scheduling appointments for three people; it was a follow-up to the Appointment Problem, which we’d worked on in class. The last part is a restatement of the Kirkman’s Schoolgirls Problem, which is very difficult to do randomly (students didn’t get it). The last problem I adapted from a Putnam Exam problem, and it’s a lot of fun and leads to interesting generalizations. I’ve used the problem occasionally in other introductory classes; students catch on to the pattern fairly easily, and it lends itself to justifying reasoning. Revisiting this problem makes me realize I should write something about it for a math teacher’s magazine; it’s nice. 8/05
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