Combinatorics Summary

Monday - Friday, July 19-23, 2004

With the "teaching" portion of the group over last week, the two sections of the group got to work on their individual projects.

The "Applets" section began to play their games, that is, they worked through a winning strategy for a modified Nim game and then for a fill-and-pour cylinders problem. A great amount of time was spent dragging others in to try the strategies to ensure that nothing had been missed, as well as designing representations that were simultaneously understandable and useful.

The "Catalan" section (not to be confused with the Spanish language discussion group) broke up into individual activities, ranging from entry level worksheets to week-long projects covering a sample of the numerous Catalan number situations. A particular focus was ensuring that the students saw that there were bijections taking them from one situation's solution to the other. The week wrapped up for the group when they returned together and discussed how to re-incorporate their ideas into a large-scale, teacher-friendly collection of resources.

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This material is based upon work supported by the National Science Foundation under DMS-0940733 and DMS-1441467. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.