Exploring Discrete Mathematics Summary

Monday - Friday, July 14 - 18, 2008

This week, the Catalan numbers subgroup continued to edit the combinatronics project submitted by the members of the 2005 Discrete Math Working Group by rewriting some of the explanations, teacher notes, and tasks included in the project. Much time was spent developing appropriate tasks for the intended audience as well as the solutions to these tasks. It was decided that the level of mathematics from the original project was not appropriate for secondary school students. After much effort, the revised project will be more accessible for the intended audience and teachers will find the revised project a more reasonable accommodation within the courses they teach. Brian presented an expose on a further tie between Catalan numbers and sub-diagonal restricted lattice paths which seemed to strengthen the intended math objective of the project.

The Sicherman dice subgroup developed Day 1, Day 2, and Day 3 activities for the alternate dice project using generating functions. It was determined that the issue of technology available would greatly determine the route that teachers would use in implementing this project in their courses. In addition to teacher notes, a special technology notes file was developed to assist teachers in creating an Excel file that would generate sample space tables, frequency tables, and distributions. Further work needs to be spent on finalizing the Day 3 activities and writing solutions to the tetrahedral dice part of the project.

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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.