Exploring Discrete Mathematics Summary

Monday - Friday, July 9 - 13, 2012

The Discrete Mathematics group spent the second week working on their projects.

The Voters (Carl, Debbie, and Peter) have set up a series of lessons on voting/elections. The unit contains data for teachers to use and templates for self-gathering data. They are still working on a Powerpoint demo for teachers to use in the classroom. Debbie has put together the templates for teachers and the teacher's notes. Carl has written the reflection/final project. Peter has come up with the data and started the Powerpoint demo. This unit-long project is nearing completion and the group anticipates being finished on Tuesday.

The Geometers (Shaffiq, Aziz, and Carol) continued working together and independently to weave lessons using discrete math dissections throughout the geometry curriculum. They are focusing on area, Pythagorean theorem, and volume. Careful attention is being paid to making lessons accessible and sophisticated enough that students will be led naturally to understanding the complexity and beauty of dissections as well as the necessity of generalizability and rigor, and therefore, proof. Aziz has worked almost independently to develop a lesson on the dissection of a cube and the derivation of the formula of the volume of a pyramid, through dissections. In his sections students will make three-dimensional objects and consider the dissections more abstractly. Cavalieri's Principle will also be part of the understanding and proof. Carol and Shaffiq worked closely together with Philip to understand how to help students dissect two smaller squares to construct one larger square in order to be prepared to discover the Pythagorean Theorem. The Exeter Math 2 curriculum, CME Geometry Textbook, and the book "Trimathlon" have all proven to be good resources.

The Mappers (Nadine, Amanda, and Rachell) have created some activities for lessons on map coloring. They are still working to complete the tasks that they outlined last week.

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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.