Geometrical Concepts from Constructions, Models, and Investigations Summary

Wednesday, July 3, 2002

We have generated a list of topics we would like to work on. These include:

  • Philip Mallinson's notes
  • Troy's project from 2001
  • Joyce's project from 2001
  • Analyzing the tee shirt
  • Non traditional constructions of conics
  • Area and volume of a sphere
  • Geometer's Sketchpad

In working with Philip's first lesson (that we worked on yesterday), we came up with some hints, additions, ideas to include with it. These are:

  1. a teacher's suggestion to review angle measures of an n-gon
  2. a hint might be something like: Suzanne immediately checked the problem by using her calculator while Steve grabbed a handful of cardboard shapes.
  3. we could include background information such as links to sites with background information (ones already available)
  4. not too much preliminary stuff
  5. nets for some of the shapes so participants could generate manipulatives
  6. photographs of people working on problem or models
  7. java scripts for sketchpad to have on the web site

Then we worked on Philip's second lesson on "Tesselating the Plane with Regular Polygons. Since we didn't have MAT tiles, we spent most of the time analyzing the picture that includes 4-gons, 5-gons, 6-gons, 7-gons, and 8-gons. We talked about how many of the shapes could be regular and which could be regular and which could not and under what conditions.

Last, we again spent some time with Troy's project using his physical models that he had brought in.

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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.