## Investigating Geometry Summary

### Monday - Friday, July 7 - 11, 2008

Monday, July 7
Art spent the one hour going through through an overview of The Geometer's Sketchpad®. He showed everyone much of the functionality, and talked about the broad view of constructions based on paper folding, compass/ruler, and technology.

Tuesday, July 8
Used Sketchpad to explore and create different conics (parabolas, ellipses, and hyperbolas) using loci.

Thursday, July 10
Spent some time brainstorming different projects possibilities. Ideas included:

• 3D volume and surface area
• Transformational geometry
• Tessellations
• Scale factors
• The box volume problem
• Relationship between perimeter and area
• Using Sketchpad to build nets for polyhedra
• Using GSP as your axiomatic system
• Pythagoras Unplugged (CMP)
• Points of concurrence
• Compare/contrast different geometry software (Cabri, GSP, Cinderella, Geogebra, etc.)

Friday, July 11
Continued working in smaller groups of projects.

The middle school partnership in the geometry working group is working on developing graphical representations of the Pythagorean Theorem in Geometer's Sketchpad. Two of the members are working on several proofs of the theorem. Two of the members of the group are working on developing pages in Sketchpad that is the preperatory work leading up to the proofs. Some of these ideas are coming from the Looking for Pythagoras unit in CMP.

The other group is working on a constructivist approach to Geometry using GSP (and maybe other software). The group began working on a template for overarching questions in a geometry class. A few of the resources that were looked at include: A Euclidean Geometry course using GSP: http://www.calvin.edu/~venema/eeg/eeg.html

An article addressing the "big picture" discussion we've been having: http://investigations.terc.edu/library/bookpapers/geometryand_proof.cfm

The use of GSP in a Geometry classroom: http://academic.sun.ac.za/mathed/MALATI/Files/future.pdf.

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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.