Park City Mathematics Institute
Investigating Geometry
Project Abstracts

Drafts of Project Files (password required)

Triangle Trips: An Exploration of the Pythagorean Theorem
Ana Castro, Jen Outzs, Lou Shoe, Kim Wollard*
Triangle Trips is a project that embraces exploratory concepts that lead to the Pythagorean Theorem. It is a Geometer's Sketchpad file that is designed to be a dynamic tool for the students to study the Pythagorean theorem and related concepts. It is intended for users with some Sketchpad experience.
Constructing Mathematicians through Geometric Play
Janet Meyer, Andrew Shaw, Carol Spice*
The purpose of this paper is to discuss a software-based, constructivist approach to teaching geometry. Software tools free students from the tedium of pencil-and-paper diagrams, allowing them to engage in geometry in a more personal and creative way. In this environment, students can focus on mathematical play and on the type of exploratory thinking mathematicians actually do. Our objective is that students will finish this course with a greater ability to create conjectures and write convincing proofs. We will include discussion about the philosophy and methodology behind the approach, the actual strategies for building the lessons, and the classroom environment.
A Comparison of the Dynamic Geometry Software
Avery Pickford
This is an introductory comparison of four popular geometry software packages, Cabri, Cinderella, Geogebra, and Geometer's Sketchpad. Beforehand, I had some experience working in GeometerŐs Sketchpad, limited experience with Cinderella and Geogebra, and no experience with Cabri. My goal is to give an individual teacher or a school with little or no experience in any of the four software programs a general overview of the functionality and ease of each of the four programs so that they can find the most appropriate software. I first compared platform compatibility and cost. I then created a checklist of functionality, broken up into the following categories: construct, transform, measure, and manipulate functions. I then attempted to build six exploration tasks in each of the four programs to analyze the ease of each. My goal was to create files that can be used in the classroom, but at the same time demonstrate different functionality within the programs.

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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.