Connecting Algebra and Geometry through Technology

The National Council of Teachers of Mathematics (NCTM) Vision for School Mathematics invites us to "Imagine a classroom, a school, or a school district where all students have access to high-quality, engaging mathematics instruction." Our goal in writing this book is to provide examples of how a symbolic geometry system, Geometry Expressions, can begin to make this happen. Geometry Expressions provides a playground where students can discover their own mathematics. They will begin to see mathematics as something that is created, not just a set of facts made up long ago. Once students take ownership of their mathematics, they will be more apt to "work productively and reflectively, with the skilled guidance of their teachers." The graphical, interactive nature of Geometry Expressions brings life into a field that might otherwise seem irrelevant. The symbolics embedded in Geometry Expressions offer an algebraic view of the mathematics in concert with a geometric view, blurring the artificial line between the two. The smooth interface between Geometry Expressions and Computer Algebra Systems (CAS) adds another powerful resource for solving problems. These technologies can work together to change the way mathematics is done, in the same way that technology has changed the way architectural design is done; with computers managing the details while humans create the grand vision. The units presented in this book are a jumping-off point for using Geometry Expressions in the classroom. Use the units to gauge the potential of this powerful software, and as a guide to applying Geometry Expressions in your own classroom. We trust that you will enjoy using the units and the software.