Visualizing Algebra Using Dynamic Geometry® Software

Abstract

Grade Level:  9-12 Abstract: In the last decade interactive geometry software has established computer-based visualization can bring value to students' conceptual understanding of geometry.  The developers of The Geometer's Sketchpad, including the author of this talk, have articulated a set of characteristics of interactive geometry environments as enabling: * The interactive and continuous manipulation of geometric shapes and constructions; * The rapid expression of mathematical relationships; and * The tangible experience of their mathematical consequences. If, however, one substitutes the words "mathematical objects" for "geometric shapes and constructions" in the first principle, one gets a new set of principles not specific to geometry: * The interactive and continuous manipulation of mathematical objects; * The rapid expression of mathematical relationships; and * The tangible experience of their mathematical consequences. Although usually thought of as a tool for geometry, with the addition of non-geometric dynamic objects and on the basis of the principles above, The Geometer's Sketchpad has become an excellent tool for visualization across the curriculum, including algebra.  In his talk, the speaker will share new algebra activities that deepen students' conceptual understanding of algebraic domains using The Geometer's Sketchpad.  Unlike most activities done with graphing calculators, the computer software permits students and teachers to interact directly with the mathematics in its visual form, often unmediated by algebraic abstraction, to deepen their mathematical understandings. Note to organizers: Feel free to change the strand indicated in my registration form if you think this talk would better fit in a different strand other than "Mathematical Research and Teaching Using Technology."