Visualizing Algebra
Using Dynamic Geometry® Software
Steven
Rasmussen mkolota@keypress.com Publisher Key
Curriculum Press USA
Abstract
Grade Level: 912 Abstract: In the last decade interactive
geometry software has established computerbased 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
nongeometric 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."
