Sketchpad 3 is the largest single upgrade to The Geometer's Sketchpad program yet. It reflects both our findings in four years of (NSF-sponsored) research into how the original Sketchpad was being used in classes across the country (and more recently: the world), as well as the shifting nature of geometry in today's math classroom. As the role of the new Standards has begun to shift from that of elegant rhetoric to an actual foundation for classroom action, so too has the purpose and nature of geometry and geometry education. In addition to being one of the traditional math disciplines most readily adapted to some form of "laboratory" practice, geometry is one of the most versatile in its connections to other mathematical subjects, to the sciences, and to general logic, analysis, and reasoning. Sketchpad 3 delivers on all of these fronts.
Here's a preview of what you can expect:
- Improvements in the program's ease of use. This encompasses a variety of enhancements, from simplified commands to continuous visual, textual, and tactile interface feedback (no more questions: "how close is 'close enough?"), to the ability to configure the program's geometry menus to a level appropriate to your students, to specific functionality aimed at special populations (a keyboard interface for people who aren't agile with the mouse; "large text" option for the vision-impaired and for presenters using inadequately-lit projection devices), and so on.
- Script Tools. These allow you to turn Sketchpad scripts -- geometric constructions which you've recorded -- into full-blown interactive drawing tools. Are your students interested in the applications of geometry to architecture? If so, they can augment the standard Compass and Straightedge tools with tools to draw Ogee arches, to calculate building-facades in the Golden Ratio, to add fleur-de-lys and quatre-foil ornamentation...tools which they've authored themselves, using Euclid's tools to define Le Corbusier's, and then Le Corbusier's to define their own. Are you instead interested in introducing them to the Poincare disk? Then turn off the Construct, Transform, and Measure menu, and give them a custom-built microworld based on script tools which draw hyperbolic lines, segments, bisectors, etc.
Script tools extend the geometric vocabulary of the program indefinitely, by allowing you, your students, or other Sketchpad curricula developers to define new easy-to-use primitives and add them to the program transparently.
- Analytic geometry. In addition to being able to create coordinate systems, grids, and axes, and measure coordinates and equations of objects with the coordinate system, Sketchpad 3 lets you plot measurements and calculations--from whatever source--directly onto your coordinate system. Because Sketchpad's dynamic, every calculation is an equation, which you means you can not only move from geometry to algebra, but from algebra -- or trig, calculus, physics, personal finance, what have you -- back to geometry.
The program inherently supports both rectangular and polar coordinate systems. But by allowing you to plot -- and dynamically vary -- any calculation or measurement, you can readily model other coordinate systems: complex, conjugate, etc. In addition, coupled with the program's ability to construct loci, the ability to plot calculations allows you to define new objects analytically: conics, quartics, Bezier and B-splines...if you can come up with an analytic definition, Sketchpad can create it. (You can use regular geometric measurements, coordinate values, and the coefficients and parameters of measured equations as terms in your calculations.)
- Mathematical notation. In the days when computer displays were limited to text characters, and when processors ran as quickly as the last drops of ketchup from its bottle, symbolic notation like "sqrt((dx^2)+((dy^2))" was, if not acceptable, a necessary inconvenience. Since that time, such notation has been foisted on the math classroom by the calculator industry largely without good reason. Sketchpad 3's notation -- for measurements, calculations, geometry and algebra -- is the same you'll find in your textbooks.
- And other stuff. Arcs, arc segments, sectors, and loci round out the program's built-in constructions; greater control over labeling lets you easily recreate existing diagrams or develop your own notation; animation is more powerful, transformations and fractals can be computed by any calculation, the calculator has received a face-lift, etc.
We've also significantly improved the dynamic geometry engine (short version: drag anything, anytime), extended the on-line help, and greatly increased the program's ability to serve both as an exploration environment, for students and researchers, and as an authoring environment, for teachers and curriculum developers.
Sketches, scripts, and web pages by Bill Finzer and Nick Jackiw.