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Topic: Please recommend geometry software
Replies: 6   Last Post: Apr 3, 1995 1:07 PM

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Nicholas R. Jackiw

Posts: 65
Registered: 12/3/04
GSP 3.0 (was Re: Please recommend geometry software
Posted: Mar 17, 1995 5:08 AM
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EASILY-INCENSED-READER-ALERT: I work for Key Curriculum Press, and though
I don't speak for them in this post, I shamelessly plug their products.
If you find such blatant self-promotion an unseemly use of the Internet,
please stop reading this article now. Thanks, Nick.

In article <>, (Art Mabbott) wrote:

> Recommendation #1: THE TEXT.

Absolutely; this is certainly the top priority. It's a shame that
textbook development cycles are governed largely by state adoption
cycles and other marketing concerns: it means that the average life of a
textbook is far longer than the average life of any particular version
of a computer program. This in turn makes it difficult to find a good
working text/technology solution, with up-to-date ingredients in both

While Sketchpad was originally developed outside Key Curriculum Press,
Serra's book was my model during early Sketchpad conception for how
geometry >could< be taught, if not how it >should< be. Since Sketchpad's
become commercially associated with Key Curriculum, the company's
_Exploring Geometry_ book of Sketchpad activities has a detailed
correlation of computer investigations to those found in Serra's
_Discovering Geometry_ book.

> Recommendation #2. Dynamic software. Again the choice is simple.
> We have Geometer's Sketchpad on our macs in a schoolwide lab.
> It is great!!

Thanks! Teachers'--and more importantly :-), students'-- enthusiasm for
it keeps us working hard on Sketchpad. No matter how "great" many
people find, there's always lots more that can be students and
their teachers constantly tell me!

> GSP is supposed to be coming out with a new version (3.0) this
> spring and I have no idea what bells and whistles it will
> contain...

In that this seems to be public knowledge these days, and in that we've
finally made our "official announcement" (in a mailing to Sketchpad 2.x
customers last week), I suppose I can spill the beans here about
Sketchpad 3.0:

Sketchpad 3.0 will be released at the NCTM national meeting in Boston
next month. If you're there and have a chance, please come to the User's
Group Meeting--which Bill Marthinsen announced in this forum previously--
for a demo and more information.

For those of you who are upgrade-happy, the general terms are the same
as in our previous upgrade: if you have a site-license, Key Curriculum
will send you the new version for free next month. If you have a single-
user version or a ten-pack, you should be receiving a mailing soon, or
have already received it, that offers an inexpensive upgrade (I think
it's under $30) and a discount on a site-license. For new users, the
price is the same as previous versions. You'll have to call Key
Curriculum for specifics.

Sketchpad 3.0 is the largest single upgrade to the 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
have 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 3.0 attempts to
deliver on all of these fronts.

Here's a preview of what you can expect:

(Because I'm writing this, instead of Key's marketing department, I get
to present its features in the order >I< think they're relevant.)

- 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.

However, since you're reading, I assume
you already find programs like Sketchpad relatively easy to use, so
I won't dwell on these improvements more than this.

- 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 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 3.0 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 co-
efficients 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 3.0'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

I will post a demo version here on the forum shortly after the NCTM
meeting. (I'd post one now, rather than all this verbiage, but it
won't be ready til early April.) Again, if you're in Boston and have
time, please come to the User's Group meeting; if you're in Boston
and >don't< have time (I know that feeling), stop by the Key booth
for a personal demonstration.


Nick Jackiw
"The Sketchpad's Geometer"

Nick Jackiw
Key Curriculum Press, Inc.

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