THE
MATHWRIGHT LIBRARY NEWSLETTER, September
2001, VOL 3, #5
A publication of Bluejay Lispware
Special Teachers' Issue
James E. White, Editor
The official publication of the New Mathwright Library and Café:
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In this issue:
1] Where
have we been?
2] Beyond Applets: Mathwright Microworlds
3] Some ways the Library can help you put active Mathematics on your own web
pages
This
special issue is directed to teachers and instructional technologists, especially
those interested in teaching mathematics on the web. It introduces and describes
a new technology developed at the Library, but must treat it superficially here.
Visit the Library for details. If this seems overly technical, or if it came
to you by accident, please read the Student Issue which can be found in Hypertext
form from the Home Page of the Library.
1] Where have we been?
Some
of you may be wondering why you have not received a Newsletter since last April.
You will see the answer when you next visit the Library. We have been developing
the new 32-bit Java version of Mathwright called MathwrightWeb, and have
begun translating many of the WorkBooks in the Stacks into the new, expanded
and enhanced form.
We
call these new WorkBooks at the Library: Mathwright Microworlds. We will
discuss this new technology and some of its implications for teaching on the
web in the two articles below. But the introduction of MathwrightWeb has had
some collateral consequences for the way that the Mathwright Library is organized,
and we will discuss those here.
Perhaps
the most important change in our organization is this. All of the Players that
read Mathwright WorkBooks or Microworlds are now free downloads. They may be
freely downloaded onto any (Windows™) machine, whether or not the user
is a member of the Library. Consequently, there is no longer a Player 2.1. Simply
download Mathwright Library Player 2000 instead. If you already have Player
2.1 installed, you may want to uninstall it first, but that is not necessary.
The two other principal Players for our new Microworlds, MathwrightWeb and Mathwright32
Reader, (discussed below) are also free downloads. They may all be downloaded
from our Free Stuff page.
These
Players will give readers free access to the 5 Demonstration WorkBooks, and
to 5 additional Demonstration Microworlds at the Library. For full access to
the 170+ WorkBooks (including 11 new Microworlds) one must be a Library member.
In
the next few months, we will be translating all of our WorkBooks to Java, so
that they will be available to members in two forms: as WorkBooks and as Microworlds.
The Microworld forms of our WorkBooks are in general more expressive and colorful,
and mathematically more perspicuous and powerful than the earlier WorkBook forms.
Also, MathwrightWeb is optimized to work as well in Windows 2000 as it does
in Windows 95/98/Me.
Another
consequence of our introduction of Microworlds is the removal of Lava
from our website. Lava served us well as a prototype, but has been completely
replaced by MathwrightWeb. The latter is much faster, friendlier, and is far
better tuned to the Windows operating system than Lava was.
Finally,
we will be de-emphasizing our 3D Graphics program MindScapes, because, in the
next version of MathwrightWeb, we will have almost all of its functionality
in the graph3D windows of our Microworlds. This version of MathwrightWeb should
appear late this year, or early next, and, of course, will be free. We will
then begin translating some of the gorgeous 3D animations and simulations of
MindScapes into Library Microworlds, also.
That
said, let us tell you what Microworlds are, and where you will find them at
the Library.
2] Beyond Applets: Mathwright Microworlds
Mathematical
applets are a somewhat paradoxical solution to the problem: How to bring interactive
and live mathematical learning environments to students on the web. They are
paradoxical because, while they make use of some of the most advanced and sophisticated
technology available to the web, and they harness the power of a truly elegant
and powerful language: Java, they have placed the creators of these applets
in the prehistoric conditions of the early '80s, where programmers had to build
pretty much everything from scratch. So we see a proliferation of dedicated
"appliances" on the web, each devoted to the illustration of some particular
mathematical point, with very little - if any - communication between them.
Of
course, it is the virtue of Java that programmers can easily develop reusable
class libraries that make possible an object-oriented approach to the development
of mathematical applets - building them from components. But very few teachers
have the time or the inclination to use Java in this most elegant way to place
mathematical explorations on their own web pages. So they (and their programmers)
often have to "reinvent the wheel" again and again to do such simple things
as parsing input expressions, or drawing graphs.
What
was needed was a powerful Java class library that would integrate all the mathematical
components (computer algebra representation, parsing, and simplification of
algebraic expressions, rational, complex and decimal number types, functions,
vectors, matrices, sets, differential equations, and so on) with the objects
that display them (graphing windows that can display sprite animations, data
tables, windows for displaying mathematical formulas correctly, as well as matrices,
etc.). And these must of course be tied to built-in programs that handle such
tasks as solving equations, differentiating and comparing algebraic expressions,
solving differential equations, or inverting matrices, and so on. To be effective
and useable, such a class library needs a high level language, so that authors
can actually turn their ideas into learning environments that students can use
easily.
MathwrightWeb
is our class library, and MathScript is our high level mathematics scripting
language for manipulating it. With these tools, we create Mathwright Microworlds,
which are multipage interactive learning environments (like Mathwright WorkBooks,
but much more powerful) that run in the browser. In a sense, MathwrightWeb is
like an applet that can "play" an infinite variety of interactive lessons and
stories on web pages.
To
be more specific, however, MathwrightWeb is a Java ActiveX Control that
resides on your computer. So the language (the class library) does not have
to be downloaded for each Microworld that it reads - as Lava did. It is always
ready to go, and since the Microworlds it reads are cached on your machine,
it only ever downloads the actual books once. It is better than that, but this
is not the place to discuss the differences. See the About
MathwrightWeb page at the Library.
What
this means from a teacher's point of view is that students who install MathwrightWeb
in their ActiveX-enabled browsers may read and do mathematics in their browsers
by visiting any web page that displays a Microworld.
But
we realize that a browser is not necessarily an ideal place to think hard about
mathematics. So we give students the opportunity to visit any Microworld on
the web with MathwrightWeb, and to create what we call a "Disk Version" of the
Microworld on their machine. This is usually much faster than visiting the Microworld
in Applet mode anyway, because the Microworld comes across in compressed form
and is automatically decompressed on the client machine.
Once
this is done, the student may continue to read the Microworld at any later time
with our free Mathwright32 Reader, which is an application that runs
independently of the browser. Thus, they may later read these Microworlds offline
if they choose to, without having to be connected to the web at all! They need
only go to the web once, to get the Microworld in the first place. Mathwright32
Reader is actually quite a bit faster than MathwrightWeb (The Java virtual machine
it uses seems to be peppier than the one the browser uses, but that may change.)
And in this mode, using Mathwright32 is essentially the same as using the Mathwright
2000 classic with our WorkBooks.
Our
Microworlds represent one solution to the interesting question raised at the
beginning of this article: How to bring interactive and live mathematical learning
environments to students on the web. Please download MathwrightWeb from Free
Stuff, read the instructions on the About
MathwrightWeb page to be sure your browser is ActiveX enabled, and try it
out for yourself. You needn't be a Library member to read our Demo Microworlds,
but we hope to convince you to join.
3] Some ways the Library can help you put active Mathematics on your own web pages
If
you have asked yourself some of the following questions, the Mathwright Library
may have an immediate answer for you.
Our
authors, all of whom are also teachers of mathematics, chose Mathwright in the
past as the vehicle for finding answers to these questions for themselves. Of
course, Mathwright provided those answers before the Internet blossomed, but
it was developed to provide the same point-and-click, hypertext and object-oriented
intuitive interface with which students have become familiar in recent years.
During
the last eight years, we have developed and refined over 170 multi-page books
for the Library, and every one of them will, in the next few months, be translated
to our Microworld format. Our free plugin,
the Java MathwrightWeb ActiveX Control (always available for download
at the Free Stuff page) will make it possible
for students to explore the themes of our books while they remain in their
browsers in an active way. They can do this at their leisure, at their
own pace, and, in the best cases, at their own level of understanding.
But
you may ask, "What does this have to do with me and my web course?"
There are at least three answers to that question.
First Answer:
For
those who do not program and do not plan (or have the time) to program, we can
give you what you need to place the Microworld version of any Mathwright
WorkBook currently in the Library on your own web page. You must be a member
of the Library to select this option. You then submit an email
order for a 1-year lease of a Microworld for your website. You
may specify the size and location of the Microworld in your HTML.
If
the Microworld is currently available in the Library only as a Mathwright 2000
WorkBook, then we will create the Java version and post it at the Library for
your approval. This will take a day or two from receipt of your order. If you
approve the newly posted Microworld, then we will email you a few lines of HTML
that will put the Microworld on your web page.
Aside
from inserting this HTML in your web page, absolutely no programming is required
on your part. The insertion (a few lines) is very easy and, with our instructions,
should take only a minute or two with a text editor.
Your
readers may download the free MathwrightWeb control from the Free
Stuff page to view the Microworld in your web page. You may of course add
any documentation or commentary to your page that you feel would explicate the
exploration. They need not be members of the Library, and there is no charge
or check-in at all for them to view your Microworld.
Second Answer:
If
you would like to place a Microworld on your web page that has no counterpart
among the WorkBooks and Microworlds of the Library, you have two options:
If
your idea differs only slightly from a current WorkBook, then you may consider
submitting the idea to us at our suggestion page.
We will be pleased to quote you a consultation fee for creating the Microworld
you describe and making it available for you to license. Of course, the estimate
will depend on the nature and size of the job.
On
the other hand, if you would like to try your hand at either modifying a current
WorkBook, or creating a new one from scratch, then you might like to purchase
the Author program: Mathwright Author 2000,
along with the Web Author Upgrade.
Mathwright
Authors who own the Web Author Upgrade will have everything (including the instructions)
they need to post their Microworlds at their own website. This includes a free,
redistributable version of MathwrightWeb that they can distribute to their readers,
thus avoiding any mediation at all by the Library.
Third Answer:
Perhaps
the simplest option for faculty is to obtain a 1-year Institutional
License. It provides a license for general use for one year either on the
Local Network at a school, library facility, or other educational institution,
or on the students' private machines..
When
you purchase the license, you receive a login password that will give any user
of the network access to all of the WorkBooks and Microworlds of the Library.
This will allow you and your students to visit the web library on the network
and download any WorkBooks or read any Microworlds they choose. The license
also allows network users to read the WorkBooks at home, or on non-networked
campus machines.
James
E. White, Ph.D.
Library Director