Why does the Web need a Mathematics Library? Sometimes the idea of a Library conjures up images of a dark and dusty place where ancient and venerable wisdom is stored in archives like the lost scrolls of the despoiled Library of Alexandria. And these images may also resonate with the ideas that many people have about mathematics itself! Who needs it?
But it is more likely the case that, unlike a tomb, the Alexandrian Library was an Institute for Advanced Study, where people came together to discuss and debate the pressing problems of commerce, politics, religion and philosophy of the day, and, like a University, it was a good place to learn what had been discovered.
And mathematics has always been more than the dessicated specimens that reside on the pages of the books that our rituals require us to read. Mathematics is the thing that is born in each of us, when we see clearly that it MUST be so. It is the thing that gave our thought wings when we were children, and that we loved for its clarity and certitude.
Something however is lost in that forced march we take in our school days down all the avenues of myriad facts, strategies and computational conventions that have been discovered over the centuries. When the mathematical discovery is no longer ours, and when we no longer feel AHA! but rather a resigned OK, then the subject has lost its magic. And we have become mere spectators, passing quickly through the colonnaded gardens of discovery, rather than stopping to play, as we did as children.
There is really no solution to the problem that all genuine knowledge is acquired through sometimes painful adjustment. The mathematical conventions we teach in the schools are well worth learning, if only because they contain some of the finest achievements of our culture. But we should keep an open mind to the fact that participation and gratuitous play are very important for understanding, and that since each of us learns at his own pace, we are not always ready to pause and reflect on new ideas, as we did unhesitatingly as children.
If a Web Mathematics Library simply replicates the static configuration of facts available in text books, then there really is little need for one, except perhaps that it puts the information more readily at hand through hyperlinks, and, so, organizes it in a convenient way for the reader.
The Mathwright Library, on the other hand, aims to help learners participate in their study of mathematics by exploring a new dimension of mathematics education. Our Microworlds and WorkBooks are dynamic and responsive, and they allow the reader to play and to ask questions at her own level of understanding. In Marshall McLuhan's words, the medium we develop is "hot" in the way that static texts cannot be.
Our books add dynamic simulations, under reader control, to explanations in order to help the reader visualize new constructions and concepts, and this naturally elicits new questions from the reader herself. It is with her own questions, and only with her own questions, that she may feel the AHA! behind the explanation.
The Mathwright Library is a collection of interactive, electronic mathematics and science "WorkBooks" and "Microworlds." Members of the Library may download them freely during their subscription period. These WorkBooks have been developed by College and Secondary School mathematics and science teachers (and sometimes by their students) since 1991. Initially funded by the National Science Foundation and supported by the IBM Corporation, it has been in place on the web since 1995.
This Library is an experiment in computer-based pedagogy. Its aim is to invite students to come into the world of mathematics and science through structured Microworlds and WorkBooks that will allow them to ask their own questions, to read at their own pace, and to experiment and to play with those topics that interest them.
Microworlds are Mathwright WorkBooks that you can read in your browser. The browser must be ActiveX enabled, and you should download the plugin, our new MathwrightWeb ActiveX Control first in order to enable your browser to view them. You may read about this new technology for Mathwright here.
Briefly, MathwrightWeb and the Mathwright32 Reader are our new 32-bit Java version of Mathwright, designed to operate both in Windows 95/98/Me and in Windows 2000. Mathwright32 Reader is the application version of the program that runs independently, and does not use the browser or require you to be online to read a Microworld. MathwrightWeb is a plugin for the browser.
If you are new to these ideas, we recommend you read about MathwrightWeb, and then download the MathwrightWeb ActiveX Control, and select some Microworlds on the Free Stuff page to view.
Each Mathwright WorkBook attempts to place the player, the learner, in the driver's seat. All WorkBooks have been created by teachers at the Undergraduate and Secondary levels, with the exception of a few in the Young Players category that were created by students. Readers may contact the authors of our WorkBooks, if they have questions, through the email link on the Title Page of each WorkBook or Microworld.
In order to encourage active exploration, the WorkBooks are designed (to the limits of our ability) to be easy for students to use, but at the same time, to be truly interactive. The computational environment recedes into the background so that the mathematical or scientific topic of interest comes under the spotlight.
This means that students may often ask questions or explore ideas that even the author of the WorkBook did not anticipate. It requires an expressive and flexible reading environment. So we place that environment, an object-oriented computer algebra and graphics language, on the player's machine. It is called the Mathwright Library Player, or, in its 32-bit form, MathwrightWeb. The Mathwright Library uses the web, not principally as a repository of "information," but as a source of "experiences."
Thus, the Library is the web conduit to a collection of interactive explorations that are brought to the Player's machine. Once on the Player's machine, each WorkBook has full access to the language that will bring it to life. Players create structure as they read Mathwright WorkBooks, and that structure requires the full services of a complete language if the players will be allowed to transform and compare what they build, view it from different viewpoints (i.e. algebraic and geometric) and to ask their own questions.
Also, players read at their own pace. This is true even for the browser version, MathwrightWeb. Our free Mathwright32 Reader may read Microworlds brought down by MathwrightWeb offline, and it is a good bit peppier than the browser version. Genuine learning requires time and reflection. It is much more natural for them to print the documentation that accompanies each WorkBook, read it, and then to experiment and play on their own (or on lab) machines, rather than to be required to log in to the internet each time they want to explore another WorkBook.
Library WorkBooks and Microworlds are hypertext documents. They vary in size from 1 page to 45 pages, or more. Most of them look and feel like web pages, and that fact leverages the experience that students already have with the web. Since our Microworlds are embeded in web pages, authors may provide all the rich hypertext documentation that HTML allows for them. But within our WorkBooks and Microworlds, students will be able to do very interesting and exciting things. They may place a satellite into geosynchronous orbit, launch a space shuttle, create an airline routing system and ask it to find routes satisfying conditions they set, or ask for step-by-step explanations as the program solves an equation they create.
They may, in fact, teach the program how to implement new functional identities (such as the Pythagorean identity) to simplify an expression or to solve an equation. They might define a differential operator such as the Laplacian, and then draw the level sets of the Laplacian applied to functions of their choosing. Or they might define a "curl" operator and draw integral curves of the curl of a vectorfield they choose.
An important fact about authoring in Mathwright is that all Library WorkBooks are available to be modified and extended if an author wants to improve one. Object-oriented Mathwright Author 2000 allows authors to "cut and paste" whole pages of a WorkBook, or individual objects and scripts. Many authors base their own new WorkBooks on existing Library books, cutting and pasting objects and pages as they see fit. This is OK. The authors of Library books provide their WorkBooks as "clipmath" and give their permission to other authors to modify those books if they desire.
Of course, courtesy dictates that authors acknowledge their sources. Thus, the Library is an evolving and dynamic entity, not a static one. We have also attempted to make it easy for teachers or students to find what they want in the Stacks. One may search the stacks in a variety of ways to locate items of interest. The Library is continually growing, and while it presently has holdings in a wide range of topics, we hope in coming years to enrich and enlarge these holdings to fill out many of the lacunae that still exist. For that, we will depend on teacher/authors to build ever more exciting and engaging WorkBooks.

We have archived our earlier newsletters, and you may read them here:

    - James E. White, Ph.D. , Library Director,
    author of this website, Mathwright Author 2000,
    Mathwright MindScapes, and MathwrightWeb

( Back to top )

(c) Copyright 2000 by Bluejay Lispware

Zoom in

About Mathwright

About the Author