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THE MATHWRIGHT LIBRARY NEWSLETTER, Mar 2004, VOL 5, #9
A publication of Bluejay Lispware
James E. White, Editor

The official publication of the New Mathwright Library and Café:

In this issue:

1) See a preview of Interactive College Algebra (a complete Live College Algebra Textbook)

2) Applets and Oranges: Hints for Web Course Development

1) Interactive College Algebra, by Samad Mortabit

Interactive College Algebra is a fresh new approach to the subject that begins with the premise that an interactive web textbook should be designed from the start with an eye to the dynamical structure of the book. The reader interaction is an integral part of the design of the text. It is wedded so seamlessly with the crisp, discursive style of the book, that it appears on every page, as a fluid movement from the voice of lecture and presentation to the Socratic voice of dialogue and inquiry. This is due in no small part to the visual organization of the book itself, in which the "dialogs" blend naturally with the publisher-quality text. But what makes this possible is the functional design of the entire work that orchestrates the movements from one voice to the other.

Such a design is simply impossible in hardcopy textbooks for obvious reasons. And when those books are only supplemented with computer programs, these tend to distract from the flow of the story because they are neither visually nor functionally a part of it. Interactive College Algebra was written and tested over many teaching cycles, both in classroom and distance learning contexts by the author, Professor Mortabit. In all cases, the simple idiom of the Mathwright Microworld Integrated Development Environment made it easy for him to fine tune the dialectic between presentation and function in his developing work. You will see a preview at the Mathwright Library of the finished product.

This book demonstrates the fact that an Interactive Web Textbook is an entirely new, and very promising, medium for teaching and learning. When it is written from the beginning, as this one was, with the dynamics of reader interaction foremost in view, it enters a new pedagogical dimension that both encourages and guides the reader to ask meaningful questions, and provides the tools to help them discover the answers to the questions they pose. It is a genuinely new effort to provide students with the right tools and the appropriate level of discussion that are necessary for a successful learning experience.

Preview Chapter 2 of the new 10-Chapter Interactive Web Course on College Algebra here at the Library. The Chapter headings are:

  1. Real Numbers: A Review
  2. Cartesian Coordinate System
  3. Exploring Functions
  4. Linear Functions
  5. Quadratic Functions
  6. Operations on Functions
  7. Exponential and Logarithmic Functions
  8. Polynomial and Rational Functions
  9. Linear Systems
  10. Introduction to Probability

Each Chapter is divided into several sections. The Preview version, Chapter 2: Cartesian Coordinate System of this book (70 printed pages with 9 embedded explorations) contains the sections:

2.1 The Cartesian Coordinate System
2.2 Graphing Equations
2.3 Exploring Symmetry
2.4 Exploring Lines
2.5 Exploring Circles


Chapter Review
Chapter Project

You may view it here or at the MATH Cafe as a demonstration of this new style of pedaogy. You will need the Library MathwrightWeb Control. The entire text is available for purchase at the MATHLORAN website.

2) Applets and Oranges: Hints for Web Course Development

If you have visited our Microworlds in your browser, you have probably noticed that they are not applets in the conventional sense of that term. While they are written in Java, they are all built on top of a LISP-based mathematics language (Computer Algebra, 2 and 3 Dimensional Graphics, and so on) that gives them an expressive range that it is difficult to support in an applet that downloads in real-time.

The basic difference between Microworlds and Java applets is one of intercommunicability. The various mathematical objects that readers must be able to create in order to have realistic experiences: exact polynomials, functions and graphs, differential equations, matrices, 3-dimensional geometric objects, and other models are related semantically, and a system of Java programs that would use them would have to "talk" to one another. But this means that a "language" has to be available for them all to speak. For us, that language is Mathscript and once you download MathwrightWeb, it is already there, a Java Application, running on your machine. So multi-page Microworlds that may easily run 30 or 40 pages still come down to your browser quickly, because all of the heavy-duty code that is required to interpret them is already on your machine.

A simple example of the need for language intercommunication can be found in our Conservation of Energy Microworld in Chapter 2: Satellite orbits of our new book, Calculus in Action.

Consider the integration of tools required to place your reader in the cockpit of the space shuttle and to allow him to navigate the craft into docking position with a space station in circular orbit over the Earth. He may change the thrust and attitude of his craft with continually updated manual and visual controls like the following:

And has (in the best circumstances) visual contact with his target, realistically presented as a spinning satellite that changes size and relative speed as the shuttle looms closer:

But this is not a video game! The point of the exercise is to teach about Newton's equations of motion, and conservation of energy and momentum. Simply pointing at the satellite and turning on your thrusters will not usually get you there. It is a complex matter of matching orbits (energy and angular momentum) and so the manual controls respond by solving Newton's second-order differential equation in real-time and giving the appropriate visual feedback.

Such an integration of tools is difficult to manage in an applet, especially if on the next page (of the applet), you will use computer algebra in a different way to illustrate the 2-dimensional geometric notion of radius of curvature, and its relation to angular acceleration. The MathwrightWeb Control contains our mathematics scripting language: Mathscript, that can regulate all of the intercommunication that is necessary for the various mathematical objects and screen objects (like the satellite) to intercommunicate. Sometimes data needs to be printed in exact algebraic form, sometimes it needs to be printed to a spreadsheet table, sometimes in needs to be graphed, and sometimes it simply needs to move a sprite or a 3D model around. All of these things happen within the context of our language. And for the forseeable future the language will have to be on your machine, because to place it on the server would spoil the realism of the interaction. It would "break the spell" that might capture the learner's imagination.

The Whorfian hypothesis in linguistics, that the language you use constrains the ideas you can have, has an analog in Web development. The mathematical stories that Mathwright authors can tell are enriched by the dual possibilities of orchestrating many tools, and of reusing those tools, from one story to the next, without having to worry about the overhead of downloading the entire mathematical engine each time a reader wants to interact with it in his browser.

This brings us to another difference between Mathwright Microworlds and applets. We realize that a browser is not necessarily an ideal place to think hard about mathematics. So our Microworlds are ambidexterous. Readers may download any Microworld and add it to their permanent collection on their own computers. When they then read it offline with our free Mathwright32 Reader (which is an application that runs independently of the browser) they do not have to be connected to the internet, and they usually experience somewhat peppier performance than in their browsers. Otherwise, the Microworlds are identical to their online versions.

Finally, a third difference between Microworlds and applets is this. Many of our new Microworlds use a feature called Compiled HTML Help to tell the story within the Microworld. If you looked at the College Algebra Text in the first article, you will have seen beautifully formatted, publisher-quality mathematical text on the web pages, with the Microworlds embedded within. Our Text Version of Calculus in Action is similar. But compiled HTML Help provides the same presentation within the Microworld. It has two advantages. The first, is that, being compiled, the mathematical expressions and formulas appear instantly on the pages (there is no need to download gifs -- which can be numerous). And the second advantage is that, since they do not depend on the web, this information is equally available offline in Mathwright32 Reader. But notice, each compiled help page is an HTML page, and as such has full access to the internet, anyway, so you can create links in offline Microworlds to web pages anywhere. Your machine automatically goes online to access them.

What makes all of this intercommunication possible: the use of OpenGL 3D graphics, Access Data Tables, Compiled HTML Help, the ability to "plug" our Microworlds into browser environments like WebCT and BlackBoard so that they integrate seamlessly with the other content, and countless other options, is our use of ActiveX controls, and generally, of Microsoft's Component Object Model (COM).

That model, like the new model that we have recently adopted, called Microsoft .net, were designed to make it possible for separate programs to "talk" to one another. We believe that this is important for the development of sophisticated web applications that can support a wide and rich variety of reader experiences. Our decision to implement our Microworlds in ActiveX controls reflects a design choice that, after two years experimentation with Java Swing, we felt compelled to make. While we built a Java 2 prototype of our Microworlds in 1999, we decided that, in order to achieve a simple WYSIWYG author interface to create learning environments that will not distract students from the mathematical story, we need the full attention of a single compliant and mature operating system.

The Microsoft Windows operating system is the canvas on which we have chosen to paint. Like a Java Applet, a Mathwright Microworld is designed to elicit and invite reader questions by presenting a simple User Interface. But a Microworld has the power and range that a generic applet can seldom achieve, and this makes possible a wide variety of reader experiences. It invites students to play. If you would like to take a closer look at what our authors, all over the world, are up to, please visit our service page.


James E. White, Ph.D.
Library Director