As you have probably guessed, a Mathwright combines the dramatic talents of a playwright, the imagination of a teacher, and the insights of a mathematician to tell mathematical and scientific stories on the magic stage of your computer screen. Unlike traditional plays, these stories are dynamic and participatory. They cannot really be appreciated in a passive way, but each player must actively unfold the drama for herself. In this way, Mathwright WorkBooks differ from traditional texts. Indeed, this is one of the giant steps that the digital age promises to take beyond Gutenberg – the opportunity to create for the player (once the reader) entirely new experiences that bring her into a world not of sight, nor of sound, but of imagination and of ideas.
Of course, the most enduring portal to the Great Ideas will always be the stories the Masters themselves told in the traditional way. The lively imagination of a Galileo, a Newton or Leibniz, of a Poincare, or a Bohr or Einstein lies in the quality of their thought as they presented it to us in their words and works. Those words were meant to be savored carefully and digested slowly. The digital age can offer no Royal Road to that terrain.
But teachers know that there are many simple preparations to be made, obstacles to be crossed, many wrong turns to be taken and corrected, before a student can even glimpse such lofty terrain. By creating an environment in which each student can ask her own questions, the Mathwright offers an alternative (but not a substitute) for traditional texts.
A simple example of this may be found in the Quadratic Functions WorkBook, where a student may graph a quadratic function that is created for her, and may watch the program solve the corresponding equation. But she may also change the function to see how that affects the graph, and how it affects the solution.
Another example is in the Bernoulli Trials WorkBookl where a student can experiment with the “Law of Large Numbers” or with the Binomial Distribution, by setting the success parameter, and experimenting with random trials.
A final example here is to be found in the Modeling Populations WorkBook of the Differential Equations Set where students can set the parameters for various models of 2 population systems (predator-prey, competing species, cooperating species, and so on) and can set initial conditions to see what each model will predict.
Examples of WorkBooks of this type are common in the Mathwright Library. The interesting question is: How do they get there? The simple answer is that teachers create them. I did not say programmers, or graduate students, or elves that work in the night. I said: teachers. Most teachers are inclined to think that they have to accept and use what is created for them if they are to step beyond Gutenberg in the classroom. But Mathwright Author 2.1 has changed all that.
All of the WorkBooks in the Mathwright Library, and a number of web courses that are separate from the Library have been created using Mathwright Author 2.1 by Mathwrights who decided that they wanted to translate their own pedagogic visions into interactions for their students.
The Library WorkBooks can serve as ‘templates’ from which other Mathwrights can build new structures. It is as easy to ‘cut and paste’ whole pages from one WorkBook into another as it is to cut and paste word processing documents. More than that, though, is the fact that creating the dynamic interaction in a WorkBook is easy and fun. The screen design elements (various windows) are object-oriented. It is just a matter of specifying the locations on the screen, and then giving the objects their various attributes. Individual objects may also be copied and pasted from one WorkBook to another.
The functional elements (the underlying mathematical objects, such as functions, vectors, sprites, etc.) are manipulated in a mathematics scripting language, called MathScript, that allows Mathwrights easily to assign behaviors to objects (like buttons and scroll bars) in a step-by-step and top-down way.
All of the Library WorkBooks are available as ‘clip math’ to be used as templates or as building blocks for new WorkBooks. The WorkBooks you create may either be used with the Mathwright Player on a campus intranet, may be submitted to the Mathwright Library for worldwide free distribution, or may be distributed from your own website in support of your courses. So if you are thinking of teaching a web based mathematics course, and if you wonder how you can support the necessary mathematical interaction for the course, you need wonder no more. Write to us to inquire about the capabilities of the program and whether and how it can support your pedagogic needs.
James E. White,
Editor
If you came here from the old building,
