Speaker: Ladnor Geissinger, University of North Carolina
Title: Mathwright Library: Interactive Math Workbooks on the Web
Abstract: With funding from the NSF, Prof. James White and I and other authors and editors are building a library of interactive workbooks using the authoring system Mathwright (MW). The workbooks, as well as the MW Library Player, can be downloaded freely from the Web site called the Mathwright Library (MWL). The MWL now contains many small interactions or experiments, as well as several coherent collections of laboratory workbooks on calculus, differential equations, and finite mathematics. In my presentation I will describe the library and the authoring environment, demonstrate some workbooks, show how to quickly build a small experimental setup, and mention some uses of such workbooks in math classes.
When a user turns the "pages" of a MW workbook, exploratory math microworlds are created. A book is a hypertext document and the pages may contain text, calculations, symbolic expressions, 2&3D graph windows, video or sound clips, animations, and code to be executed by the underlying math engine. Students can use powerful built-in tools to explore math topics, they can experiment with new functions and create programs, and they can write reports which include snapshots of any region of the page. This computer algebra system and its object-oriented math language was developed specifically for learning math and science. It was designed to make it easy for teachers to write workbooks and for students to use them in explorations. Pages are built from 12 kinds of math screen objects (windows): 2D graphics, 3D graphics, video, text field, math edit, program, data, push button, vertical & horizontal scroll bar, check box, and hotspot. These independent objects can be tied together by scripts attached to the objects to produce complex mathematical behavior.
Some examples of MW workbooks are: 3D curves/ribbons/tubes, surfaces, lunar lander, Riemann sums, recursive sequences, periodic functions (high school), Bezier curves, Heron's formula, gravitation (Galileo/Kepler/Newton), Mandelbrot (high school), Bernoulli trials, polar curves (high school), derivatives, chaotic pendulum, discrete dynamical systems, harmonic oscillators, ODE movies, eigenvectors. Some of the library workbooks were built by participants in our workshops on writing interactive math books and so are simple, short, and not polished. In other more sophisticated books you can play mastermind or pool, or teach the computer new reduction rules for a class of expressions, or teach it to solve cubic equations.
The Mathwright Library URL is ike.engr.washington.edu/mathwright/