For more information
Robert Panoff, rpanoff@shodor.org
Champions of educational reform--especially within the sciences, mathematics, and computing--find lessons and activities that allow the student to interact with learning material to be essential in improving student performance in these fields. They believe that interactive learning encourages deeper understanding of the information, and captures the students' interest more than a lesson learned from a textbook. The suite of MASTER (Modeling And Simulation Tools for Education Reform) tools developed by the Shodor Education Foundation, Inc.--in collaboration with the National Center for Supercomputing Applications and George Mason University--accomplishes this objective by providing students with engaging simulation environments and modeling activities, all available over the Web.
Using GalaxSee Students Work with Images from Space
(HST image courtesy of W. Keel and R. White III, University of Alabama, and NASA).
"What's important about the MASTER tool suite," says Robert Panoff, executive director of the Shodor Foundation, "is that they're not just stand-alone computer activities. As we develop each of the simulation environments we are also developing related curriculum materials so that the tools can be used most effectively in the classroom." The curriculum is designed in accordance with national science and mathematics education standards.
Inspiring Math Appreciation
With their unique and often beautiful composition, fractals and the Fractal Microscope help students appreciate the mathematics behind art and nature.
Currently, instructional materials are available for GalaxSee, SimSurface, and the Fractal Microscope. Also in the suite are various environmental models, software for plotting gnuplot graphs, models from medicine and the biosciences, and even a math lesson that uses the storyline of Edgar Allen Poe's The Pit and the Pendulum to help students compute the differences between a simple pendulum and a physical pendulum. Finally, there is Project Interactive, an extensive set of interactive explorations for middle school mathematics developed with support from the Presidential Technology Initiative of the U.S. Department of Defense.
The GalaxSee software bundles together the philosophies and capabilities of MASTER and the Hands-on Universe (HOU), a five-year project Lawrence Berkeley Laboratory funded by the National Science Foundation, the Department of Defense, and the Department of Energy. HOU gives students access to scientific instruments--research grade telescopes and related observing equipment--and image processing tools which are identical to the data and tools that real scientists use. MASTER gives students access to the same scientific computing resources and environments used by scientists to study and test their theories of the laws governing cosmological phenomena. The software also allow students to download images of distant galaxies, star clusters, and nebulae for classroom use.
These images serve as one possible starting point for classroom research on galaxy structure. Students can also use the MASTER modeling tools to simulate the formation of a galaxy starting from initial conditions that they choose. By changing parameters in the model, or by changing the model itself, galaxy explorers can design numerical experiments that will help them understand the patterns of interaction among individual stars that may cause spiral, elliptical, and unique galaxy types. Other explorations include planetary capture, colliding galaxies, and the observation of stellar movements near black holes.
SimSurface is an instructional tool for teaching the general principles of computational science and specific numerical techniques used in modeling. With the program, students try to solve a problem in minimization of potential energy. They're presented with a series of variables and options for the types of equations that could be used to solve the problem. Depending on the option the students choose, they're expected to input different values for the problem set. Throughout the project, they're introduced to the technique of simulated annealing, an often-used method for finding global maxima and minima of complicated multi-dimensional functions. A modeling tool in the software allows the student to create a visualization of the final solution to their equation.
"Using SimSurface, the student has to take known start-up conditions, theorize an answer to the problem being posed, and then test their theory through experimentation--a process that scientists engage in every day," says Panoff. "Our hope is that students will find enough interesting questions to ask about the events they observe when using SimSurface to awaken their curiosity, which is the real driving force behind scientific inquiry."
The Fractal Microscope is a tool for exploring the Mandelbrot mathematical set and other fractals. Based on the concept of a microscope--with which a student could zoom in on a specimen to discover more detail about a selected area--the software allows a student to change the parameters of the fractal and then see it at different "magnifications." They can also view the orbits created by the calculation of points in the Mandelbrot Set.
"As students explore the images created by the Mandelbrot set or other fractals, they come to understand fractals as geometric figures, but with different properties than the ones we traditionally think of--squares, rectangles, circles, or triangles," says Panoff. "Recognizing how fractals often look like objects and shapes we find in nature also helps them identify the math that surrounds them in everyday life."
"The whole compilation of MASTER tools makes science and math more relevant to students by providing them with opportunities for hands-on experimentation and discovery," he says. "Through use of authentic computational tools, students emulate the work done by scientists and are rewarded with visualizations that make their experimentation concrete. As they develop mastery over the material, our hope is that their interest in science and mathematics grows, enticing them to pursue further studies in these fields while at the same time deepening their knowledge and increasing their likelihood for academic success."