The Sights and Sounds of Mathematics
What does mathematics look like? What does math sound like?
Image to right: MathTrax presents mathematical information in a variety of ways. Credit: NASA
If those questions don't seem to make sense to you, then you're probably not familiar with MathTrax, a computer application from NASA's Learning Technologies program, available for Windows and Macintosh platforms. Designed for students in mathematics classes beginning with pre-algebra and continuing into college-level courses, MathTrax provides users with a more concrete presentation of the concepts they are studying.
"I think of MathTrax as a way to visualize mathematics," said Stephanie Smith, a member of the team developing the application. "It's another modality for people to understand mathematic presentations."
MathTrax includes the kinds of tools you would find on a graphing calculator, but takes those to another level. While a graphing calculator turns a mathematical equation into a visual form, MathTrax includes additional features that provide different methods of visualization. While a graphing calculator only draws a graph of an equation, MathTrax provides a text description of the graph. It also provides an audio version of the graph, generating sounds that correlate to the visual image.
"They'll see how equations look if they're looking at it," said team leader Robert Shelton. "They'll hear how they sound if they're listening to it."
MathTrax helps users of all backgrounds and ages better understand math through their other senses. For users who are vision-or hearing-impaired, this tool has enabled them to explore, discover and understand math in a whole new light. The text description and the "audio graph" allow them ways to "see" and "hear" mathematical equations, providing them ways of accessing information that might otherwise have been unavailable to them.
"If you're an educator with blind or vision-impaired students, it's a tool for your students to participate in mathematics that maybe they weren't participating in before," said team member Terry Hodgson.
It's easy, she said, for students with special needs to get left behind in more advanced math classes when teachers believe there's not a way to let them access the material. "A lot of [those] students are in mainstream classes, so they just get shunted away," Hodgson added.
The idea for MathTrax came from Shelton, a NASA engineer who is blind. Over the years, Shelton developed computer tools to make the information he was using more accessible to him. MathTrax takes a few of those tools, and makes them available to the public.
"There were many times that I had to deal with simulations, and tons of data," he said. While a person with sight would have graphed the information to create a visual representation, Shelton built a tool to turn it into sound.
"What happened was, over 30 years of doing this work I had a pretty sizable bag of tricks."
"This will take you about two minutes to download and install, and it's a great graphing calculator," Shelton said.
MathTrax can also help prepare students for a career in engineering. The program is similar to the sort of application that engineers might use in their work, he said, but is simplified to a level where students can easily use it.
"It looks pretty simple, but there's a lot of complexity under the hood," Shelton said.
Many students with vision impairments are in mainstream classes with teachers that may not be aware of specialized tools to help meet their needs. The MathTrax team hopes that the application's broad potential will find its way in to their classrooms.
Image to left: Students at the "Rocket On" camp built and launched their rockets using information from MathTrax. Credit: NASA
"That's why we wanted to make a powerful mathematics tool that would stand on its own right," he said.
The application was a vital part of "Rocket On," a science camp for students with vision impairments, which NASA held in partnership with the National Federation of the Blind. Students at the camp used MathTrax for mission planning, trajectory planning and data analysis. (The application includes a special set of features specifically dealing with rocketry.)
"There was no other tool on the planet that would have let them do that rocket camp without an engineer helping them," Shelton said. "And this year the kids did it [on their own]."
Shelton said that the team would really love to receive more feedback from users of MathTrax. Since the application is still under development, input from users will guide the team in improving the program and adding new features.
"Without that feedback and reinforcement from teachers, there's not going to be the sustainability of the tool," he said. "We don't mind getting a lot of mail, either."
Hodgson stressed that the team wants to know not only whether MathTrax benefits students with visual impairments, but also how much it helps other students as well.
"Help us. Experiment with it. See if it does add value to students' ability to understand the material," she said.
In addition to improving the application itself, the team is working to put together some usage tips to help students and teachers make the most of MathTrax.
"If you just hand somebody a chainsaw, they may not know to start it before they start trying to chop down a tree with it," Shelton said.
The team, Shelton said, would also be interested in working with other groups to find new applications for the MathTrax technology. The program, he said, is built with a reusable library of Java components, which could be used for other applications. For example, he said, a Web site with dynamically generated graphs might benefit from MathTrax's text description tool.
MathTrax can be downloaded for free from the project's Web site, where more information is available.
MathTrax Web site
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MathTrax Web site Grades 6-12
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David Hitt/NASA Educational Technology Services