UW News

January 8, 2009

Taking math to the streets: Students solve real-world problems with mathematics modeling

UW News

Say you’re hiking for a week — how much food and equipment should you bring? Or you’re delivering hot meals to clients, or arranging a carpool — what’s the most efficient route?

Students in Math 381, Associate Professor Sara Billey’s Discrete Mathematical Modeling class, use math to help solve such practical questions and more. The students showed their work to an audience of 100 or more in the course’s first-ever poster session in the Mary Gates Atrium in early December, an event Billey called “a fantastic success.”

Mathematics modeling is the process of translating real-world problems into quantitative terms for interpretation, suggestions of improvement and future predictions. But Billey takes the process a step further by adding a service learning component to her class — she requires a final project where students use mathematics modeling to address a real problem they want to fix somewhere in the outside community.

“I want the students to know that they have the math skills to tackle hard problems after they graduate,” Billey said in an e-mail. “They can make an impact in the community with their mathematics.”

She said in past 381 classes she asked her students simply to work on “a problem that bugs them.” But she noticed that the best projects each year tended to involve a real person or business. So she made a change: “I challenged the student to find a problem in the community and make an impact through their project.”

It worked well. “The students used their own contacts and the result was a much wider range of projects than I could ever have dreamed of. I believe the whole class was more motivated and more successful because they were helping people with problems they really cared about.”

Billey added that it was “one of those ‘Ah-ha!’ moments when a small change makes a big improvement. Why weren’t we doing this all along?” she asked herself.

The students worked on the projects in teams — which mirrors the frequent group nature of such public work — and wrote and revised several drafts of their findings before submitting them to peer review by classmates as well as to Billey.

Their work was impressive indeed.

Students Stephen Barr, Alisher Khussainov and Richmond Newman’s project was titled “Outdoor Expedition Planning for Boy Scout Troops.” They weighed factors including weight and cost to help determine the appropriate type and amount of supplies for the scouts to pack for a weeklong trip, resulting in a program that can advise troop leaders how much to buy and pack along. Barr said he’d like to eventually create a free Web site that people could use to make such calculations for themselves.

Kevin Cooke, Tyrone Palmer and Jeff Huyler’s project, “Effects of Faculty and Student Contributions on Textbook Cost,” showed that relative textbook costs would decrease if more faculty submitted book lists to the UW Book Store the quarter before the class is held. The store does not buy back students’ books from one quarter until it knows the book will be used again. That change, together with students participating fully in the store’s rebate — only about 55 percent do now — would result in significant savings, they learned.

Alyssa Harding, Charles Boyd and Stephen Du Bois studied campus routes to determine their relative safety, taking into consideration factors such as lighting, openness and the number of people around.

Other projects were:

  • “Increasing Route Efficiency for Meals on Wheels Deliveries”
  • “Optimizing Volunteer Carpooling Routes for the Washington Trails Association”
  • “Optimizing Office Space Layout at Starbucks”

Clearly proud of the work her students accomplished, Billey said, “It can be challenging to face a real-life situation, translate it into a mathematical problem, solve it, test it, and communicate the solution in an accessible way to the people who need it. Every one of these students has succeeded in this challenge.

“The work these students have done is making a real impact on the community and it was wonderful for them to get the exposure and recognition for their work.”