Model Learning: USU Undergrads Use Math Modeling to Practice Critical Thinking, Problem-Solving

Renowned physicist Enrico Fermi (1901-1954) challenged his students with head-scratching estimation problems designed to encourage scholars to draw on their creativity and imaginations in attempts to solve extreme order-of-magnitude puzzles.

Utah State University undergraduates Sandra Benallie, Tayden Bitsoie and Sage Yazzie stepped up to solve a classic Fermi problem as participants in USU’s 2025 Native American Summer Mentorship Program. The challenge? How many piano tuners are there in Chicago?

“You don’t have much information to answer this question, so it may seem impossible,” said Sindura Kularajan, assistant professor in USU’s Department of Mathematics and Statistics and a NASMP faculty mentor. “But use what you’ve learned this week about the mathematical modeling cycle — how to clarify and simplify a challenging situation — to formulate a problem-solving model.”

Benallie quickly sketched a grid and mapped out a box diagram to produce an estimate. Bitsoie looked up the number of piano tuners in Logan, Utah, along with the populations of Logan and Chicago, and extrapolated a total for the Windy City. Yazzie chose a historical approach, seeking out the first mention of a piano tuner in Chicago (at the beginning of the 18th century) and estimating the profession’s growth as the city’s population expanded.

“These were all innovative approaches,” said Professor Brynja Kohler and principal investigator for USU’s National Science Foundation-funded Noyce Program project, who had guided the students through mathematical modeling exercises earlier in the day. “Even advanced mathematicians go through these steps and ask themselves, ‘Are the numbers I’m coming up with making sense?’”

Benallie, Bitsoie and Yazzie are among 18 early undergrads from USU Blanding participating in the monthlong NASMP gathering. In its 10th year, the program brings scholars to the Logan campus to learn about USU’s broad range of four-year bachelor’s degree programs and to experience, firsthand, undergraduate research in varied disciplines. Additionally, NASMP participants learn how these degree programs and experiences are building blocks to graduate and professional school opportunities.

Moving from piano tuner estimations, the NASMP scholars tackled a real-world challenge led by doctoral student mentor Lily Roth in estimating how to determine a fair-market price for hand-woven baskets. The first order of business? Making their own baskets.

After crafting models from paper, the students learned about varied natural materials and techniques used by varied Native American communities in California.

“You have to consider the expertise and labor that goes into each project,” said Bitsoie, who earned an associate’s degree in general studies and a certificate in heavy equipment operation from USU Blanding.

Benallie, who completed an associate’s degree in general studies and is currently working toward a bachelor’s degree in psychology with a minor in social work, quickly looked up wages in Utah.

“Minimum wage would not be enough for an artisan basket weaver,” she said. “No one could live on that.”

As the students prepared a pricing model for finished baskets, they discussed how artisans source materials, including deergrass, sumac, juncus; willow, hazel and redbud branches; feathers, pine needles and porcupine quills, along with preparing natural dyes used to create the baskets’ intricate designs.

Yazzie, who earned a welding certificate from USU Blanding and crafts metal sculptures, chose to develop a similar model for his creations.

In addition to participating in research projects in varied labs throughout campus, the NASMP participants are visiting varied sites and attractions in the Cache Valley area.

“Our group visited some hot springs and I’m looking forward to a trip to Bear Lake this weekend,” Bitsoie said. “I’ve lived in Blanding all my life and it’s fun to visit the other end of the state.”

Participants in the 2025 Native American Summer Mentorship program present their research experiences 9-11:30 a.m. June 10 in MAIN 121. All are welcome.