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ADV Mathematical Modeling Team Earns Top Recognitions in Global Competition
By Dylan Howlett

They had spent afternoons at Barnes & Noble, hours more on their computers at home, squinting at cells in Google Sheets and punching variables into calculators. And now they were out of time. It was mid-November, and four students from the Advanced (ADV) Mathematical Modeling course at Durham Academy Upper School had toiled over “Problem B,” a scenario set forth in the 2023 High School Mathematical Contest in Modeling (HiMCM). The students — Michael Hansen ’24, Claire Hong ’24, Riley Kim ’24 and Sarah Muir ’24— had, for the two weeks permitted by the contest, used little more than multiplication and addition to craft models and tables and charts, all of which they had crammed into a 25-page paper and dotted with 42 footnotes. They had determined, in a direct answer to Problem B, that fully transitioning its fleet of city buses from diesel to electric would save Washington, D.C., more than $75 million, and spare the atmosphere more than 27 million kilograms of emitted carbon dioxide.

They were up against two additional teams from DA, plus 964 others from 416 schools around the world. Only 1% of those teams across 18 countries and regions would receive the distinction of “Outstanding,” awarded to the nine teams that devise the most exemplary solutions. They couldn’t solicit or receive any input from Forrest Hinton or Jarrod Jenzano, their mathematical modeling teachers. Hansen opted for hope when he typed out a title for the team’s working Google Doc: outstanding winner in progress. With 30 seconds left before the Nov. 14 deadline, the team submitted its entry.

“Honestly,” Kim said of the Google Doc title, “I think it did manifest it.”

Two months passed, during which judges for the contest sifted through more than 24,000 pages of reports. On the afternoon of Jan. 26, Hansen was at a DA Speech & Debate competition in Atlanta when he received an email from Hinton. “DID YOU SEE THIS???” it read. On the Upper School campus, Muir hadn’t seen anything until Hansen called and suggested she check her inbox. Muir called Kim and Hong in the Learning Commons to celebrate the news: Their team had been named one of nine outstanding winners at HiMCM, and one of just two additional award winners from The National Council of Teachers of Mathematics. Six of the nine “outstanding” teams hailed from schools in China. One came from Canada, another from Massachusetts. And one came from DA, where mathematical modeling started in an organized capacity a mere 14 months prior to the 2023 contest.

The mathematical modeling program began as a club in the fall of 2022 — when Hansen and Hong were both members — and debuted as an ADV course in the fall of 2023.

“It felt like we’d learned a lot through this course,” Hansen said. “And the fact that we were able to apply math in a clear and precise way to actually generate a solution that could resolve a real-world problem, and that was deemed one of the winners of the competition? That definitely felt really good.”

HiMCM served as the “grand finale” of the course, Hinton said. Three groups of four students each eventually turned in refined versions of their final papers as a class grade. The other two DA entrants — Ben Hodges ’24, Sam Shi ’24, Jack Vail ’24 and Andy Ye ’26 on one team; Hutch Levinson ’24, JJ Wilcox ’25, Anand Jayashankar ’24 and James Robb ’24 on the other — would ultimately earn an “honorable mention” from HiMCM, which positioned themselves between the top 22nd and 48th percentiles of math modeling teams around the world. But their progress in the class was, by design, a little more halting. The vast majority of class time was spent working on projects — for instance, defining the “compactness” of congressional districts or redesigning the Electoral College — in service of finding real-world solutions to real-world phenomena. “It often felt like I was taking shots in the dark,” Muir said.

“I think with math modeling, there is a lot of initial frustration,” said Hinton, who also serves as the Upper School’s mathematics academic leader. “What is good? What makes something a really robust solution or a really well-written paper? And it’s something you can’t just tell people, ‘Do this, this and this, and you’re done.’ The growth definitely took time — a lot of blood, sweat and tears, but it happened.”

The success of Hansen, Hong, Kim and Muir started long before they arrived in ADV Mathematical Modeling. The four had been longtime teammates on the DA Speech & Debate team; Hong and Muir have partnered in Lincoln-Douglas debates since they were ninth-graders. They were predisposed to distilling complex problems into digestible language — and in their preparation for past debate competitions, they had already combed through studies about climate change and electric vehicles. Muir and Hong tackled the environmental consequences of transitioning a major city to an all-electric bus fleet, using multiplication to assess the impact of converting 1,600 diesel buses that drive multiple routes every day. Hansen and Kim confronted the financial implications, employing a linear regression model to demonstrate the declining cost of lithium ion batteries over time Each duo constructed a model to illustrate the long-term effects, as required by the contest. They also teamed up to craft a 10-year roadmap for the transition, as well as a one-page letter to the city’s transportation agency to advocate for the change.

HiMCM judges each team on the clarity of its model and understanding of the problem, not on mathematical complexity. The contest’s parameters were well suited to Hong and her teammates, all of whom possess inclinations beyond mathematics or computer science: sociology, Asian-American studies, public policy, history, economics.

“Everyone has a different way that they look at social problems, right?” said Hong, who earned an honorable mention in the 2022 HiMCM as part of a DA team. “But for me, the tools that I can use to actually think about them are quantitative tools. For me, math has always been a class that I’ve been interested in. It’s just the way I can approach those problems. And I think math modeling helps you actually start putting those into action. You’re not just thinking about those problems, but you’re also figuring out ways that you can address them.”

They grew exponentially, in a true mathematical sense, throughout the semester. Muir said she had never felt so adrift in the class as Hinton and Jenzano, with great patience and deliberateness, watched their 12 students stumble and work through solutions that felt beyond their reach. Kim considered dropping the course during the allowed two-week period at the beginning of the semester. Hong said she felt intimidated by the absence of direct instruction, clear answers or visible paths. But they found their way amid the uncertainty. They refined their research skills. They gained more practice in writing technical papers. And they leaned into the intentional independence that Hinton and Jenzano afforded. “I think leaving us alone was the best thing they could have done,” Hong said. Hinton sensed it. “They’re at the stage now,” he said, “where they’re ready to do this on their own.”

Upper Schoolers are alone again, too, for yet another approaching competition: the MathWorks Math Modeling Challenge (M3), which begins Friday and features two DA teams of five students each. The teams will have 14 continuous hours across a three-day window to write a solution paper that addresses an open-ended and timely problem. One of those, Muir and Kim said, easily could be representation in STEM. A 2023 study from MIT found that women only make up 28% of the STEM workforce. It wasn’t lost on Muir or Kim that they, along with Hong, were the only three girls among 12 students who enrolled in the fall’s inaugural ADV Mathematical Modeling class. Yet after working on separate teams at the start of the semester, they found each other in the end, just in time to partner with Hansen and ascend to the top 1% of math modeling teams in the world. Representation matters, Kim said, and it means all the more when young girls see successful women in STEM. “They have faith that they can do things, and they can build confidence through that,” Kim said. Perhaps, she said, her team can provide that faith. “That’s one of the things I’m proudest of,” she said.

Their outstanding work is, it turns out, both a winner — and progress.