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Playing with Math

By Sandra Santana
Last week at Morning Reports, Mathematics Instructor Alexandra Schmidt shared how her students are creatively using math outside the classroom and collaborating with other area students. 

In addition to teaching at Emma Willard School, Alexandra Schmidt advises the Albany Area Math Circle (AAMC), a group of high school students from all over the Capital District who meet regularly to collaborate on challenging problems and interesting applications of mathematics. Ms. Schmidt shared:

“AAMC’s overarching goal is to bring together students from different schools who enjoy mathematics and might otherwise not know each other, and to build bridges of collaboration to solve harder problems than one might be able to tackle alone.” 

Each year Emma Willard School, in cooperation with AAMC, hosts the American Mathematics Competitions. The competitions, designed for middle or high school students, are a series of challenging questions that test problem-solving skills and mathematical knowledge. The first of these competitions, sponsored by the New York Metropolitan Section of the Mathematics Association of America (MAA), took place in 1950. Today, the competition has grown to over 300,000 students participating annually in over 6,000 schools. This year the competition moved to a virtual format to accommodate the safety of participants. 

The AMC 10/12 is the first in a series of competitions that eventually lead all the way to the International Mathematical Olympiad, with students who perform exceptionally well getting an invitation to the American Invitational Mathematics Exam (AIME). This February, over 50 local students competed in the AMC 10/12 with 12 students qualifying for AIME. Of those 12 students, four were girls… three of whom were Emma Willard School students!

The recreational math doesn’t stop there. Ms. Schmidt and a five student team (Caroline A. ’21, Lillian L. ’22, Irene N. ’21, Coco W. ’21, and Gabby Z. ’22) plus an alternate (Grace P. ’22) competed in the Mathworks Math Modeling Challenge (M3). High school juniors and seniors in the United States and sixth form students (age 16-19) in England and Wales form teams of three to five students and one teacher-coach per school. The competition allows students to experience what it’s like to work as a team tackling a real-world problem under time and resource constraints, akin to those faced by professional mathematicians working in industry. Ms. Schmidt described the challenge during morning reports: 

“We all know how much we’ve been relying on the internet this past year.  How do we make sure everyone—especially those who are at a socio-economic or geographic disadvantage—has access? How do we predict the costs and the demand?  We’ve discovered that mobile internet—that is to say your phone—has been critical. How do we use demographic information to decide where to place cell towers?

No one on the team had any expertise in broadband distribution or availability, but the team strategized, asked questions, researched, and developed mathematical models that took past data into account while projecting future patterns.

Twelve hours later, the team had produced a polished 20-page paper that laid out their assumptions and provided mathematical predictions that considered internet speed, household age, income, and population density.”

What is more astonishing is the physical location of the team. “Last year's team worked in the library's Melligheri workspace, surrounded by whiteboard walls and with shared snacks to power them through their research and analysis,” Ms. Schmidt explains. Due to the pandemic, the Emma Willard team, officially entered as team 14847 and worked virtually to tackle the challenge. Papers are judged anonymously by number rather than school name.

“They worked around the globe and around the clock—Irene started at midnight in Vietnam. Coco, Gabby, and Caroline started at noon in New York, and Lillian, who was in California and has been starting her school day at the crack of dawn for months, started at 9:00 a.m. All these students are good math students, but they are also good writers, good brainstormers, good thinkers, good programmers, and good communicators. These gifts together are what make mathematics really meaningful in the real world—as well as a lot of fun.”

The hard work paid off. Team 14847 earned an honorable mention at M3, placing in the top 9% of the 535 papers submitted in the US and UK. The team’s performance also earned each member scholarship funds for college. Ultimately, Ms. Schmidt hopes the challenge offered the team “a major sense of satisfaction and pride in their work together.” 

In efforts to continue to foster a love of mathematics, AAMC recently invited the entire Emma Willard community to join a panel discussion about studying mathematics in college.  The panel featured two college alumni from the Class of 2020 and Aparna Anderson, PhD, a high school calculus classmate of Ms. Schmidt who majored in applied mathematics and is presently the chief science officer of Statistics Collaborative. Alumna Katie Gonick '16, who graduated in 2020 from Lafayette College, was one of the featured speakers , drawing on her experience double majoring in Policy Studies and Mathematics with minors in Russian and East European Studies. 

Up next for Ms. Schmidt and the AAMC are two competitions: Purple Comet!, an online, team-based challenge, and the New York State Math League (NYSML) competitions. Last year's NYSML was cancelled due to the pandemic, but is back this year in virtual form. At the last NYSML, wo years ago, AAMC took the top spot in the B division (the A division is mostly New York City and other major urban regions). We are excited for the future of AAMC and "look forward to a time when competitions will bring students together in person again."

Congratulations to Ms. Schmidt and our Emma students on a strong showing this year!


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    • Mathworks Math Modeling Challenge Team 14847. Caroline A. ’21, Coco W. ’21, Lillian L. ’22, Gabby Z. ’22, and Irene N. ’2.

    • Mathworks Math Modeling Challenge 2021

    • Mathworks Math Modeling Challenge 2021

    • Mathworks Math Modeling Challenge 2021

    • Mathworks Math Modeling Challenge 2021

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