For the past several years, Rutgers Prep has fielded teams of four students each to compete with over 1300 other teams in the annual High School Mathematical Modeling competition, or HiMCM. This contest represents an opportunity for talented and intellectually adventurous math students to try their hand at real-world problems which often seem insurmountable at first glance. Teams that do exceptionally well in this round continue on to the IM2C (the International Mathematical Modeling Competition). The organizers of both competitions state, “Real problems require a mix of different kinds of mathematics for their analysis and solution. And real problems take time and teamwork. The IM2C provides students with a deeper experience both of how mathematics can explain our world and what working with mathematics looks like.” In order to tackle each year’s problem, students work in small groups of up to four students over a period of several days of intense concentration and collaboration. This year’s problem had an existential cast to it; students were asked to use mathematics to determine “the Earth’s carrying capacity for human life.” Of the 278 teams from the United States who advanced to the IM2C, only two would be tapped to continue on to compete at the final, elite international level, and earlier this year we received the news that Rutgers Prep had fielded one of the two winning teams in the United States Region!
With the help of their advisor, Rutgers Prep Math Department Chair Scott Neal, we connected with all four members of the winning team to ask them to share some of their experiences and lessons with us.
Three years ago, Rutgers Prep fielded a team that was comprised of three upperclass students and a freshman. The freshman was Zhaoyi “Richard” Xiang ‘20, and when the seniors who had tucked him under their wings had graduated, he found himself stepping up to keep things going. This year’s problem, as challenging as it was, felt almost comfortable to Richard. “As soon as I saw the problem, I started having ideas about how to approach it,” he shared with a smile. His teammates also found that the problem itself sparked ideas. Jack, the youngest member of this year’s team, said, “This was my first time participating in this kind of competition, but the juniors treated me like one of them. For the first few days of the competition period, we were actually in a kind of meta-analysis mode. We talked about all the different kinds of ways we could approach the question, until we all felt like we had a pretty good idea of how to move forward.” Richard chimed in, “In between intense working sessions, we also played a LOT of gomoku — a game where two players face head on to be the first to place five connecting stones on a 19-19 grid. This really helped us relax while still keeping our brains going. And Jack was arguably the best player at this game.”
Within the team of four students, each one had their strengths and specialties. Holly was selected for both her mathematical ability and for her strength as a writer. In remembering her team’s process, she shared, “We had several plans at the beginning, and struggled to figure out which one we would focus our attention on; we had three possible approaches to the solution and spent a lot of time talking about which would be the best approach. We found an approach that we liked early on, but then by the fourth day we had changed our mind about which approach we needed to move forward with. One lesson I learned from this experience was, ‘Trust in the process.’ You really need to believe in your own power. There were times when each one of us wanted to give up, especially on the third day, when we had really started to work but the end still seemed SO far away, but we cheered each other on and wouldn’t let each other quit. (Later we learned that quite a number of US teams had quit before submitting a final paper!)”
Charlotte was selected in part because she had more experience with mathematical modeling than most of the rest of the crew. “We had worked together on one previous challenge,” she shared, “which was helpful. And then we had some conversations about how best to avoid conflict; we made an agreement not to interrupt each other when someone started speaking, and that pretty much worked. We did a lot of brainstorming and research, and we discovered that every approach had limitations and advantages. We ultimately decided to really lean into the logical element of our argument… if someone who didn’t really understand math wanted to think about this problem, how would we explain that our method would work? This became the core of our paper. The most important lesson of this experience for me was, ‘Never give up.’ We were fully expecting to get a result of ‘successful participation.’ I don’t think any of us would have predicted that we be one of the two teams that made it all the way to the international competition!”
We are so excited and proud that our students found a way to shine in this very challenging context. And if you’re remembering the original question, you might be wondering, so what IS the carrying capacity of the Earth? Our winning team’s conclusion, coming after about ten pages of model and assumption descriptions as well as a ton of complex calculations, was that the Earth’s carrying capacity is approximately 11.6 billion people, while the world’s population is currently somewhere around seven and a half billion. So while our planetary resources are declining, we do still have some time to innovate and problem-solve. Contests like the IM2C, which help encourage students to find their “next level” as learners, can help make our situation seem a little less dire. Congratulations again to the Rutgers Prep IM2C team on their extraordinary success!