Modeling the World Through Math
Four juniors qualified to take on real-world challenges in the High School Contest in Mathematical Modeling Challenge and the International Mathematical Modeling Challenge.
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Juniors Rebecca Bao, Theodore Landa, Eli White, and Eric Zheng participated in the International Mathematical Modeling Challenge (IM²C) after finishing in the top 10 percent globally in the High School Contest in Mathematical Modeling Challenge (HiCMC) for their mathematical analysis of colony collapse disorder (CCD) and its impact on bee populations and food security. The HiCMC is an international math contest in which up to four students from various high schools around the world use their modeling, problem-solving, and writing skills to model and develop solutions to real-world problems. The juniors’ exemplary submission, created under the guidance of Stuyvesant mathematics teacher Patrick Honner, marks the first time Stuyvesant has participated in the HiCMC and qualified for the IM²C.
Honner noted the unique opportunities that the competition can provide for participants. “These competitions give students the chance to experience what applied mathematicians do every day: use the tools of mathematics to study and solve important real-world problems,” Honner said in an e-mail interview.
During the HiCMC, the juniors focused their efforts on addressing the impact CCD has on bee populations. CCD is a disorder that causes worker bees to lose their sense of navigation and thus suddenly disappear, leaving behind the queen and immature bees.
The juniors took an organized approach to the problem, working together to conduct research, brainstorm, and construct models. “We sort of started by brainstorming the [...] parameters of the problem [and] the variables we can change, and how we build a model that can work with that. We drew [on] our mathematical knowledge [and our knowledge of] computer simulations because we’re all in AP [Computer Science A],” Landa said.
The teammates used various online web applications, such as Desmos, and programming languages, such as NetLogo, to create their models. “I created a Desmos model which took the normal distribution of the temperature and rainfall throughout the year and modeled its effect on the bee populations. [Landa] made a NetLogo program, [which] had different patches with flowers on them where each patch was a honeybee hive, and you could model the bees’ movement and how often they have to go to hive and how much pollen they had to get from each flower,” White said.
The students demonstrated determination throughout the process of creating their model, recognizing the significance of its practical applications. “This sort of modeling has real-world consequences; political leaders basically use this kind of decision-making to actually put into use the resources we have as a community,” Zheng said.
The team wrote a 25-page paper describing and using their models to evaluate the ideal conditions for bee populations with CCD. “The paper we wrote […] based on the models […] was on the optimal spacing of hives in order to pollinate the most, and how to model the population of a hive,” Zheng said. “[It] also [included] a summary, abstract sensitivity analysis, popular audience piece, [and] appendix.”
The juniors’ hard work yielded remarkable success, allowing them to qualify for the IM²C. Honner emphasized the immense achievement of the four juniors’ submission. “Rebecca, Teddy, Eli, and Eric have already accomplished a lot, just by being invited to compete in the IM²C. They earned that invitation by finishing in the top 10 percent worldwide in the [HiMCM], where their mathematical analysis of [CCD] and its impact on bee populations and food security earned a ‘Meritorious’ distinction,” Honner said.
During the IM²C, the group took on a new problem where they investigated issues in optimizing land usage. Unfortunately, due to conflicts with publicly releasing information for competitions before results are released, further information on the specifics of the project cannot be disclosed.
The next level of competition did not come without difficulties. “The [high school contest] was a lot more casual; we did a lot of research and [had] fun. The [IM²C] was actually a time crunch because [there were only five days to do it and] research takes a really long time, especially when it’s citing sources, and our final product had to be over 20 pages,” Zheng said. “So it was really stressful.”
The students feel that they gained a lot of skills from the contest experience. “One of the big [skills] I got out of the competition was learning to reduce a problem to its parts, and that’s a pretty important skill for problem solving in general. The other thing is that these are real-life problems, so I learned how to better balance being too hyper-realistic and simplifying the models,” White said.
The students appreciated the opportunity to work together toward a collective goal. “Thanks to Mr. Honner for giving us the opportunity and meeting with us and talking about strategies and how to approach the problem. And thanks to my teammates; they did well and we all worked really hard,” White said.
The juniors described their hopes to continue participating in such competitions. “In the future, I definitely would like to keep doing these kinds of competitions. I think our group does, and I think that we would all like to grow as mathematical modelers […] [in] our ability to apply math to real-life situations,” Landa said.
The team believes that their experience paves the way to allowing similar opportunities for underclassmen. “We should publicize this because I don’t think a lot of people know about this. It makes it more accessible to fresh[men] or sophomores,” Zheng said.
Honner agrees and highlights the importance of applying math to the real world. “By preparing and participating in these competitions, students learn about the infinitely many ways math can be applied to important real-world problems,” Honner said. “This not only broadens their perspective of what math is, but [also] opens up new and exciting ways for math to have meaning in their lives.”