Stuyvesant Succeeds at SCUDEM!

All too often, math is perceived as a field of numbers and numbers alone. This perception is founded on formative years spent defining math on number lines and graphs, rather than considering the real-world, research-backed applications that this subject encompasses. However, as students explore the upper echelons of mathematical ideas, they begin to understand and appreciate the many facets of mathematical thought. This rings true for six accomplished Stuyvesant students who recently earned meritorious designation at the SIMIODE Challenge Using Differential Equations Modeling (SCUDEM).

SCUDEM is a university-level contest that asks students to apply mathematical modeling to various real world situations using differential equations. Teams are allowed to choose a challenge problem in the areas of physics/engineering, chemistry/life sciences, and social sciences. This year was Stuyvesant’s first year participating, and two teams of three students each, both coached by math teacher Patrick Honner, won Meritorious designation. 

The competition was run by the Systemic Initiative for Modeling Investigations & Opportunities with Differential Equations (SIMIODE), an organization founded by Dr. Brian Winkel. Before his work at SIMIODE, Dr. Winkel taught mathematics at the U.S. Military Academy in West Point, New York, where he found a passion for applying math to real-life situations. “My personal Eureka moment of learning the excitement and joy in seeing mathematics applied to solve real-world problems shaped and continued to form and motivate my teaching style, which is to use a modeling opportunity first and then to get students to discover the mathematics to solve the modeling situation they were facing,” he recounted in an email interview.  Winkel continued, “So [SCUDEM] is a modeling-first approach, as opposed to ‘let’s all learn the mathematics and somewhere downstream (or never!) we would find an application or use for it.’” It was with this experience that Dr. Winkel moved forward with creating SIMIODE and the SCUDEM competition. Dr. Winkel described his motivation in founding SIMIODE, writing, “I thought I would try to form an online Community of Practice in support of colleagues who wanted to teach a pivotal mathematics course for STEM students, namely differential equations.”

SIMIODE was founded in 2013 and has been hosting SCUDEM for nine years. Despite its relative newness, SCUDEM offers a special opportunity for student’s knowledge in math to be showcased nationally through creative projects. “Originally, the concept was to offer students three problems in which they were to use the mathematics of differential equations,” Dr. Winkel elaborated. “Student teams of three would come together at regional centers in the U.S. and several places around the world, to give a 10 minute talk for local judging, receive scores and feedback, be presented with awards and then go home, knowing they had been engaged in something intellectually exciting.” However, after COVID, this process was moved online and students began submitting slides or videos as opposed to in person presentations.

Dr. Winkel believes that it is this intense modeling and feedback process that makes SCUDEM unique. He wrote, “The uniqueness is that there are no large cash prizes, no big ceremonies—just judge feedback.” SCUDEM is different from other mathematical competitions in its emphasis on learning and growing as opposed to fancy prizes and awards. As such, teams receive feedback from eight to 10 volunteer judges in the form of scores and extensive comments. “The main point is that this SCUDEM event just offers students the opportunity to work in teams, to learn modeling by applying mathematics, to learn mathematics and discipline materials, and to celebrate the joy of completing a challenging modeling opportunity,” Dr. Winkel summarized.

The competition took place over three weeks between October and November. “I chose to participate since I was interested in learning more about using differential equations in modeling,” senior Ethan Sharma explained in an email interview. Sharma worked with junior Jackson Hayes and senior Jackie Zeng to model high levels of dangerous metals in chocolate. “Our goal was to determine the effect of these metals on a child consuming the chocolate at different rates [and] times,” Sharma described. “Our model split the body into compartments [...] The purpose of each compartment was to either measure the amount accumulated in it or to facilitate moving metal throughout the body.” 

In order to complete this ambitious project, Sharma’s team chose to distribute their tasks. “I researched the physics [and] biology behind the processes so that the compartment model made sense and implemented the model in [a mathematical programming software called] MATLAB,” Sharma recalled. Despite the team’s determination and organization, time management posed a significant challenge. “We wanted to try to implement some partial differential equations to model internal blood flow (like diffusion of metal at organ boundaries), but this was difficult to implement with MATLAB, and we ended up not doing it in the interest of time,” he detailed. 

Even while feeling rushed, Sharma found the experience of competing in high-level mathematics against undergraduate students rewarding. “The competition was a nice learning process for actually implementing models and familiarizing myself more with solving differential equations,” he said. “This competition also helped our High School Mathematical Contest in Modeling—a different modeling competition—solution as I was able to use MATLAB to simulate a similar model,” Sharma added. 

Senior Connor Yau also participated in the competition along with junior Armistead Williams and senior Sascha Gordon-Zolov. Together, they used differential equations to determine how early humans fought megafauna. “They wanted you to model spear penetration on various animals,” Yau said. “There were two main methods that we explored: throwing spears and hiking spears, and basically you built a model that helped determine which of the two of those were primarily used.” 

This task came with a host of challenges, including the research involved to learn more about this niche topic. Yau noted, “We had to read a lot of papers on how spears were thrown and the kinetic energy required to penetrate animal flesh and skin with a spear.” However, the library of resources on this particular topic had its limitations. “No one studies spears so we used an analogue, which was a javelin,” Yau explained. This strategy opened up more pathways to information and allowed for more accurate data collection. 

Williams worked alongside Yau and Gordon-Zolov to research neolithic spears. When asked about group dynamics, Williams explained, “Initially thinking through the problem, we all worked together to learn and understand the physics concepts and approach the question.” However, the group soon diverged based on individual skill sets. “In the end, [Gordon-Zolov] was the only one who could edit the slides, so he would write the slides while [Yau] would do most of the modeling using the MATLAB software, and I would be creating ‘diagrams’ and providing research,” Williams elaborated.

For Williams, the competition offered new insight into math beyond the confines of the classroom. “It gave me a new perspective towards how math and analytical thinking can be applied in the real world, how the skills learned in school can actually be used,” he described. Engaging in extracurricular math activities expanded Williams’ horizons. “In terms of skills, I am only beginning to understand how to approach this type of problem and how to model in general,” he said. This competition marks an entrance into a whole new world of modeling, and these students still have much to learn and explore.

Both teams were advised by mathematics teacher Patrick Honner, who was familiar with SIMIODE through his work in linear algebra and modeling. “When I learned about [SCUDEM], I didn’t think that I was ready to work with the students to compete in the competition,” Honner explained. “But after a couple of years, when I had become more comfortable with modeling and had built up more of a modeling club [at Stuyvesant], I brought it as an option.” Students quickly expressed interest in the competition. 

The role of an advisor ended when the competition started. However, Honner cultivated a space to prepare students through the Math Modeling Club at Stuyvesant. “We learn about how to mathematically model applied problems in general,” Honner described. “Modeling is a way to bring mathematical tools to real world scenarios. We learn general tools and specific techniques for modeling in different contexts.” These tools helped the teams participating in SCUDEM, a competition specifically designed for differential equations. “I [...] give them resources. We talk about general modeling techniques and then, once the competition begins, the students are on their own.” Honner added. 

Though SCUDEM is primarily for university students, the experience was a gratifying success for Stuyvesant, despite the age difference. “This is our first time going through the competition, so I have a better idea of what to expect. Having debriefed with the students about their experiences, I learned what might’ve helped them more, like access to [...] more explicit resources about physical models,” Honner reflected. The competition revealed how Stuyvesant students were able to tackle university-level academic challenges. “This is another example of how incredible the students here are, how they can be pointed in a direction, and [how] with a little bit of guidance, but with a lot of self determination, drive, and passion, they can do exceptional work,” Honner said. 

SCUDEM offers students a unique opportunity to explore applied mathematics and modeling. Regardless of age and experience, this year’s students persevered to create successful projects based on real scientific and mathematical problems. Both teams were given a meritorious award for their work and proved that other high school level students can accomplish the same distinction through hard work and motivation. From gaining skills in teamwork to high-level mathematics, SCUDEM is a great opportunity for students to build interest and push their mathematical skills out of the classroom and into the real world.