Math Modeling Workshops for High School Students

The University of Utah’s Department of Mathematics recently launched a new program that introduced high school students in Salt Lake County and the surrounding areas to mathematical modeling. The program, which ran throughout September and October 2021, sought to prepare students for mathematical modeling competitions like the High School Mathematical Contest in Modeling (HiMCM) and MathWorks Math Modeling Challenge (M3 Challenge), a program of SIAM.

Over the course of eight weeks, participating students learned the fundamental concepts of mathematical modeling frameworks—including difference/differential equations, regression, and parameter fitting—as well as basic programming and writing skills. Regardless of whether they ultimately formed teams to compete in the upcoming modeling competitions, all students developed useful technical and problem-solving expertise that will help them as they continue to hone their mathematical abilities.

Due to the workshop’s online format, high school students from all over Utah were able to partake. The Utah State Board of Education even advertised the workshop in its twice-monthly science, technology, engineering, and mathematics (STEM) educator newsletter. As such, the program had attracted motivated students from all types of mathematical backgrounds by the time it commenced in early September.

Participants met virtually for two hours each week, ultimately leading up to HiMCM in November. The first hour of each session consisted of an active lecture wherein volunteers familiarized students with programming techniques, data analysis, model fitting, sensitivity analysis, and report writing, among other topics. These lectures engaged attendees with discussion-based activities and group coding sessions in Python via Google Colab (see Figure 1). Presenters had creative control over their sessions and often incorporated their own modeling experiences into the conversation. For example, Julie Sherman (University of Utah) adapted a discussion about sea turtle population dynamics from a previous workshop at the University of Minnesota into a larger conversation about difference/differential equations (see Figure 2).

During the second hour of each session, students split into small teams and worked on real-world problems from previous M3 Challenge years. These questions addressed issues like food waste and insecurity and the rise of e-cigarette use among teenagers. Students were encouraged to make and justify assumptions, define relevant variables to serve as model inputs and outputs, and discuss the types of mathematical frameworks that would effectively encompass the scenarios. In just an hour, participants developed an initial plan of action to tackle the competition questions. Attendees appreciated the applicability of these tools to a wide variety of real-world situations. “Prior to the workshop, I never thought of attacking economic problems like world hunger using math,” Caelum van Ipselen, a junior at Rowland Hall in Salt Lake City, said. “It was intriguing to find out how mathematics could offer solutions to these problems.”

In the second hour of the following week’s workshop, volunteers walked students through winning solutions as well as a stratified set of anonymous non-winning solutions. Students then analyzed these solutions and discussed the validity of assumptions, the choice of variables, and the structure of the mathematical models. By the end of the workshop series, participants could think critically about their own work, make stronger arguments for their assumptions, create more robust models, and recognize the important organizational aspects of a competitive contest submission.

The workshop’s content was based on two modeling handbooks that are published by SIAM: Math Modeling: Getting Started and Getting Solutions and Math Modeling: Computing and Communicating. These resources are freely available online. Though this program was meant to prepare students for HiMCM (sponsored by the Consortium for Mathematics and Its Applications), much of the material came from SIAM’s M3 Challenge — an annual mathematical modeling competition for high school juniors and seniors in the U.S. and sixth form students in England and Wales. Teams of up to five students have 14 hours to generate mathematical models for a given set of questions and communicate their results in a comprehensive written paper. The Challenge problem generally contains a three-part, data-focused question; students may choose to utilize statistical analysis and/or programming knowledge of MATLAB, Python, or any other software (or combination of software) to predict future events. The competition awards annual scholarship prizes of more than $100,000 and designates additional extra credit scholarship awards for teams who choose to submit code with their solution papers. M3 Challenge aims to motivate young people to study and pursue careers in applied mathematics, computational science, and technical computing by bringing together students and applied math practitioners.

Historically, not many teams from the Salt Lake County area have participated in M3 Challenge or HiMCM, so the workshop increased awareness of mathematical modeling for local students. For instance, it provided van Ipselen’s first glimpse into the world of math modeling and its associated competitions. “It was great to receive pragmatic advice from former competitors,” he said. “They invariably gave experience-based answers to my questions, and I walked out confident in what I needed to do well.” Van Ipselen competed in HiMCM in November 2021 and plans to partake in future competitions. Some educators who are interested in incorporating mathematical modeling into their classrooms have also expressed interest in partnering with the program leads on future projects.

After the program concluded, planning immediately commenced for the next workshop series, which will take place in mid-January to February — just before M3 Challenge. With the help of SIAM and MathWorks, this forthcoming workshop will adapt hands-on coding examples into MATLAB (MathWorks’ signature software) and reach a larger group of motivated high school students and their teachers/coaches. Sessions from the program will be recorded and all code and other materials will be available online so that interested students can learn about—and start coding for—math modeling. High school and sixth form students, as well as secondary teachers who might serve as coaches, can register for the January-February 2022 workshop series and access information about session dates and times online.

Acknowledgments: Wesley Hamilton (University of Utah) and Sheina Rodriguez (Orlando Math Circle) prepared the program’s original slides with the help of Kate Daftari, Austin Ferguson, Andrew Ford, Scott Hallyburton, Anne Talkington, and Wenzhong Wang (all of the University of North Carolina at Chapel Hill). Lindsey Henderson (Utah State Board of Education) graciously advertised the workshop to her network of Utah STEM educators. Moreover, this workshop could not have occurred without the time and effort of the following faculty and applied mathematics students at the University of Utah: Anil Cengiz, Owen Koppe, Xiao Shen, Julie Sherman, and Nathan Willis.