From Real Estate to High School Mathematics: An M3 Challenge Journey on the Joy of Open-ended Modeling Problems

By Kathryn Smith

Teaching mathematics was not my first career. I spent 12 years in commercial real estate development, during which I collaborated with architects, building owners, space designers, engineers, and contractors to lease and develop commercial spaces for large clients. Each client had complex logistical needs that required me to make assumptions, provide justifications, and generate predictions based on the company’s expected growth. I routinely modeled scenarios to determine projected optimal solutions that—given a variety of constraints and parameters—would best suit the current and growing space demands of my commercial clients.

After more than a decade in real estate development, I decided to switch careers and become a teacher. I wanted to work with students in the Philadelphia, Pa., public school system; the schools were chronically understaffed and in specific need of math and science instructors, and I thought that I could help fill this void.

In 2006, I took a job at Julia R. Masterman Demonstration and Laboratory School within the School District of Philadelphia (after having taught in the district for 10 years). Masterman is a public magnet school that offers robust and rigorous curricula for academically talented students in grades five through 12. Many of my students go on to pursue degrees in mathematics, engineering, physics, and computer science. I taught algebra, honors precalculus, and Advanced Placement calculus courses throughout my tenure at Masterman, and I founded the math club and robotics team soon after I arrived.

Despite my industrial modeling experience and the excitement of quantifying real-world scenarios with mathematics, I did not incorporate extensive, open-ended math modeling exercises into my classes until a poster for MathWorks Math Modeling Challenge (M3 Challenge)—then called Moody’s Mega Math Challenge—came across my desk 15 years ago. From that moment on, I became actively involved in the contest as both a coach for student teams and—upon my retirement from teaching—a judge for the competition.

The poster advertised $100,000 in prize money for successful teams, and I was certain that I could find enthusiastic and motivated students to participate. I shared the poster with a colleague, and we worked to identify a few students who might be interested in competing for the $20,000 first-place prize. Five students showed up to an introductory meeting, and our math modeling team was born. We barely made the deadline for entry that first year and only had a few days to prepare. We prepped by sorting through and thoroughly evaluating the winning papers from previous years, which were available on the M3 Challenge website. Our goal was to do our very best work within the constraints of the problem.

For the next 14 years, this is exactly what my Challenge teams at Masterman did. We experimented with different types of training strategies but always took full advantage of the available resources, including math modeling handbooks, judges’ commentary, practice problems, and previous winning solutions. We usually put forth both a junior and senior team so that seasoned veterans could lead preparation efforts and bring new participants up to speed. Each year, I was in awe of the students’ work, thought processes, and results.

As the contest changed over the years to allow for more sophisticated modeling and technical computing, our teams benefited from students who could write code and utilize more advanced modeling software. However, our emphasis on context and creativity remained the same. It was critical to me that my teams understood the relevance of the Challenge problem and the significance of their solutions. Students addressed the importance of their models’ real-world applications in the synopsis of their papers, and this understanding formed the basis for all subsequent modeling efforts both within and beyond the classroom.

As a result, a Masterman team received an M3 Challenge honorable mention award during 13 out of my 14 years as a coach. Only about six to eight percent of all participating teams are distinguished with any type of recognition, so this was a big deal. In 2021—my final year of teaching and coaching—our team finished in the top six as a finalist, which meant that they presented their solution at the M3 Challenge Final Event (which took place virtually due to the COVID-19 pandemic). This team’s stellar performance had a notable impact on the popularity of our math club, and membership doubled over the following year!

The senior members of Julia R. Masterman Demonstration and Laboratory School’s 2021 MathWorks Math Modeling Challenge (M3 Challenge) team hold a cake that commemorates their impressive performance at an end-of-year math party in Philadelphia, Pa., in May 2021. The team finished in the top six and was honored as a finalist. From left to right: Tanay Bennur, Ethan Soloway, Tobias Beidler-Shenk, and Owen Moss. Junior team member Hayden Gold is not pictured. Photo courtesy of Kathryn Smith.

After experiencing M3 Challenge’s remarkable effect on my modeling teams firsthand, I realized that all of my students would significantly benefit from open-ended math modeling. The 14-hour M3 Challenge was invigorating and stimulating in ways that traditional mathematical problem solving was not. Every year, the junior team members were eager to compete again. Students enjoyed the opportunity to be creative and collaborative, and they appreciated the intellectual demands associated with producing mathematical models that provide reliable, robust insight into profound universal issues. M3-style modeling offers more advanced challenges that connect mathematical thinking to real-world applications; I had already incorporated content from the American Mathematics Competitions problem banks and the Art of Problem Solving curricula into my classes, and I began to introduce open-ended modeling projects as well.

For example, my precalculus students annually completed a long-term project during which they developed a retirement portfolio for a fictitious client. They had to conduct research, make assumptions and justifications, generate parameters, perform sensitivity testing, and employ the same types of modeling strategies that M3 Challenge requires. In doing so, they learned about the importance of retirement planning, the power of compounding funds over time, and the value of investment diversification to mitigate the effects of market downturns. One year, my seventh-grade algebra students generated happiness scales that used weighted averages. The students had to justify the various parameter weights in order to plausibly quantify happiness.

I retired from teaching at the end of the 2020-2021 school year. One of the things that I loved most about my time at Masterman was the chance to work with students to prepare for M3 Challenge. Former students often say that the contest was the best academic exercise they encountered in high school.

In 2022, I served as an M3 Challenge judge for the first time. This new role offered a different perspective on the competition and greater insight into the processes that I observed as a coach. Once again, I was incredibly impressed by the participants’ talent and creativity. I also continued to find myself wanting to remind them not to forget why they are doing the math in the first place. Students must refrain from becoming so caught up in the procedural aspects of number crunching that they subsequently fail to thoughtfully connect their predictions to possible social, economic, or environmental impacts. The purpose of the Challenge problem should always remain at the forefront of solution development. When students prioritize the objective, they are more likely to produce a solution paper that provides critical insight into the current, real-world issue at hand.

As a long-standing competition coach and now as an M3 Challenge judge, I am absolutely certain of at least one thing: On any given day, a group of creative and motivated students can deliver extraordinary work in response to an open-ended prompt about an issue with relevancy to their everyday lives. They just need the opportunity and encouragement to do so.

Kathryn Smith is a retired math teacher in the School District of Philadelphia, where she taught for 25 years. She currently works in real estate development.