The white board is filled with mathematical computations and equations. The team of three, seniors Allie Frymire, Rishi Vas and Matthew Toudouze, have spent weeks solving just one single problem. This problem isn’t just your basic calculus computation or geometric proof -they’ve successfully completed optimization of all financial portfolios for Chapwood Investments, a wealth management company in Addison, Texas.
Mathematical Decision Making, a trimester-long course taught by Upper School Math teacher Dr. Youssef Oumanar, contextualizes advanced math problems in the real world. The difference between this class and other traditional math classes, such as Algebra II and Precalculus, is that students are posed with questions that challenge them to incorporate the math they learn from the classroom into real-life situations.
Last year, there were three juniors and three seniors who took the course when it was offered for the first time. This year, there are five students enrolled, three seniors and two juniors. Senior Theo Lauriette said he decided to take the course this year because the concept of relating math to real-life situations appealed to him.
“When I read the class description, the idea of using math in an actual, complex, applied way was interesting, especially since it appears to me that the higher in math you go, the more theoretical and grounded real-life examples become less frequent,” Theo said.
The process of problem-solving is student-driven. Every day, Dr. Oumanar gives students a set of data to work with, and he allows them to formulate their own questions regarding the data and solve them.
“I don’t make them solve a specific question. Often, they have a question in mind, but then they come up with another one, so we end up solving another version of the problem, which is really cool,” Dr. Oumanar said.
Because students are required to work together frequently, senior Allie Frymire said that she developed important social skills from collaborating with other students during the course.
“Sometimes, a certain student would ‘lead’ the problem because they understood it better than others, but most of the time it was really just us working together to find a solution, and that’s extremely vital to developing teamwork skills,” Allie said.
According to Dr. Oumanar, the course was created without a formal curriculum to give students the freedom of applying math to their personal areas of interest. It shows students that math is a critical skill to have in order to succeed in other professional fields, such as physics and business.
Dr. Oumanar said that applying math to other disciplines is necessary because math can provide solid evidence for reasoning behind a certain decision.
“Today, in a variety of fields, applied mathematics is not only important, but necessary. In many situations, decision makers tend to trust and follow their intuition. They sometimes think a certain idea is the right approach, but when modeled mathematically, it fails to achieve the goal. Math is a neutral tool that helps to exclude human biases from the decision-making process and to find the optimal solution to a given problem,” said Dr. Oumanar.
The class incorporates standard mathematical concepts such as linear algebra and matrices with other professional areas like business. In last year’s
class, students worked with problems dealing with asset optimization and currency arbitrage–trading money for money. Senior Rishi Vas, who was also in last year’s class, said the course’s interdisciplinary nature brought realizations about the real-world applications of his mathematical knowledge.
“A lot of people lose track of the real world in school, especially when you’re learning a lot of math and science. It was really good to realize that everything I’ve learned at Greenhill, at least in the math department, could be used in the future, whether in college or as a profession,” Rishi said.
Although the course encourages students to extend their knowledge to different types of problems, the solution is not always easy. Due to the problem solving, hands-on nature of the class, the students look at long-term projects that require extensive thought and planning. While students in Algebra II take multi-question tests in 55 minutes, students in “Mathematical Decision Making” often don’t even produce a concrete answer for two weeks.
Allie said that the problem-solving experience is difficult, but rewarding.
“There was one problem in which we had to memorize a grid where the boxes were either filled with red squares or gray squares. Initially, I thought it had something to do with memorizing patterns, but eventually we realized that there was a quantitative method to memorizing them: binary numbers. It took us two weeks to arrive at that answer, which was difficult, but everything seemed to fall together in the end,” Allie said.
One of the biggest projects last year’s class took on was handling financial portfolios for Chapwood Investments. After meeting with the CEO of the company, Ed Butowsky, the students analyzed the 10 years’ worth data given and addressed the specific needs of the company. Their job was to allocate money to over 100 assets, maximizing return and minimizing risk. According to Rishi, working with a professional company was a rewarding learning experience.
“It was a cool project for us. The experience was great because it was definitely a hands-on project that involved a real-world situation. It was a great opportunity to further develop presentation skills since we met with the people at Chapwood Investments and gave presentations to the Greenhill administration,” said Rishi.
According to Dr. Oumanar, this class has shaped students to have more of a problem-solving mindset. Dr. Oumanar said that he thinks his students were successful in building skills needed in the real world from Mathematical Decision Making.
“Beyond the mathematical topics and formulas, the students from last year took away numerous problem-solving strategies, including how to break down a problem into smaller pieces and how to generalize it in a thorough way. I believe that one of the most important strategies they learned was how to listen to an idea that may not make sense at first instead of dismissing it quickly. By the end of class they were able to fix its flaws, which would put them a step closer to the solution,” Dr. Oumanar said.
Allie attests to developing problem-solving skills and values the knowledge gained over the course of Mathematical Decision Making.
“It was a really amazing experience, and honestly, probably one of the most influential educational experiences I’ve ever had,” she said. “Being able to practice these real-life applications this early on in my education is incredibly invaluable.”
Photo by Alice Zhang
Originally published in the December 2017 print issue