This course goes beyond the traditional high school mathematics curriculum by engaging students in open-ended problem solving, computer simulations, and collaborative work. Students use a mathematical approach to model real-world situations through the application of algebra, geometry, trigonometry, and statistics.
It’s been a Mass Academy tradition for all students to take part in the HiMCM math modeling competition. Within this competition, teams of four students solve one of two real-world mathematical modeling problems within a span of 36 hours and write up to a 25-page report on their methodology and findings. Our group—Anne, Marlon, Nathan, and I—modeled a bee colony population over time, taking into account a variety of ambiguous factors such as bee diet, predators, sickness, and the overall plentifulness of food. We chose this problem due to the myriad of possible approaches and the creativity that this problem offers. We approached this problem by splitting the bee population by developmental stage, and considered the various factors that affect the mortality and prosperity of each population.
As evidenced by the name of the class, we solve numerous problems that involve mathematical modeling. Much of this work is done in groups, such as the Epsilon School problem. Within this problem, a hypothetical STEM school received additional funds to expand and significantly increased their incoming class size. To supplement this, the school expanded their teaching staff. Given the enrollments for each class within all grades during the current year, we were tasked with determining the most effective placement of each teacher. For this problem, our group decided to utilize gradient descent to determine the placement of teachers that would enable the allocation of teachers to most closely maintain the prior student-to-teacher ratio.