Mathematical Modeling

The goal of the mathematical modeling curriculum is for students to pose their own questions about both real and possible worlds and to use mathematics to answer those questions. The curriculum's culminating modeling experience is a project that has student groups create an original model and analysis for a question that they generate.

 

Our students design projects reflecting a wide range of interests. One group decided to design a movie theater with unimpeded viewing angles. They discovered that the constantly sloped floor of most theaters was not optimal and that certain curved floors were better. Other groups have explored pricing schemes for a record store, how to evenly illuminate a room, how to seat friends and enemies at the United Nations, and how to model heart tissue and study the disruptions that lead to heart attacks. Some questions are more playful: how can you eat a Reese's Peanut Butter Cup with the same ratio of chocolate to peanut butter in each bite? As with all real-world problems, none of these settings and questions come with instructions such as "use the quadratic formula now" or "see the example on page 27 that is like this one." Students learn to identify which of their many skills will help them solve a problem and learn how to teach themselves new mathematics when necessary. 

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Class activities include discussions, investigations, computer explorations, presentations by students, and peer evaluations of each other's writings. Major assignments linked to these activities include a poster, essays, problem sets, papers, experiments, and projects.

This curriculum has been used as a yearlong required course for all juniors at the Massachusetts Academy of Mathematics and Science and at Meridian Academy. It can also be adapted as a modeling strand interwoven across grades seven through twelve. While the curriculum is well established at these two schools, a version that lays out all of the components of the course in a way that will be useful for other schools is a work in progress. Early versions of some chapters ("Original") will be shared here soon and will be updated and accompanied by additional materials in the coming months. Sign up below to be notified when new material is posted. ​​​