Math Trails: Exploring Mathematics in the Real World

How might teachers use math trails and field-based education to explore mathematics in our environment?

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Inspired by the MƒA Equity Webinar Series STEM Education That Cultivates a Just, Thriving, and Sustainable World with Dr. Megan Bang, MƒA Master Teachers Ramona Fittipaldi and Andrea Kung wanted to approach the idea from a mathematical perspective. 

Initially designed as a single session, Math Trails: Exploring Mathematics in the Real World expanded into a MƒA mini-course where teachers took part in a math trail throughout Madison Square Park (MSP) in Manhattan.

What is a math trail? 

A math trail is an outdoor education discovery walk aimed at uncovering and solving mathematical problems around natural objects, ultimately providing students with real world mathematical experiences. During the MSP math trail, MƒA teachers calculated angles and areas of the iconic Flatiron Building and analyzed patterns in architecture, nature, and movement. In later course sessions, they created their own trails, modified existing ones, and planned future class field trip trails. 

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“Having a collaborative environment allowed teachers to share ideas, discuss challenges, and explore ways to make math more engaging and relevant for our students,” said MƒA Master Teacher Cesar Fabela, who participated in the course. “The trail was a fun and enjoyable way to learn mathematics outside the traditional classroom setting.”

Teachers eventually used a feedback protocol to reflect on their work and collaborated with one another to continue to bring back resources to their own classrooms with some planning interdisciplinary projects involving different subject teachers at their school. Some of the resources they shared included MƒA math trails, a Math Trails book by Joel Schneider, Henry Pollak, and Mary Margaret Shoaf, and a guide titled Designing Places for Outdoor Learning by Dr. Megan Bang.

“My advice for teachers introducing field-based instruction in their own classrooms is to start small. You can explore your school building, local community or nearby park,” said Ramona. “It’s important to have students feel comfortable and excited about seeing and using math everywhere.”