Have you ever heard of a math trail? If you love math and walking, this is the perfect combination of the two. Read on to discover more about math trails and how you can start blazing your own.
A math trail is a walk to discover mathematics. And it can be almost anywhere—a neighborhood, a business district or shopping mall, a park, a zoo, a library, or even a government building. The math trail map or guide points to places where walkers formulate, discuss, and solve interesting mathematical problems.
Anyone can walk a math trail alone, with family, or with another group. Walkers cooperate along the trail as they talk about the math problems. There’s no competition or grading. At the end of the math trail, they have the pleasure of having walked the trail and of having done some interesting mathematics.
The earliest math trails appeared in England and in Australia. In 1985, Dudley Blane and his colleagues blazed a trail around the center of Melbourne as a holiday-week activity for families.
The trail’s mathematical ideas included investigating a circular pattern of bricks in the pavement (to discover the invariance of pi), studying the timetables in a train station, looking at the reflection of a cathedral in a pond (to estimate its height), trying to estimate the speed of water rushing down a spillway, counting the number of windows in a wall of a skyscraper, and looking for patterns in the numbers of post office boxes.
Australian mathematics educators constructed many more trails based on a variety of themes and venues, including preparing for prospecting in a gold rush town, acting as an apprentice keeper in a local zoo, and working on the ship works and sailing boats in a historical nautical village.
Like any good idea, the idea of a math trail has spread and people have adopted it. Carole Greenes of Boston University created a historical mathematics trail in Boston centered on the Common and the Public Garden. Unlike Blane’s Melbourne trail, walkers on Greenes’ trail followed a human guide who knew the historical and mathematical aspects of the trail and who could give hints and suggestions to walkers who got stuck on a task or idea.
Kay Toliver, an award-winning New York City schoolteacher, leads her students on walks while guiding them to discover mathematics in their school neighborhood. Student walkers do not write their ideas and solutions on paper, but informally discuss their discoveries on the spot and then take the discussion back to the classroom.
While there is a basic model for a math trail, you can adapt it to your location and match your interests. But to get you started, here are some common characteristics of the math trail model:
Are you ready to get started on your first math trail? These resources will help:
Submit your math trail story here to be considered for a future article on this blog. Of course, we at COMAP are particularly interested in trails that feature some mathematical modeling or optimization problems, but any math students find is good math. Happy trailblazing!