The Math Trail
##### By Kay Toliver

As math teachers, we have the responsibility not just to develop students’ mathematical skills, but to prepare them to be able to use those skills in life. The Math trail presents an exciting way to do just that.

I first heard about the math trail through a presentation made by Australian educator Dudley Blane at Long Island University’s Foundation for the Advancement of Mathematics Education (FAME) program.

In this activity, I saw a way to get my students working constructively with each other, a way to have them become active learners, and a way to increase their respect for their own community.

To give a context for the activity, I start by having my students read a short book about the history of East Harlem. They are usually surprised to discover how East Harlem has changed over the years, and are excited to learn about famous people who graduated from our school. We discuss what they have learned. I have also had good results from bringing in neighborhood “old-timers” to talk about how things have changed, or special aspects of the community.

We then bridge over into the math trail activity. Although one can focus on one particular math topic, such as geometry, I prefer to make the math trail a year-end activity in which students draw upon-and demonstrate-all of the math they have learned throughout the year (and in the years before).

There is, however, one specific topic that I usually take up as part of the math trail activity: networks, circuits and paths. I introduce this subject with a discussion of the routes of postal workers or sanitation trucks. Students then make booklets with their own examples of paths and circuits.

I start the math trail lesson by explaining to the students that they are going to go into the community. They will find examples of math problems along a route that they choose themselves-and they will create a book that presents both the trail and the problems they have created. And, of course, they must provide solutions for each problem in the book.

I then take the entire class out myself on a “trial run,” showing them where I want their trail to start and then walking around the community and finding a few examples of math problems. (It helps that I have 90-minute block periods in which to do this.)

Next, I put students into working groups. Each group must have a manager, a recorder, a photographer and other members, and each person must know his job. (Sometimes I let students choose their own groups, but more often I assign them myself, perhaps with some mathematical scheme. In life, they won’t always be able to choose who they work with, and I want them to develop the ability to work well with many different people.)

I tell the students that their book must have an introduction, a map of the community, and instructions as to exactly how to follow their trail.

Students take one or two periods to go out and determine the sites and problems of their trails. Then they work out how they will divide up the work of putting their book together, and do so in the next two periods.

One of the results that I want to achieve with this project is a sense of achievement among the students. I emphasize that they should be very proud of the final product before they turn it in to me. Whether they type it on the computer or hand-write it, I tell them it should look very good.

Before they turn their books in to me, the groups present their results to their classmates. This is yet another opportunity for learning, and for the students to feel pride in their accomplishments.

When I evaluate the books, the main thing I’m looking at is the math problems and their solutions. But I also look for the quality and effectiveness of the presentation, and good language skills.

It’s surprising what can happen when you take mathematics out of the classroom and onto the sidewalks. For example, I had one young student who didn’t do very well in geometry during the regular class. But as we were doing a trial run of the math trail, she looked up at the top of a building and saw one very large triangle and a smaller one on the edge of the roof. She looked up to me and said, “Miss Toliver, those are two similar triangles!” I had thought that this student hadn’t listened to anything through the whole section on geometry! She went on to explain to me just why they were similar, using the concept of proportionality.

Not only can the math trail give students a new view of mathematics and of their community, it can give a teacher a new view of his or her students’ understanding.