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Hitting the Math Trail
Curriculum Center

The National Math Trail program shows teachers how their students can create mathematics problems based on what they see in their community. Students also use computer technology to submit their math problems to the National Math Trail Web site. Included: Examples of real Math Trail problems.



Graphing points scored by Phoenix Suns basketball players and calculating commuting costs on a Philadelphia trolley in the late 1800s are just two of the more than 800 National Math Trail expeditions that students across the United States have embarked on during the past two years.

The Math Trail expeditions, in which students explore their communities, find real-life illustrations of math concepts they are studying, create problems based on their discoveries, and then post their problems to the Web, are part of a U.S. Department of Education (DOE) telecommunication project. The project also is supported by the DOE's Satellite Educational Resources Consortium (SERC), the NEC Foundation, the Verizon Foundation, and Texas Instruments.

Following the Math Trail

Angelique Conner's third-grade class at Robert Shaw Theme School in Scottsdale, Georgia, created the following Math Trail problems.

This is Mr. Diggs. He is our principal. When you come into Robert Shaw, make a left, and his office is the first one on the left.

Problem: If Mr. Diggs gets to work at 6 a.m. and leaves at 5:30 p.m., how long does he work?

Answer: 11 hours and 30 minutes

Solution: Start at 6 a.m. and count up the hours: 7, 8, 9, 10, 11, 12, 1, 2, 3, 4, 5. That is 11 hours. Then you have to add 30 more minutes to get to 5:30.

Problem: If Mr. Diggs gets 12 calls a day, how many calls does he get in a month?

Answer: 360 calls

Solution: You have to multiply 12 calls each day times how many days in the month, which is about 30. 12 x 30 = 360


Most National Math Trail projects start with students exploring their community -- or even just their school. In James Unger's fourth-grade class at Austin Elementary School in Dunwoody, Georgia, for example, students tour their school to find real-life examples of relevant math concepts and then draw pictures showing the concepts they are studying.

Only after students can correctly characterize the math problems, determine how to solve them, and communicate the information to their classmates, are they allowed to photograph the problems with a digital camera and post the information to the Web.

Angelique Conner, a third-grade teacher at Robert Shaw Theme School in Scottsdale, Georgia, also took her students on a Math Trail expedition around their school and grounds. The students took pictures of potential math problems and discussed the concepts in groups. Conner said she was able to assess students' critical thinking skills as they created their problems. "The students do math problems every day, but they've never before had to come up with their own problems. Math Trail really gets them thinking and talking about math and about working together," Conner noted.

In other Math Trail activities, first graders from Garden Lakes Elementary School in Avondale, Arizona, made graphs to track baskets scored by the National Basketball Association Phoenix Suns players. Students from Overlook School outside of Philadelphia, Pennsylvania, figured the cost in the 1800s of commuting by trolley from Philadelphia to then Willow Grove Park, six days a week at a cost of 15 cents each way.


Creating a Math Trail is not just about equations, however. Communication skills also are an important aspect of Math Trail activities. Students must document background information about their math problems, and they must be able to effectively present the problems to their classmates.

Master teacher Kay Toliver, who taught math and communication skills for more than 30 years, and who helped develop the Math Trails concept in her own classroom, places heavy emphasis on the students' ability to communicate mathematics concepts.

"Mathematics is a subject in which we have to create thinkers, not memorizers," Toliver said in an interview with National Math Trail project producer Racquel Skolnick. "Math is a subject that involves history and literature as well as numbers; it is more a communication art than anything else. If students are to become the thinkers of tomorrow, we can't just concentrate on getting them to pass tests. We have to show them the real reasons for learning various mathematical concepts. Those reasons have to do with math being alive and related to every aspect of life. I want students to discover that for themselves."

Math Trail also is a good way for teachers to integrate technology into the curriculum. Classes post their Math Trail problems to the Internet, supplementing them with narratives, photographs, drawings, and audio and video segments.

David Hendry, curriculum director of the Foundation for Advancements in Science and Education (FASE), was instrumental in expanding the Math Trail concept into a national Internet-based project. "The National Math Trail brings together a lot of elements that we know are important in teaching and learning," Hendry said. "National Math Trail gets students working together, which is a vital job skill. It helps students develop problem-solving skills by forcing them to not only solve problems but also to formulate problems. It enables teachers to assess both their students' understanding of concepts and their acquisition of skills. It makes an abstract subject concrete by placing it within the context of the real world. And the icing on the cake is that the Math Trail forwards the use of technology in a way that integrates naturally into curriculum objectives."


Teachers who want to learn how to launch Math Trail projects with their classes can attend the National Math Trail Training Institute, a two-day professional development program. There, teachers learn to integrate real-world connections into mathematics instruction, engage students, and help them develop problem-solving skills. The program combines technology training with a hands-on math trail experience. About 600 teachers already have attended Math Trail training institutes.

"The National Math Trail Training Institute received the highest rating of any staff development program we have ever provided to our teachers," said Barry Doran, Pre-K-12 mathematics coordinator for the Dekalb County School System in Decatur, Georgia.

In fact, most teachers who have attended the institute give the program high marks, according to a study done by Hezel Associates, evaluators of Star Schools programs for the U.S. Department of Education. "Teachers agreed ... that Math Trail is a good way to introduce and review math content they already are required to teach. Teachers also report that the time needed to develop a Math Trail is quite flexible," according to the report.

The exposure schools and students get through Math Trail also is beneficial, Conner noted. "The National Math Trail is a way of letting the world know what you're doing," she said. "The kids feel really great about themselves when they can use a computer and go on the Internet. Parents can pull [it] up on the Web at home, and everyone can see what the students are doing."