November 25, 2014 at 9:41 am

Can You Solve the Navajo Sheep Problem?

Take a peek into the Navajo Nation Math Circle with a New York Times “Numberplay” problem, prompts Dr. Robert Klein.

The number problem was provided by Kansas State University math professor Dave Auckly, who along with Klein is a co-director on the Navajo project.

Born in Albuquerque, NM, Klein returned home to the Southwest last summer to help support the project and create a mentor network for the Navajo math circle.

The Navajo Sheep Problem

The Navajo people are known for weaving some of the most delicate and sophisticated textiles in the world, working with wool from local sheep. One day a sheep trader arrives at a market with 12 sheep to sell. Representatives from three clans — the Black Sheep Clan, the Mud Clan and the Water’s Edge Clan — want to divide each string of sheep. The clans know the sheep will breed, so they are quite interested in getting the right balance of different colored sheep. In particular, the Black Sheep Clan representative wants her strand to be exactly half black sheep, the Mud Clan representative wants exactly half brown sheep, and the Water’s Edge representative wants exactly half white sheep.

See the New York Times for the puzzle graphics needed to solve the problem.

Klein, Associate Professor of Mathematics at Ohio University, has been promoting math circles with youth and math teachers from Athens to Puerto Rico.

Bob Klein leads a session during the Navajo Nation Math Circle Project’s summer math camp.

Bob Klein leads a session during the Navajo Nation Math Circle Project’s summer math camp.

“It is a great project, and I was so impressed with what they are doing,” Klein said of the NNMC. “But I know from our work with math circles that to be sustainable you have to have a big group of people committed to it. The Navajo Nation Math Circle Project was a place where I felt that I could contribute and where I really wanted to contribute..”

Klein approached one of the co-directors of the NNMC, Tatiana Shubin of San Jose State University, and asked how he could help. When he saw Shubin again at a Joint Mathematics meeting, she took Klein up on his offer. Klein is now one of four co-directors of the NNMC, joining Shubin, Auckly, and Henry Fowler from Diné College.

In July, Klein helped operate the project’s summer math camp, a two-week non-residential camp offered to about 30 students, grades 6-12, from throughout the Navajo Nation. The students are bused in every day for the program, which is hosted by Diné College in Tsaile, Ariz. A network of dozens of mathematicians contributes to the program, which just concluded its second year.

Have Fun Playing with Mathematical Concepts

“Numberplay readers have certainly discovered the joy of playing with mathematics. People in the math circle movement believe that one of the best ways to help others learn mathematics is to show them how to have fun playing with mathematical concepts. In an effort to encourage more Native Americans to pursue professions in science, technology, engineering and mathematics, a group of mathematicians formed the Navajo Nation Math Circle project,” says Auckly in the Times.

The NNMC has attracted the attention of a documentary filmmaker. George Csicsery of Zala Films spent time this past summer in the Navajo Nation filming footage for a documentary he is developing on the math circle project. Among the individuals he interviewed for the film was Klein.

Watch the just-released Zala Films trailer.

Klein described the time he spent working in the Navajo Nation as extremely rewarding. Follow the Navajo Nation Math Circle on Twitter.

“The entire area was simply amazing – from the scenery to the people,” he said. “The Navajo people we met were giving and friendly as well as very interested in having their children participate in our program and very grateful for the efforts we gave.”

In addition to exploring mathematics problem-solving, the summer camp also features prominent Native American professionals working in the STEM fields who serve as role models and talk to the students about opportunities that are available to them. And, a unique aspect of the summer camp is that while most of the time at camp is devoted to math, one-third of the program is set aside for instruction in Navajo language and culture.

“Their language is one of those things that is dying out, and it’s not a particularly easy language to master,” Klein explained, noting the efforts he’s taken to pick up bits and pieces of the vernacular.

In addition to assisting with the NNMC summer camp, Klein has also participated in fundraising efforts for the program and in generating scripts that can be used to help guide educators interested in starting their own math circles.

Angela Woodward contributed to this report.

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