Educational Media Reviews Online

Navajo Math Circles features mathematics students of the Navajo Nation who reside in the remote, sparsely populated Four Corners region of the southwestern United States (northeastern Arizona and northwestern New Mexico). These young Native Americans, ranging from grades 6-12, participate in the Navajo Nation Math Circles project. Math circles offer an innovative educational experience designed to instill a love of mathematics in students. Participation in a circle is a convivial, extra-curricular, and informal way to learn math. These collegial groups are led by mathematicians and focus on the processes of problem solving or the exploration of topics, rather than emphasizing the attainment of the correct answer to a problem. Thinking about ideas is encouraged rather than simply performing computations. Circles are not textbook-based, but rely on interactive, creative methods. Some circles may meet periodically over a stretch of time, while others hold intensive workshops or camps over a shorter span. The Navajo Nation Math Circles project began in 2012 (under the auspices of the Mathematical Sciences Research Institute) and was organized by mathematicians Tatiana Shubin (San Jose State University), Henry Fowler (Diné College), Dave Auckly (Kansas State University), and others. Fowler had already created a cultural math program that tied mathematical principles to Navajo culture and philosophy. The concept of aesthetics or beauty is key to his program—both mathematics and Navajo culture are deeply rooted in the love of beauty and in nature. Math circles, first appeared in the U.S. in the 1990s, brought from Eastern Europe, and the concept partners well with Fowler’s ideas. The annual Baa Hózhó Math Camp started the following summer of 2013. The film documents the Camps held in 2014 and 2015, the Teacher Workshops at Monument Valley High School in 2014 and Diné College in 2015, and also shows math classes at Many Farms High School, Rock Point Community School, and St. Michael Indian School.

The first interviewee is Diné College mathematics professor Henry Fowler. He describes the mathematical patterns he perceived as a child while watching his mother weave, noting the rhythmic sounds of the loom, the geometric design, and her measurement of the textiles with the span of her hand. The Navajo Nation Math Circles project promotes math literacy and walking in harmony with the spirit of math. The film echoes this symmetry; it is beautifully plotted and executed. The editing interweaves the perceptions of local teachers, students, family members and visiting mathematicians with footage of the Math Camp activities. They range from the sublime to the silly, such as: cooperative problem solving, demonstrations of proofs, juggling, a hike in Canyon de Chelly, and a good-natured water fight. The cast is well-balanced between the genders and across the roles of student, parent, grandparent, sibling, teacher, and mathematician. The Camp’s lessons are rooted in Navajo culture and in daily life: the vectors of billiards, the intervals of juggling, the geometry of art and design, as well as cosmology, cooking, games, and architecture. The students radiate enthusiasm and their testimonies give the film’s narrative both authenticity and dramatic arc. Natanii Yazzie explains that focusing on the process of problem solving makes him enjoy math and causes him to think beyond the ordinary. Irvilinda Bahe and Stephan Joe both appreciate the discovery of patterns. Cheyenne Bedonie is pleased that open ended questions or unexpected solutions are encouraged. Jaime Tsosie and Brandon Hobbs praise the program for teaching them to look at things from multiple angles and to find alternative solutions, which has improved their overall grades. High school teacher Corvina Etsitty says that Math Camp students are more willing to take risks and ask questions. The DVD’s bonus features provide added information about Navajo culture and language.

The film is obviously suitable for mathematics educators and students of Native American studies. But it has a potentially wider audience: educators and students in all fields could find it inspiring and beneficial because mathematics is universally human and inherent in so many endeavors. And the film could serve as an example for educators seeking to build cultural competency or to integrate cultural knowledge, critical thinking, and problem solving into their courses. The filmmaker has fashioned an elegant proof of the efficacy of Math Circles. The result is a cinematic, symmetrical framing of inner and outer beauty. The expansion of confidence within the Diné students is a beauty to behold; their potential seems boundless like the blue sky, red rocked-mesas, and sage-dotted juniper forests that encircle and extend in all four directions.