Directed by George Paul Csicsery
Zala Films (2016)
Review by Paul Gilon
This superb documentary presents the Diné version of the “math circles” teaching model as it is being implemented on the Navajo reservation. The film records math circles sessions held in summer math camps and in several local schools. The film also presents interviews with students and their parents regarding various aspects of the program.
Mathematical outreach of this nature has been practiced in Bulgaria for over a century, and in Russia since the 1930s. In the United States, math circles programs were initiated in 2001 by the Mathematical Sciences Research Institute in Berkeley, California. At the time of the making of this film, there were 180 math students’ circles and 60 math teachers’ circles in operation stateside.
The math circles teaching model differs from the customary teaching method in that mathematics is presented as a beautiful investigative tool of analysis to be explored and enjoyed, not just a technique to solve specific problems. The instructors who teach this model function as facilitators or mentors. They are accomplished mathematicians who do this work on a volunteer basis. As mentors, they encourage and challenge the student to explore approaches to solve a problem rather than to seek immediate results. In accepting the challenge, the student is considered to have taken charge of the learning process.
The Navajo math circles model differs from the typical math circles model in that it incorporates elements of Navajo culture. One such element is the Navajo maxim “to walk in beauty and harmony,” which correlates well with the concept of mathematics as a beautiful tool. Dr. Henry Fowler of Diné College implemented this model to improve on the low-level math literacy skills of many Navajo children, especially those students living in rural areas of the reservation that are underserved by the education system.
The film is composed of a series of clips or vignettes, each consisting of an instructor who stands in front of students and presents a carefully selected mathematical problem. As described earlier, the instructor advises them to concentrate more on the approaches to the solution than on the solution proper. Following scenes show students tackling the problem, either in teams or individually. During that time, the instructor explains the pedagogic aspect of that problem to the film audience. Lastly, a student, representing himself or a team, goes to the blackboard and explains the analytical process that led to the solution. Classmates and instructors display their approval by applauds and kudos. The instructor then comments on the analysis just presented. These scenes are followed by an interview with the student who presented the results of the analysis. Many of the students express pride in their Navajo identity and credit both parents and elders for their encouragement and support. In several vignettes the parents are interviewed in the presence of the student during which they, in turn, express pride in their child’s accomplishments. Respecting and paying deference to elders is a fundamental Navajo custom, and Dr. Fowler has managed admirably to fuse it with the math circles model.
Spectacular scenes of the landscape accompanied by Indigenous music provide transitions between vignettes. This section of the film closes with a poignant plea from Dr. Fowler, exhorting the student to become proficient in math and return to the reservation to contribute to the well-being of the Navajo Nation.
The film shows clearly the impact of the model in breaching the math phobia prevailing among many students. This is attested by the exuberance of the students upon tackling problems and finding solutions. Several model factors stand out for contributing to the success of the program, including the absence of testing and grading, students’ control of the learning process, the mentoring by professional mathematicians, and pride in one’s Navajo identity.
Removing the testing and grading tasks from the teaching process, especially in math courses, has enormous benefits for students as well as teachers. Furthermore, allowing students to take charge of the learning process changes the role of the teacher from instructor to mentor. An additional factor that may have contributed to the learning process is the positive effect of being sympathetically observed by the mentors, the film crew, and the implied audience. This factor, known as the Hawthorne Effect—though difficult to measure—cannot be ignored.
Scenes of teacher workshops are also presented in the film. The sessions were designed to provide some of the techniques used by professional mentors to enable the local teachers to implement them in their own classes. Several teachers are already doing this. In addition to breaking the math-phobia, this may be the second most important ramification of the program, namely, the training of local teachers to become proficient mentors in their own school’s math circles.
Five bonus features are included with the film. The last three, “Exile and Return,” “Languages,” and “Tatania” add to the understanding of the Navajo culture. “Exile and Return” presents historical data of the forced conversion of Navajo children to Christianity, historical testimony on the terror of the Long Walk, and Dr. Fowler’s own difficult childhood experience in foster homes. For his own resistance to forced acculturation, he credits his mother’s admonition: “You are always going to be Diné, my child. Remember that.” The “Languages” special feature offers interesting insight into mathematical aspects of the Navajo language, while the “Tatania” feature presents comments about the program by several of the participating mathematicians. Additional interviews with students and instructors are also presented. In all, this is an exceptionally beautiful documentary.
Paul Gilon, Ph.D., a professor emeritus in the Information Systems Department at California State University, Long Beach, worked for several years at Diné College where he performed various functions, including volunteer I.T. instructor, manager of the Bureau of Reclamation Farm Project in Shiprock, and, more recently, professor of economics and statistics, in the Business Division.