This article supplements the feature "Ethnomathematics and Mathematics Professors" in the April/May issue of MAA FOCUS.
A two-hulled canoe in the Pacific, where fishermen and sailors once used patterns in nature to guide them across long distances (Photo courtesy of Pat Kenschaft).
Linda Furuto loved growing up on O‘ahu’s* North Shore, spearfishing, diving, swimming, and surfing. One of her earliest childhood memories was jumping into the dumpster behind Hau‘ula Shopping Center, grabbing out one of the cardboard boxes, flattening it, and using it to ride as fast as she could down the dirt hill behind the mall. “Those are memories that I cherish,” she says.
Mathematics class? Not so much. She struggled with mathematics. Fortunately, she had influential teachers at Kahuku Intermediate and High School and Punahou Academy who helped her realize that mathematics isn’t solely contained within the four walls of the classroom. For example, recently she went spearfishing with some friends in Hawai‘i Kai and saw mathematics everywhere, from the geometric shapes of the menpachi (squirrel fish) to the functions, slopes, and rates of maximizing my time underwater.
Today, as an assistant professor of mathematics at the University of Hawai‘i–West O‘ahu, she helps mathematics-averse students see those kinds of relations and applications with the same enthusiasm. Her efforts in using and sharing a concept called ethnomathematics earned her a place as one of the Forty under 40 honorees recognized by Pacific Business News in 2010.
Ethnomathematics is defined by Brazilian mathematician Ubiratan D’Ambrosio as intersections of culture, historical traditions, sociocultural roots, and mathematics. It seeks to answer the perennial question of students in mathematics classes everywhere: What’s the relevance? Furuto answers that question on location. Her students go on field studies each semester.
One field trip is to the Hawai‘i Institute of Marine Biology on Coconut Island. Relationships between conservation, marine biology, and mathematics become apparent when students see linear functions at work as the Super Sucker cleans invasive species of algae off the reefs in KÄne‘ohe Bay, matrices organized by trash collected and geographical locations, and quadratic equations in sustaining precious island resources.
Another outing is to the Bishop Museum in Honolulu, where students look at constellations in the planetarium and analyze the distances and angles and relationships between stars. And to prove that mathematics applies not just in modern science, but also in cultural history, she takes students to visit a traditional voyaging canoe, the HÅkÅ«le‘a, where they speak to navigators and crewmembers about distances traveled and systems of equations; about trigonometry and figuring out the different properties to help get from one location to the next; and about the shape of the sails to maximize distance and minimize resistance.
“It is important that students know what is written in our textbooks, because they contain important information,” Furuto says. “However, equally critical is that our students understand and realize that their ancestors sailed thousands of miles across the Pacific Ocean without any kind of modern navigational tool. Those ancestors used the sun, the moon, the stars, the winds, the tides, bird migratory patterns, and more. They weren’t called scientists or mathematicians; those terms are western in origin. Instead, they were called navigators and fishermen.
“The heart of ethnomathematics is acknowledging the unique identities and traits of each student. They have a significant role to play in our mathematics classes,” Furuto says, “and we should do everything we can to support them.”
Furuto's math class aboard a two-hulled canoe in Hawaii (Photo courtesy of Linda Furuto).
She calls the ship HÅkÅ«le‘a a terrific teaching tool. She has been involved with the Polynesian Voyaging Society for about five years and is training to sail with the canoe on its around-the-world voyage in 2013. The HÅkÅ«le‘a, “star of gladness,” is a Hawaiian voyaging canoe internationally renowned for the role it has played in rekindling the Pacific Island tradition of way-finding techniques, which include celestial navigation to locations such as Tahiti, Rapa Nui, Marquesas, Samoa, Micronesia, Tonga, Japan, and the U.S. mainland. The HÅkÅ«le‘a is a powerful vehicle to explore real-world applications of mathematics in the Hawaiian and global communities, and it represents resourcefulness, inventiveness, and wisdom.
Firsthand experience also tells Furuto that ethnomathematics works to engage people in mathematics. One of her students was a Hawaiian Airlines flight attendant who worked the red-eye from the West Coast, arriving in Honolulu International Airport about 4:30 a.m. He’d drive to the UH West O‘ahu parking lot and sleep in the car until my 9:30 a.m. class, which he signed up for only to fulfill a degree requirement.
This student really struggled with mathematics. However, through these ethnomathematics-based field studies, he found a desire to learn that grew within him. Even when his requirement was fulfilled, he enrolled in precalculus courses the next two semesters and participated in Furuto’s Ethnomathematics Curriculum Project during the summer.
“Watching him grow—watching him struggle and succeed—is one of the greatest joys and beauties of teaching,” Furuto says. “One of the reasons why I love my job is because of the students I have the opportunity to work with—in particular those who tell me that they don’t like mathematics and that there’s anyplace they’d rather be than in the mathematics classroom.”
She also teaches a mathematics course for elementary teachers, in which students study different pedagogies and ways to teach mathematics. She applauds the state’s efforts to improve mathematics instruction through summits sponsored by the University of Hawai‘i System in collaboration with Hawai‘i P-20 Partnerships for Education and the State of Hawai‘i Department of Education. The summits bring together mathematics faculty, secondary school educators, and administrators to discuss challenges and successes and chart the future.
In that vein, UH–West O‘ahu hosted a summer Ethnomathematics Curriculum Project with funding from the UH Student Equity Excellence and Diversity Program and the National Science Foundation. Mathematics faculty, students, and staff from UH–MÄnoa, UH–West O‘ahu, and Leeward Community College drew upon Hawai‘i’s diversities, ethnic heritages, and cultural roots to design culturally relevant mathematics curricula. Published materials were distributed to various UH campuses and the Hawai‘i Council of Teachers of Mathematics Library to supplement courses such as college algebra, precalculus, survey of mathematics, and trigonometry.
Cultural interests influence Furuto’s own research interest in number theory as well as her commitment to education. In Fiji, she was teaching at a technical college in Suva in 2000 when the election of the first prime minister of Indian descent set off riots and looting. Education trailed economic, political, and social concerns as the situation unfolded, she says. “And yet, I thought to myself, it’s education that knits together a country. It’s what we use to build a nation of educated citizens who will make wise decisions about the future of that country.”
After completing a master’s degree at Harvard and Ph.D. at UCLA, she came home to what she calls her dream job at UH–West O‘ahu, where she established the Mathematics Center (now the No‘eau Center for Writing, Mathematics, and Academic Success) to provide tutoring, mentoring, and research experiences.
These experiences “really instilled in me the kuleana [responsibility] we each have to give back to the world that gifted us with life,” she says. “I firmly believe that there exists a powerful light that burns within each and every one of us. We have unique and special heritages, languages, cultures, and traditions. Ethnomathematics allows us to tap into these treasures and find a connection between wisdom grounded in the past and hope for a bright and beautiful future.”
*This article uses Hawaiian spelling and punctuation.Cheryl Ernst is editor of Malamalama, a University of Hawai‘i publication. A version of this article appeared in MÄlamalama.
Linda Furuto is currently an assistant professor of mathematics at the University of Hawai‘i–West O‘ahu, She was a fellow at the East-West Center while completing her Ph.D. at UCLA. Over the past 10 years, she has been a Visiting Scholar the University of Tokyo, worked with students in the Boston public school system as a research-practitioner at Harvard University, taught mathematics and music at the LDS Technical College in Fiji, and collaborated with the East-West Center and Ministry of Education of Vietnam. In addition, she has researched and consulted at the U.S. Department of State in Washington, D.C., UCLA Center for International and Development Education in Los Angeles, and Pacific Resources for Education and Learning in Honolulu.