Leave it to a mathematician to describe her childhood haunts in terms of a three-mile radius.
Linda Furuto smiles when she reminisces about growing up on Oʻahu’s North Shore, spearfishing, diving, swimming, surfing around Kaʻaʻawa and Kahuku.
“One of my earliest childhood memories was jumping into the dumpster behind Hauʻula Shopping Center, grabbing out one of the cardboard boxes, flattening it and using it to ride as fast as we could down the dirt hill behind Hauʻula Shopping Center. Those are memories that I cherish.”
Math class? Not so much. “I struggled with mathematics,” she admits. 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, this past weekend I went spearfishing with some friends in Hawaiʻi Kai, and I saw mathematics everywhere, from the geometric shapes of the menpachi hole to the functions, slopes and rates of maximizing my time underwater.”
As an assistant professor of mathematics at the University of Hawaiʻi–West Oʻahu, Furuto helps math-averse students see those kinds of relations and applications with the same enthusiasm. Her successful 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.
Making mathematics culturally relevant
“Ethnomathematics is defined by Brazilian mathematician Ubiratan D’Ambrosio as intersections of culture, historical traditions, sociocultural roots and mathematics,” Furuto explains. It seeks to answer the perennial question of students in math classes everywhere: what’s the relevance?
Furuto answers that question on location. Her students go on field studies each semester.
Classes have visited UH’s Hawaiʻi 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 Kāneʻohe Bay, matrices organized by trash collected and geographical locations, and quadratic equations in sustaining precious island resources.
At Bishop Museum, 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 in cultural history, she takes students to visit the Hōkūleʻa, 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; about the shape of the sails to maximize distance and minimize resistance.
“I believe 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—by the sun, the moon, the stars, the winds, the tides, bird migratory patterns and more. They weren’t called scientists or mathematicians because 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, and we should do everything we possibly can to support them.”
Helping students succeed in mathematics
Furuto can speak of Hōkūleʻa from first-hand knowledge. She’s 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, thus far traveling to Lanaʻi, Molokaʻi, Maui, Kahoʻolawe and Oʻahu.
First-hand experience also tells her that ethnomathematics works. She describes a Hawaiian Airlines flight attendant who worked the red-eye from the West Coast, arriving in Honolulu about 4:30 a.m. He’d drive to the UH West Oʻahu parking lot and sleep in the car until Furuto’s 9:30 a.m. class, taken strictly to fulfill a degree requirement.
“This student really struggled with math. However, through these ethnomathematics-based field studies, he found a desire to learn that grew within him,” says Furuto. Requirement fulfilled, he nonetheless enrolled in pre-calculus 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 enthuses. “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 math and that there’s anyplace they’d rather be than in the math classroom.”
She also teaches a mathematics course for elementary teachers, in which students study different pedagogies and ways to teach mathematics. She salutes the state’s efforts to improve mathematics instruction through summits sponsored by the University of Hawaiʻi System in collaboration with Hawaiʻi P-20 Partnerships for Education and the state Department of Education. The summits bring together mathematics faculty, secondary school educators and administrators to discuss challenges and successes and chart the future.
Improving mathematics teaching and curriculum
In that vein, UH West Oʻahu is hosting 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 Mānoa, UH West Oʻahu and Leeward Community College draw upon Hawaiʻi’s diversities, ethnic heritages and cultural roots to design culturally relevant math curricula. Published materials will be distributed to various UH campuses and the Hawaiʻi Council of Teachers of Mathematics Library to supplement courses such as college algebra, pre-calculus, survey of mathematics and trigonometry.
Cultural interests influence Furuto’s own research interest in number theory as well as her commitment to education.
She describes a pivotal experience 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, 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 her master’s at Harvard and PhD at UCLA, Furuto came home to what she calls her dream job at UH West Oʻahu, where she established the Math Center (now the Noʻeau Center for Writing, Mathematics and Academic Success) to provide tutoring, mentoring and research experiences.
On a visit to Kahoʻolawe Island with the Hōkūleʻa, Protect Kahoʻolawe ʻOhana’s Uncle Maka told her that it was her responsibility to share with the world what she had learned, what she had seen, what she had felt, what she had smelled, what she had touched.
“These experiences really instilled in me the kuleana we each have to have give back to the world that gifted us with life,” she reflects. “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.”