Ethnomathematics Makes Difficult Subject Relevant

July 15th, 2010  |  by  |  Published in Features, July 2010  |  17 Comments

students looking into petri dishes

Furuto's ethnomathematics students learn to see math everywhere, including marine biology laboratories

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.

Linda Furuto on the voyaging canoe Hokulea

Furuto on board the Hōkūleʻa

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.”

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  1. Kalei Kanuha says:

    July 20th, 2010at 1:21 pm(#)

    Congratulations to our next generation of wonderfully creative, innovative and “natural” – in every sense of the word – teachers. Linda has a true gift: the gift of excitement in learning, dedication to teaching, and belief in self-learning through teaching. A true exemplar of praxis right here at our university!

  2. Saili Lilomaiava-Doktor says:

    July 22nd, 2010at 9:12 pm(#)

    Nice going Linda, a beautiful story and kudos to you and a job well done! Our students are very fortunate to have professors like you. Yeah…

  3. Mai Wong says:

    July 22nd, 2010at 9:27 pm(#)

    I am so glad to hear of a math teacher who began her adventures in math with a struggle, as I see this is the position of many of our students. Congratulations to UH West Oahu for hiring a teacher who is sharing enthusiasm and relevance of math with our students. I am sure there will be many more students who will discover their love of math through Dr. Linda Furuto. Thank you

  4. Mary Matayoshi says:

    July 23rd, 2010at 2:19 am(#)

    It’s exciting to learn that West Oahu College gives Dr. Furuto the opportunity to provide innovative ways of teaching mathematics. Enthusiastic and caring teachers is what makes for successful students. Congratulations, Dr. Furuto! Keep up the excitement in your teaching.

  5. Cricket says:

    July 23rd, 2010at 4:23 am(#)

    I get the impression that there is something a little dishonest going on here.

    Referring to examples of mathematics at work from different cultures as “ethnomathematics” is misleading. They are wonderful, insightful examples that can be used to illustrate mathematics, but the underlying (real) mathematics is culture-neutral. Mathematics is mathematics.

    Pre-sceintific societies developed, from experience, ways of accomplishing tasks such as ocean navigation. But what they were doing was neither mathematics nor science. They were clever rules of thumb and heuristics that became treasured parts of those cultures. There may have been underlying mathematics or science that explained why they worked, but their users did not know or understand this, and what they were doing was not some kind of “ethnomathematics”. Mathematics and science are based on abstractions, relationships and principles that lie outside of ethnic cultures and are the result of the profound insights of ancient Greece, medieval Islam, and postmedieval Europe. There is no such thing as “ethnomathematics”.

  6. Lynda Asato says:

    July 23rd, 2010at 5:15 am(#)

    Thank you for this article on Linda Furuto. She is truly giving back to our aina. My sister, Wanda Miyamoto, is an instructor at Leeward Community College, and she shares the same high regard for her students and their dedication to learning that Ms. Furuto does. The UH is fortunate to have them on the faculty, and their many other talented and committed instructors. May they carry on the great tradition to serve… “the life of the land is perpetuated in righteousness.” I miss being in Hawaii, and hope to return someday.
    Lynda Asato

  7. Kyra "Annie" Parker Nelson says:

    July 23rd, 2010at 6:54 am(#)


  8. Susan Matoba Adler says:

    July 23rd, 2010at 9:52 am(#)

    Hi Linda,

    You do us proud to see such happy engaged students! You look pretty good too, an island girl professor!!!


  9. Terry Qian says:

    July 23rd, 2010at 12:39 pm(#)

    What a great story, way to go my girl.


  10. George Wakiji says:

    July 24th, 2010at 6:13 pm(#)

    In the section “Helping Students succeed in mathematics” I couldn’t help but notice that the Hawaiian Airlines flight attendant was a quick change artist. “He’d drive to the University of Hawaii West O’ahu parking lot and sleep in the car until her 9:30 a.m. class…” Ethnomathematics works to change a man into a woman…good trick!

  11. Kanoe Douglas says:

    July 25th, 2010at 11:44 pm(#)

    I hated math… and then I was lucky enough to have Linda Furuto as my instructor. Now, I’m an elementary teacher and I will help my students to love math as much as I do.

  12. Dr. Rima Morrell says:

    July 30th, 2010at 2:02 am(#)

    How wonderful Linda, to use the valuable traditions of Hawaii nei in teaching Math. I would love to hear more about it.



    Author of The Sacred Power of Huna.

  13. Malia Morales says:

    July 30th, 2010at 3:35 pm(#)

    A wonderful article that helps to illuminate all the connections right in front of us. It’s talented and dedicated, yet humble, professionals like Linda that are key in identifying, formalizing, and implementing these key perspectives in the creation of culturally grounded scientific learning opportunities for all learners. Way to go Sis, such an honor sailing with you! Or as Uncle Maka and the boys would say…TSUA!

  14. Linda Furuto says:

    August 6th, 2010at 6:47 pm(#)

    Dear All,

    Thank you very much for your thoughtful and thought-provoking comments. I sincerely appreciate your time and support. I just returned home after traveling to Los Angeles, Portland, and Baltimore to conduct research on ethnomathematics and present at the International Conference of Ethnomathematics.

    My current research on “Bridging Policy and Practice with Ethnomathematics” is based on collaborative efforts between universities where I completed graduate studies, Harvard University and UCLA, as well as the University of Hawai‘i. As mentioned in the article, I am very grateful for the State of Hawai’i’s efforts to improve education through Mathematics Summits and salute the stakeholders involved. There is much we can accomplish by working together.

    The National Council of Teachers of Mathematics (NCTM) is the primary voice of mathematics education in the U.S., ensuring equitable learning of the highest quality for all students through vision, leadership, professional development, and research. According to the NCTM Position Statement on “Equity in Mathematics Education” (January 2008), “A culture of equity depends on the joint efforts of all participants in the community of students, educators, families, and policymakers…High expectations, culturally relevant practices, ethnomathematics, and attitudes that are free of bias, and unprejudiced beliefs expand and maximize the potential for learning…All students should have access to and engage in challenging, rigorous, and meaningful mathematical experiences.”

    Practices grounded in ethnomathematics empower students to build relationships with mathematics that are rooted in their own culture and history. Just as literacy has come to mean much more than reading and writing, mathematics must also be thought of as more than counting and calculating. Ethnomathematics encourages us to witness and attempt to understand how mathematics is adapted and used by people around the world.

    Whether your journey is at the local, state, or national level, I hope we will continue to utilize tools such as ethnomathematics to catalyze positive change. When the inventions, experiences, and applications of mathematics of all students are realized and respected, they are given equal opportunity for access and achievement.

    Linda Furuto

  15. Saili Lilomaiava-Doktor says:

    December 13th, 2010at 4:26 pm(#)


  16. Kelly Ching says:

    January 14th, 2011at 8:51 pm(#)

    We are so lucky to have you at UH West O’ahu!

  17. Cheryl Ernst says:

    February 11th, 2011at 3:26 pm(#)

    UH West Oʻahu plans an ethnomathematics calculus institute with field studies during summer 2011. Learn more.