Sabado, Hunyo 22, 2013

In mathematics education, ethnomathematics is the study of the relationship between mathematics and culture.^[1] Often associated with "cultures without written expression",^[2] it may also be defined as "the mathematics which is practised among identifiable cultural groups".^[3] It refers to a broad cluster of ideas ranging from distinct numerical and mathematical systems to multicultural mathematics education. The goal of ethnomathematics is to contribute both to the understanding of culture and the understanding of mathematics, and mainly to lead to an appreciation of the connections between the two.

The development and meaning of "ethnomathematics"

The term "ethnomathematics" was introduced by the Brazilian educator and mathematician Ubiratan D'Ambrosio in 1977 during a presentation for the American Association for the Advancement of Science. Since D'Ambrosio put forth the term, people - D'Ambrosio included - have struggled with its meaning ("An etymological abuse leads me to use the words, respectively, ethno and mathema for their categories of analysis and tics from (from techne)".^[4]).
The following is a sampling of some of the definitions of ethnomathematics proposed between 1985 and 2006:

"The mathematics which is practiced among identifiable cultural groups such as national-tribe societies, labour groups, children of certain age brackets and professional classes".^[5]
"The mathematics implicit in each practice".^[6]
"The study of mathematical ideas of a non-literate culture".^[7]
"The codification which allows a cultural group to describe, manage and understand reality".^[8]
"Mathematics…is conceived as a cultural product which has developed as a result of various activities".^[9]
"The study and presentation of mathematical ideas of traditional peoples".^[10]
"Any form of cultural knowledge or social activity characteristic of a social group and/or cultural group that can be recognized by other groups such as Western anthropologists, but not necessarily by the group of origin, as mathematical knowledge or mathematical activity".^[11]
"The mathematics of cultural practice".^[12]
"The investigation of the traditions, practices and mathematical concepts of a subordinated social group".^[13]
"I have been using the word ethnomathematics as modes, styles, and techniques (tics) of explanation, of understanding, and of coping with the natural and cultural environment (mathema) in distinct cultural systems (ethnos)".^[14]
"What is the difference between ethnomathematics and the general practice of creating a mathematical model of a cultural phenomenon (e.g., the "mathematical anthropology" of Paul Kay [1971] and others)? The essential issue is the relation between intentionality and epistemological status. A single drop of water issuing from a watering can, for example, can be modeled mathematically, but we would not attribute knowledge of that mathematics to the average gardener. Estimating the increase in seeds required for an increased garden plot, on the other hand, would qualify".^[15]

Ethnomathematics Shows Students Their Connections to Math

Cheryl Ernst

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 Kāne‘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 Hōkūle‘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 Hōkūle‘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 Hōkūle‘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 Hōkūle‘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–Mānoa, 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 Mālamalama. 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.

Ethnomathematics Shows Students Their Connections to Math

Cheryl Ernst

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).

Furuto's math class aboard a two-hulled canoe in Hawaii (Photo courtesy of Linda Furuto).

~ ~
Ethnomathematics applied to classrooms in Alaska: Math in a Cultural Context
Jerry Lipka & Dora Andrew-Irhke
Math in a Cultural Context (MCC) is a long-term response to the persistent exclusion of Alaska Native language, culture, and pedagogy from the practices and norms of schooling in Alaska. MCC has brought together improbable groups of people—Alaskan Native (mostly Yup’ik) elders, mathematicians, math educators, educational researchers, teachers, and school districts. At the heart of this successful project (see Lipka, Webster, & Yanez, 2005, is ethnomathematics. Ethnomathematics (Adam, Alangui, and Barton, 2003) includes the integration of mathematical concepts and practices from the target culture to formal mathematics. MCC is one of the few ethnomathematics programs that show consistent improvements in the mathematical performance of Alaskan students (both indigenous and other students) grounded in empirical research; the project has conducted more than 15 studies, ranging from quasi-experimental to experimental designs across math topics and across grade levels (see Lipka, Webster, & Yanez, 2005). These studies meet Demmert and Towner’s (2003) research criteria for evaluating culturally based curriculum and pedagogy and meets the U.S. Department of Education’s (Institute of Education Sciences) criteria for rigorous research (http://ies.ed.gov/ncee/wwc/). MCC has contributed to the field by adding empirical evidence on the effectiveness of culturally based education (Education Week, January 8, 2008 can be retrieved at http://www.edweek.org/ew/articles/2008/01/09/17culture.h27.html).
What accounts for this success? MCC’s approach includes the embedded mathematics of Yup’ik elders and experienced Yup’ik teachers’ ways of performing and solving everyday problems. It is only because of this project’s long-term collaboration over more than 20 years that we are increasingly able to understand the mathematical threads woven into authentic cultural knowledge and practices. Here we highlight the embedded mathematics in authentic cultural practices.
Dora Andrew-Ihrke a long-term colleague, Yup’ik educator, and budding math educator, has used her cultural knowledge learned primarily from her mother to make a variety of Yup’ik artifacts—patterns that adorn clothing, Eskimo yo-yos, and clothing to name a few. Through a careful ethnographic process of observing and analyzing Dora and elders, analyzing videotapes and pictures of the processes used, and with the insights of many others, e.g. Dr. Addington (mathematician), Dr. Rickard (math educator), and Dr. Adams (math educator), we have come to the conclusion that transformational geometry including measurement and proportionality is at the heart of many Yup’ik constructions in everyday life. Constructing patterns is such an example that directly connects Yup’ik everyday activity and its embedded math (transformational geometry, measurement, proportionality, properties, and proof). Figure1 shows Evelyn Yanez and Dora Andrew-Ihrke displaying Yup’ik parkas and border patterns. Evelyn Yanez in our professional development work typically contextualizes the math of the lesson through a form of storytelling called storyknifing.
Figure 1: Evelyn Yanez (left) and Dora Andrew-Ihrke (right) display two Yup’ik parkas with border patterns
Figure 2 shows a close-up of an intricate pattern.
Figure 2: “Pretend Window” pattern
~ ~
It’s in the construction of the border patterns on these parkas that the math is revealed. Dora always uses her body proportions to create her starting square. In Figure 3 below she demonstrates on paper how pattern pieces are created from rough uneven materials such as furs.
Figure 3: Constructing a square from uneven material
Dora begins the process of making a square by measuring the space between the first and the second knuckle, using your index finger as a way to measure; measure two of these for the length and two for the width to create a square. The “knuckle length” measure is a common unit in the Yup’ik measurement system. Cut out a square that is this size. See Figure 4 below.
Figure 4: Body Measure
Next, she establishes a process of “proofing” that she has a square by locating the center point of the square by folding it into quarters to form smaller squares.
Figure 5: Center point
She used a process of folding half one way and then another way to ensure that the sides matched and she folded along one diagonal and then along the other diagonal again to ensure that each half-square matched in each direction. Interestingly, Dr. Addington, who worked with us during a December 2007 meeting, further elaborated the math involved in what Dora was demonstrating. She commented on Dora’s approach to creating and checking and proofing to see if you had a square. Addington stated that if this was using a Euclidean proof it would require “something is a square when all four sides are equal and all angles are right angles.” She said, “Dora checked differently. Dora is using transformational geometry. . .it is about what you do to the shape that stays the same. . .that is a reflection. . .the two sides of the mirror—the image and the original match.. . .Dora’s folding along the diagonal. . .is another reflection. This goes beyond the Euclidean proof by checking in all possible ways that each reflection matches” (December 7, 2007).
In this brief example, we have provided one glimpse of the embedded mathematics that is part of Dora’s Yup’ik culture as she learned these methods from her mother and other elders. This is their mathematics and it is at once accessible to Yup’ik students who have observed their parents or grandparents performing similar activities; interestingly, this approach has been equally effective with students across Alaska’s diverse geographical and cultural groups. This approach to teaching and learning elementary mathematics is used in all MCC curriculum modules.
~ 10 ~
We will elaborate this approach at the NASGEm Ethnomathematics SIG at the 2009 Annual Meeting of NCSM.
References
Adam, S., Alangui, & W. & Barton, B. (2003). A comment on: Rowlands & Carson “Where would formal, academic mathematics stand in a curriculum informed by ethnomathematics? A critical review”. Educational Studies in Mathematics 52, 327-335.
Demmert, W. G., & Towner, J. C. (2003). A review of the research literature on the influences of culturally based education on the academic performance of Native American students. Portland, OR: Northwest Regional Educational Laboratory.
Lipka, J., Webster, J. P., & Yanez, E. (2005). Introduction. Journal of American Indian Education.Special Issue, 44(3), 1-8.
Zehr, M. A. (2008). Evidence on effect of culture-based teaching called thin, Education Week http://www.edweek.org/ew/articles/2008/01/09/17culture.h27.html.
Become a NASGEm member!
Dues for membership in NASGEm are $20.00 per year and may be paid up to three years. A year’s membership is from April through the following April. Dues are used to cover costs related to maintaining
the NASGEm organization, paying affiliate dues to related math organizations, and producing the NASGEm Journal, The Journal of Mathematics and Culture. To join or renew a membership please send your name and contact information with a check to: Jim Barta, UMC 2805, Old Main Hill, Utah State University, Logan, UT 84322. Make checks payable to NASGEm.
Please briefly describe any projects in which you are involved that may be related to ethnomathematics.

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.”

Biyernes, Hunyo 21, 2013

Agusan del Sur: Overnight with the Manobo community of Agusan Marsh

If there was a hidden paradise in the Philippines, it must be the Agusan Marsh. That's because visiting it is no walk in the park since it requires several hours of land and river boat travel to get to the marsh itself. Arranging the pump boat ride would also require some effort and a lot of funds too if you don't have the right connections. But no doubt, the Agusan Marsh is paradise.

In fact, it is such an important part of our natural heritage, the Agusan Marsh Wildlife Sanctuary is among four Philippine sites in the Ramsar List of Wetlands of International Importance. I hope the local community there initiates moves for its inscription in the UNESCO World Heritage List.

Much of the Agusan Marsh is ancestral domain of the Manobos. So to get into some of the better portions of the marsh might require permission from the local community. There are several communities in the Agusan Marsh and a lot of ways to get there. I was lucky to be a guest of the Manobo community in Sitio Panlabuhan, Loreto, Agusan del Sur. In fact, they hosted me for one night.

A trip to Agusan Marsh starts with land travel from the nearest airport which could either be Davao or Butuan. That would take several hours depending on where you are coming from. The jump-off point for the river boat ride is Bunawan, Agusan del Sur. From the pantalan of Bunawan, it took another three-hours on a pump boat to reach Sitio Panlabuhan in Loreto, Agusan del Sur.

We actually had to change boats when we neared the entrance of the marsh since in October, pump-boats have a hard time entering Sitio Panlabuhan due to the high concentration of lilies, hyacinths and other water plants. People say it looks like an enormous green quilt.

It was quite an experience riding on the boats made from hollowed-out logs as we pushed our way through the lilies. And especially since one wrong move meant an unplanned swim in the dark tea-colored water of the marsh.

The Manobos in the Agusan Marsh live in floating houses. The houses, which are quite sturdy, are built on hundreds of pieces of bamboo and rise and fall together with the level of the marsh. And depending on the current, the houses are also moved to different locations.

Take note also that there is no electricity. So you really commune with nature while you are there. Interestingly though, the mobile phone signal was very strong in Sitio Panlabuhan.

I was also quite surprised that they community had a lodge where visitors could stay. They don't come in very often. But at least visitors don't have to worry about accommodation. I was warned that mosquitoes would be a problem even with the mosquito net or kulambo. So make sure to bring a lot of insect repellent.

The community of Sitio Panlabuhan has two sectors. After settling down, we boarded the log boat to proceed to the main sector where a newly-constructed floating classroom is located. As part of required tradition, I had to meet the community elders for a Manobo ritual to pay respect to the spirits, ask permission for my presence and request for safe passage while I was there. I was told that some visitors who simply entered the ancestral area without doing the ritual met a disaster of some sort, even as they arrived back home.

I was actually asked to bring a live chicken and candles for the ritual. But the village elder decided not to sacrifice the chicken. So we offered an egg instead. The ritual began with the elder conversing with the spririts, mentioning that I was in the community. On the table was lighted candle, the egg cracked open on a plate, a bottle of beer plus a glass with a serving of beer, and a lighted cigarette. After the conversation, the village elder stood up, took the glass of beer, proceeded to the window and emptied its contents into the marsh. Then the glass was filled-up again and again and passed around so that everyone in the room was able to drink.

After the ritual, we had a town hall meeting with the community to discuss plans to open their community to tourism. They wanted visitors to come and were very frustrated with the local government because they never benefited from any of the visitors who came into Sitio Panlabuhan. Some foreigners were even rude enough to say they already paid the LGU when prohibited from entering the ancestral domain, not knowing that the community had rights to their part of the Agusan Marsh.

I've always been telling my students that tourism is a powerful tool for poverty alleviation of government makes sure that its benefits reach the grassroots. This is my way of helping the community around the Agusan Marsh benefit from tourism. So in February, we will be organizing a tour of Sitio Panlabuhan that will benefit the community directly. Tourists will have a chance to stay with the community for a night or two. If you are interested to join the tour from March 4-6, 2011, please e-mail info@ivanhenares.com so I can send you more details as they come.

Anyway, the sun had just set when we took the boat back to the opposite sector. After dinner and some lively discussions on the planned tourism program, we called it a night.

The next morning, I was up early since they community wanted to show me the floating gardens. These were literally floating plant boxes where they would have flowering plants, fruits and vegetables. Unfortuantely, I did not have time to join any of the fishing activities since I wanted to be back in Bunawan before lunch to catch a bus to Surigao del Sur.

Aside from joining the locals go fishing around the marsh, bird watching is also another activity of the Agusan Marsh being host to over 200 species of birds. The numbers swell especially during the cold months when the marsh hosts communities of migratory birds.

ETHNOMATHEMATICS AND

MATHEMATICS EDUCATION

Proceedings of the 10

International Congress of Mathematics Education

Copenhagen

Discussion Group 15

Ethnomathematics

edited by

Franco Favilli

Dipartimento di Matematica

Università di Pisa

Tipografia Editrice Pisana

Pisa

Published with the financial contribution of

the Italian Ministry of Education, University and R

esearch and

the Department of Mathematics of the University of

Pisa (Italy)

within the National Interest Research Project “Diff

iculties in mathematics

teaching/learning” – Grant n. 2001015958.

ISBN: 978-88-8250-069-1

___________________________________________________

____________________ I

Contents

Introduction.......................................

...................................................

........ III

Franco Favilli

Preface............................................

...................................................

.............. V

Ubiratan D’Ambrosio

Foreword...........................................

...................................................

..........XI

Bill Barton

Occurrence of typical cultural behaviours in an ari

thmetic

lesson: how to cope?...............................

...................................................

...... 1

Pierre Clanché and Bernard Sarrazy

Multicultural classrooms: contexts for much mathema

tics

teaching and learning..............................

...................................................

..... 9

Philip C. Clarkson

Notes on teacher education: an ethnomathematical

perspective ........................................

...................................................

.......... 17

Maria do Carmo Santos Domite

Quantitative and spatial representations among work

ing

class adults from Rio de Janeiro...................

............................................... 29

Maria Cecilia de Castello Branco Fantinato

Intercultural mathematics education: comments about

a didactic proposal ................................

...................................................

..... 39

Franco Favilli and Stefania Tintori

The electronic yupana: a didactic resource from an

ancient

mathematical tool..................................

...................................................

..... 49

Giuseppe Fiorentino and Franco Favilli