How do we take Mathematics out of classrooms and into the real world of work, tradition, and everyday life? Making abstract mathematical concepts as real and concrete to mathematics learners has always been a challenge. This is certainly the case too for Indigenous students.
One possible answer is ethnomathematics, the study of the intersection of mathematics and culture, which is now finding its way int the Philippine government’s Indigenous Peoples’ Education (IPEd) program.
Brazilian mathematician Ubiratan D’Ambrosio conceptualized ethnomathematics as ethno [culture] + mathema [explaining, understanding] + tics [techné, arts, techniques]—“the art or technique of explaining, knowing, and understanding diverse cultural contexts.” Ethnomathematics as a field of study began in the latter part of the 1980s. A decade or so earlier, movements toward teaching basic education among culturally diverse peoples began to grow globally.
“It’s a worldwide movement born out of the realization that IPs have been marginalized for so many years, including within our educational systems,” explains Dr. Wilfredo V. Alangui, math professor at the UP Baguio College of Science. Through colonization, the IPs’ knowledge systems were supplanted by Western knowledge systems. This included Mathematics, which—despite being called “the universal language” and “the door and key of the sciences” that makes it seem removed from things like cultural bias—is a Western, mostly Eurocentric, strain.
In his paper, “There’s a Theory Behind What We’re Doing! Ethnomathematics and Indigenous Peoples’ Education in the Philippines,” which he presented at the 13th International Congress on Mathematical Education at the University of Hamburg in July 2016, Willy noted that in the Philippines, IPEd initiatives have been taken by the Department of Education (DepEd), civil society groups, IP organizations and other community-based efforts since the 1970s. Then in 2011, the DepEd issued Department Order 62, adopting the National Indigenous Peoples Education Policy Framework and creating the Indigenous Peoples Education Office (IPsEO) in 2012.
The need for schools for indigenous students is dire, as IP communities are often located in remote areas far from any public schools. And too often IP children face discrimination in these schools. Alangui has heard stories about Mangyan children in Occidental Mindoro making long journeys to the closest public school riding on the roof of a jeepney, only to have their teacher call them “stupid” and “ignorant” during school assemblies. Is it any wonder then that IP students lose any motivation to continue schooling and settle for an early marriage and a life spent merely surviving?
There are breakthroughs, however. Dr. Alangui and Dr. Ma. Theresa de Villa, an education professor at UP Diliman and the UP Open University, did a research for the Department of Education – Indigenous Peoples’ Education Office where they visited 16 schools, gathering information on their experiences and processes in implementing IP education so as to generate insights on developing an IP curriculum framework. The schools revealed varying approaches in the handling of indigenous knowledge systems and practices, ranging from the insertion of cultural elements in specific subjects, such as counting in indigenous languages and using localized math problems, to an IP curriculum where emphasis is given to teaching IP competencies more than DepEd prescribed competencies. This research resulted to the 2015 issuance by the Department of Education of D.O. 32 providing for a framework for the development of an IP curriculum.
Among the partner schools of the study, one in particular stood out: The Paaralang Mangyan na Angkop sa Kulturang Aalagaan (Pamana Ka), an indigenous school built in 1999 by and for the Mangyan community in San Jose, Occidental Mindoro, with the help of the Franciscan Missionaries of Mary (FMM).
At Pamana Ka, IP education is done right. Pamana Ka, for example, has an IP curriculum they call “Banig ng Buhay” that is anchored on the life of the Mangyan community, where lessons in different subjects are developed around a yearly calendar of activities approved by the community elders. For instance, the school has an annual activity called Tukawan, which is guided and led by the elders. In this week-long activity which happens in March, they bring the children to the forest to teach them important activities like hunting, fishing, harvesting honey, other indigenous resource management practices, including Mangyan games, while incorporating lessons in Biology, Chemistry, Social Studies, Music and Art. (Incidentally, Alangui noted that many some of the teachers who initially volunteered in Pamana Ka in the mid-1990s are products of the UP Los Baños Ugnayan ng Pahinungod, and they continue to help the school in various ways.)
The same treatment is given to Mathematics, admittedly a difficult subject to teach. At Pamana Ka, Math comes to life in the Mangyan traditions. For instance, a lesson on fractions begins with a discussion on the honey-harvesting practices in each student’s community and ends with a reflection on the values of sharing and fairness.
Pamana Ka teachers find ways to teach mathematics concepts that start with things familiar to the Mangyan student. For example, the Mangyan’s practice of harvesting cassava tubers by counting the number of cracks on the ground around the cassava plant becomes an entry point to discuss variables and algebraic expressions—the the number of cracks on the ground are known values (constants), and the number of tubers under each crack is an unknown variable).
Teachers take advantage of the knowledge of crossing rivers to discuss the Pythagorean theorem: Mangyan do not cross the river in a straight line. They start from point A on the other side of the river, and wade and move at an angle with the current until they arrive at point B across the river. In short, they cross the river along the hypotenuse or the longest side of (an imaginary) right triangle. And patterns and sequences abound in the Mangyan world, for example, in steps that need to be followed in the performance of a ritual, or in preparing the land for the gahak or kaingin. And Pamana Ka math teachers utilize these realities in Mangyan life to teach number sequences.
In short, Mathematics is not just a bunch of abstract equations, but a real part of the Mangyans’ daily lives. And since every lesson begins and ends with a reiteration of their values, their understanding of their own culture is not only respected but enhanced as well.
“Pamana Ka changed everything for [the students].” When Willy asked how shifting from a mainstream school to Pamana Ka changed their lives, the students replied that it restored their self-esteem and their motivation to study. The Pamana Ka style of culturally responsive education returned their dreams to them.
“So it’s important for us to have IP schools that have this clear orientation of helping our indigenous students. This is why I’m so involved. I have a commitment to that school because as I see it, if we are looking for a model for IPEd, we should all go to Pamana Ka,” Alangui says. The DepEd agrees, which is why Pamana Ka became an immersion school on IP education for teachers and administrators from other regions at the start of the implementation of IPEd.
Ethnomathematics may help in ways that go beyond merely passing Math class. “The hope is that students both IP and non-IP don’t become alienated from Mathematics, but for them to see that math means something to their lives. And then, if they become curious enough, they can pursue math in the university, and even earn a graduate degree. These are possibilities opened up by making them see, realize and experience the connection of Mathematics in their lives as IPs.”
At least this is what ethnomathematics is trying to do. Because Math isn’t separate from culture. Math is culture.