Math as a Human Activity

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Wool bag woven by hand by Vivian Campbell. Photo by Robert DeAbreu

Considering some of the readings about the role of context in the mathematics classroom, I’ve been feeling skeptical lately that ethnomathematics would work with all students. Jo Boaler (1993) states that choosing contexts for mathematics that replicate the complexity of the real world as much as possible benefits students’ learning. I wondered if Langdon’s suggestion was correct: “students acquire a better understanding of mathematics by discovering that it is already a part of their environment than by studying local cultural examples” (in Boaler, 1993, p. 16). Therefore, while an ethnomathematical approach to the classroom can cause a valuable shift in students’ worldview (Eglash, 2009), are we hindering their mathematical understanding by introducing concepts in a cultural context so radically different from their own?  As Nel Noddings says, “slaving away at someone else’s real-life problem can be as deadly as doing a set of routine exercises and a lot more difficult” (Noddings, 1994, p. 97).

Our Mathematics, Community and Culture class visited the Musqueam Community Centre to learn the mathematics embedded in mat weaving and other cultural practices. My experience there essentially summed up the benefits that various readings expounded. According to Mukhopadhyay et. al. (2009), “ethnomathematics draws attention to mathematics as a human activity” (p. 68). Rather than distancing me from mathematics, Vivian Campbell’s weaving presentation drew me in to learn more about Musqueam cultural practices and the mathematics behind them. Even more striking was that, upon my return home, the experience catalyzed an investigation of photos and video I had taken of cultural practices in different countries during my travels. I sought to see “mathematics as a human activity” in weaving, fishing and canoe making in Myanmar; weaving, rice paper making and rice harvesting in Vietnam; and weaving, wood carving, and drum making in Ghana. By “incorporating the mathematics of the cultural moment, contextualized, into mathematics education,” (D’Ambrosio, 2001), I was inspired to learn more about the culture (Musqueam) being presented, and prompted to further investigate cultures that I had experienced, bringing me a much richer understanding and appreciation of culture and mathematics.

In other words, it didn’t matter that Musqueam culture is so drastically different from my own; learning about it was interesting and caused me to look for mathematics in other things that I had seen. Generally, I’m a curious guy, but this was a cool experience. I would love to explore some of this stuff with students (when i finally have a class of my own again!) as I am intrigued by the benefits that can be reaped by widening the cultural paradigm in the mathematics classroom.

References

Eglash, R. (2009). Native-American analogues to the Cartesian coordinate system. In B. Greer, S. Mukhopadhyay, A. Powell, & S. Nelson-Barber (Eds.). Culturally responsive mathematics education (pp. 281-294). New York: Routledge.

D’Ambrosio, U. (2001). Ethnomathematics: Link between traditions and modernity. The Netherlands: Sense. (Chapter 2).

Boaler, J. (1993) The role of contexts in the mathematics classroom: Do they make mathematics more ‘real’? For the learning of Mathematics, 13(2), 12-­‐17.

Noddings, N. (1994). Does Everybody Count? Reflections on Reforms in School Mathematics. Journal Of Mathematical Behavior, 13(1), 89-­‐104.

Mukhopadhyay, S. Powell, A. & Frankenstein, M. (2009). An ethnomathematical perspective on culturally responsive mathematics education. In B. Greer, S. Mukhopadhyay, A. Powell, & S. Nelson-Barber (Eds.). Culturally responsive mathematics education (pp. 65-84). New York: Routledge.

Ethnomathematics

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Image by Ron’s Iteractions (note: not Ron Eglash). Original photo by NASA/GSFC/METI/ERSDAC/JAROS, and U.S./Japan ASTER Science Team

I’ve just recently been doing some readings on ethnomathematics. From what I’ve been able to figure out, ethnomathematics is the study of mathematics of different cultural groups. Its goal is to teach value for one’s own culture, respect for another’s culture, and curiosity to learn more about different cultures while teaching mathematics in a cultural context. That being said, it is a fairly new and ever-growing and changing field of mathematics education, so the definition can vary significantly at this point, informed by the life experiences and culture of the person giving the definition!

Ethnomathematics is likely controversial because it does not conform to the needs of advocates who support traditional, computational, arithmetic and algebra driven curricula (see math wars). It requires a more exploratory and interdisciplinary approach to the subject. However, if one is to embrace ethnomathematics, one then opens themselves up to examining the way mathematics is done in all cultures, rather than only the canonically respected mathematics that was done in Europe that is still taught today. Often teachers balk at “multicultural mathematics” because it means an awkward application of mathematics to, say, number systems at the beginning of the year that quickly gets seen by the teacher as a waste of time because it doesn’t tick boxes on the list of curriculum objectives. This is an unfortunate misunderstanding.

Ethnomathematics also opens the door to issues of culture and representation in mathematics and in education in general, which many teachers may not be emotionally prepared and/or educationally trained for (or simply not be interested in dealing with). However, Ron Eglash (2009) exposes a way that we can use culture as a bridge to math – and nicely tick some of those curriculum objectives as well – while integrating art and mathematics in exploration of weaving or architecture or religion. While I can’t provide the article due to copyright, check out his TED Talk.

In addition, D’Ambrosio’s (2001) more philosophical piece seems to imply that ethnomathematics is a way to explore the diversity of cultures while simultaneously being something that students can gather themselves around. While cultures, such as Inuit and Navajo and Maya, may have different perspectives on the distribution of time, the heavens, and agriculture due to their proximity to the equator – in essence, they have different ethnomathematics – these cultures are united by the fact that they have come to ways of knowing through interaction with their environment – in essence, that they have ethnomathematics. Both D’Ambrosio and Eglash, it seems, agree on the rich, paradoxical “unity through diversity” that ethnomathematics can bring to the classroom.

This is an interesting area for teachers to explore if they’re looking for interdisciplinary learning to come alive in their classroom!

References

Eglash, R. (2009). Native-American analogues to the Cartesian coordinate system. In B. Greer, S. Mukhopadhyay, A. Powell, & S. Nelson-Barber (Eds.). Culturally responsive mathematics education (pp. 281-294). New York: Routledge.

D’Ambrosio, U. (2001). Ethnomathematics: Link between traditions and modernity. The Netherlands: Sense. (Chapter 2).