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.

Culturally Responsive Education in Mathematics

indigenous aboriginal education mousewoman

This artwork is of Mouse Woman, the Narnauk supernatural shape-shifter. This art was used as official artwork of the Aboriginal K-12 Math Symposium, held at the UBC Longhouse. Artist William (Billy) NC Yovanovich Jr.––whose Haida name is Kuuhlanuu––is a member of the Ts’aahl Eagle Clan of Skidegate, Haida Gwaii.

Last week, our Mathematics, Community, and Culture class discussed culturally responsive education – yet another controversial and evolving topic in mathematics education. It seems to me that culturally responsive education is a philosophy whereby a teacher (or a writer of curriculum) attempts integrate culture and curriculum in a way that emphasizes the ways of knowing of different cultures so as to provide a richer educational experience. In the context of indigenous issues consistently under consideration here in British Columbia, many of the members of the class wondered if there was bias in which culture education was meant to be “responsive” to. You can see how there can be a debate here about whether or not culturally responsive education aims to “respond” to a particular culture, or remove some of the emphasis from another.

Due to a prevailing dichotomous view of “dominant culture” and “less-dominant culture”, culturally responsive education can strongly imply a requirement of dominant cultures to recognize cultures that have long been less dominant. I agree that the role of culturally responsive education, according to Mukhopadhyay (2009), should be to treat all cultures fairly rather than equally. Education does need to recognize other less dominant cultures more than dominant ones simply because dominant cultures will prevail in other aspects of a student’s environment regardless of what we do as teachers. This does not mean total exclusion of dominant cultures, but it should mean an effort on the part of the teacher in all subjects (not just mathematics) to respond to many cultures positively and to expose students to many cultural paradigms.

How this is done is incredibly complex and likely looks different in each classroom, but, as was said by Christine Younghusband, speaker at the most recent Aboriginal Math K-12 Symposium (2012), if we want our students to be culturally responsive (or take on any other value), we as teachers need to be culturally responsive (or truly believe in that value). Storyknifing, for example, to introduce the idea of geometric visualization instead of, say, giving a worksheet and some plastic block manipulatives to students is a simple way that a teacher can introduce a mathematics topic (and tick those curriculum objectives!) while giving a strong message to students of the strong mathematical heritage inherent in many cultures. But this message will only be strong if a teacher uses a strategy like Storyknifing within a consistent effort in the classroom to invite students to think critically about culture and the perceptions that prevail. The message will only work if the cultural context of an activity, like Storyknifing, is preserved. One wouldn’t want students to see storyknifing while learning Cartesian Coordinates and get the impression that storyknifing was used in navigation.

If someone were to simply use the Math Catcher videos, for example, as one-off or as one of a few of intermittent cultural resources in their classroom, it would appear to the students as nothing more than a video version of an ordinary word problem stated in a Squamish context. Culturally responsive education is not about using storyknifing or Math Catcher videos in one’s classroom, but about a philosophy of classroom practice to expose students to different perspectives and cultures and to encourage them to investigate and question dominant paradigms.

References

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.

Lipka, J. Wildfeuer, S. Wahlberg, N. George, M. & Ezran, D. (2001). Elastic geometry and storyknifing: A Yup’ik Eskimo example. Teaching Children Mathematics. February, 337-343.