Math and Place-Based Education

A scene from Central Vietnam, Photo by Rob DeAbreu

A scene from Central Vietnam, Photo by Rob DeAbreu

Place-based education (PBE) is based on the fundamental idea that places are pedagogical – they teach us about the world and how our lives fit into the spaces we occupy. It began with community education and community-as-classroom – the idea that students could learn by paying closer attention to their community and doing work within it. The idea has since expanded to investigate the learning that happens in field-trips or long-term projects outside of the classroom, to examine the pedagogy of places of all sizes and locations, and to explore the meanings that different people attach to place. One can argue, that – to an extent – there is an activism component against the current state of the education system, which – in most cases – assumes that the school (and the classroom) is the place where learning occurs.

For Dr. David Gruenewald (2003) – who now goes by the name David Greenwood – place-based education (PBE) is in large part a response to standards, testing, and accountability, the threefold education reform movement of the last two to three decades (though grounded in some much older ideologies). As mathematics is the gatekeeper discipline to many careers and university programs – whether with a mathematics component or not – it is a discipline that, it could be argued, is the target of PBE’s response. With this in mind, it is no surprise that Gruenewald/Greenwood (in Green, 2005) expressed his skepticism about the possibilities of developing place-conscious mathematics. However, is mathematics – the very tool incorrectly used to assess students, and thus misunderstood by so many – the ideal vehicle to drive PBE’s response to misguided education reform?

Classroom, by evmaiden

Classroom, by evmaiden

Much has been written about cultural border-crossing in science education – challenges that students come to when negotiating between their life-world and the culture of the discipline of science (Aikenhead & Jegede, 1999; Jegede & Aikenhead, 1999; Jegede, 1995). Similar arguments have been made by Boaler (1993, 1998) and Schoenfeld (1989) that a similar struggle, manifesting in difficulties in knowledge transference, goes on in mathematics education. PBE acknowledges the divide between students’ life world, and the culture of school and mathematics, and Gruenewald/Greenwood (in Green, 2005) cites it as a result of the disconnected place – the school and the classroom – that students are meant to learn in each day. So, PBE can contribute to mathematics education, and mathematics can contribute to the activist elements of PBE. I disagree with Gruenewald’s challenge that place-conscious math can’t exist.  Gruenewald/Greenwood (2003) himself says, “people make places and places make people” (p. 621). PBE embraces our agency to leverage the power of place in our lives and learning just as it acknowledges the influence that place has over our identity. While learning must take place in a physical classroom in most schools, with all the aspects of schools that this entails (timed periods, separate subjects, etc.), it does not mean that we should give up trying to transcend the barriers and isolation that schools can create. In the interview, Gruenewald/Greenwood (in Green, 2005) points out that in the process of “aligning” curriculum and standards, curriculum is treated as a means to an end (to meet the standards) and is forever altered. How do we mediate the two? If we can’t, what changes can we make to enable schools to connect students better with the outside world?

Technology is a given, by Scott McLeod

Technology is a given, by Scott McLeod

One could argue that the infusion of technology in our classrooms further removes us from our world – because technology forces us to perceive our world through a screen and interact with it through a machine. There are others who would argue that technology connects us – like I am connecting with you right now having made my ideas available for comment, or like many professionals and friends connect using Twitter and other social media.  In a different way, a framework like ethnomathematics is one way to enact PBE in mathematics – by inviting students to be aware of other places and cultures that surround us. Perhaps by being inspired by the mathematics embedded in others’ and our own cultural practices, students can transcend the classroom space and acquire the learning that we seek for them. Regardless of what solution is suggested, however, can we transcend place? Or does the fact that students are located in a classroom during the day completely undermine the ability to enact PBE? And, if we can transcend place – that is, if the place they are in (school and classroom) recedes from consciousness as teachers attempt to enact PBE – does this mean that we have enacted PBE successfully or failed to enact it?

I have more questions than answers about this at the moment. One of the purposes of PBE is to catalyze a dialogue about place and education, so perhaps finding “ways” to make it “work” isn’t really the point!

References

Gruenewald, D. (2003). Foundations of place: A multidisciplinary framework for place-­‐conscious education. American Educational Research Journal, 40, 3, 619-­‐654.

Green, C. (2005). Selecting the Clay: Theorizing place-­‐based mathematics education in the rural context (Interview with David Gruenewald). Rural Mathematics Educator. ACCLAIM.

Smith, G. (2002). Going local. Educational Leadership, September 30-­‐33.

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.

Boaler, J. (1998). Open and closed mathematics: Student experiences and understandings. Journal for Research in Mathematics Education, 29, 41-­‐62.

Schoenfeld, A. H. (1989). Explorations of Students’ Mathematical Beliefs and Behavior. Journal for Research in Mathematics Education, 20(4), 338–355.

Aikenhead, G. S., & Jegede, O. J. (1999). Cross‐cultural science education: A cognitive explanation of a cultural phenomenon. Journal of Research in Science Teaching, 36(3), 269–287.

Jegede, O. J. (1995). Collateral Learning and the Eco-Cultural Paradigm in Science and Mathematics Education in Africa. Studies in Science Education, 25, 97–137.

Jegede, O. J., & Aikenhead, G. S. (1999). Transcending cultural borders: Implications for science teaching. Research in Science & Technological Education, 17(1), 45–66. doi:10.1080/0263514990170104

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.

 

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).