Research in Our Classroom

Structure, Photo by p medved

Structure, Photo by p medved

I have been questioning lately what methods I can use to understand my students better – not just their work, but their experience of mathematics in my classroom and of the subject in general. I’m taking a uniquely structured (I mean this as a good thing!) research methodology class with Dr. Susan Gerofsky and Dr. Cynthia Nicol here at the Department of Curriculum and Pedagogy at UBC (In fact, it can only be characterized as “standard” insofar as it is a course requirement for my program). Our exploration of research methods has been helpful both in learning methods that one can use for academic research and in reflecting on ways I will be able to investigate my practice when I return to the classroom.

I’ve been used to some pretty standard ways of “getting to know” students. We give them assessments to perform – a variety of types of tasks from tests to open-ended, long-term projects – to give us a sense of their understanding of the concepts of the course they’re taking. Throughout the year we might give them written surveys telling us a bit about how they’re feeling about our teaching or about the course’s progress or our teaching subject in general. We likely give formative checks for understanding through observation, a quick chat, an “exit card“, or visible thinking routines. Regardless of how much information that can be gained from some of these standard and non-standard ways of collecting data, might there be something missing? Might there be something to be gained from collecting information through a different medium – and from involving them in the information gathering process?

Freedom, Photo by Josef Grunig

Freedom, Photo by Josef Grunig

In Donal O. Donoghue‘s (2007) article on boys’ masculinity in places outside the classroom, Donoghue uses photography and a/r/tography methodology to create meaning with boys aged 10 and 11 rather than to use them to discover and make truth claims (as most research does in treating research “subjects” as if they are being used to gain knowledge about something). According to Donoghue (2007), “doing research in and through art offers opportunities to capture and represent that which is not always linguistic – that which can be more profitably represented and understood through nonverbal forms of communication” (p. 63). My conflict with this type of research is that I see both sides. I see that it offers a different way to view a sensitive topic – using non-verbal “data” (i.e.: photographs) through the view of 10 and 11 year olds – a  view that has the potential to reveal something never before explored. However, I can see also the risk of  photographs to be open to a much wider scope of interpretation than written data might be. So, based on what this method offers us – and does not offer us – Donoghue’s (2007) words make me both optimistic and nervous: “how we do and represent research is inseparable from what gets communicated” (p. 64).

Comparing our work with interviewing methods for research purposes, and reflecting on similarities and differences with the use of photography as detailed by Donoghue (2007), I notice more similarities between them. As with interviewing, photography has the potential for inviting the participant into the research process, and offers non-verbal representation (interviewing does this through gesture and tone of voice). Both need to be examined within the social and cultural contexts in which the product (speech, photograph, art, etc.) is produced. However, which is liable to produce more accurate interpretation? For example, are we more likely to get an accurate view of what a child thinks of our subject if we ask them to tell us, or if we ask them to take a picture that represents how they feel and discuss the photo choice with us? The old cliché about pictures and words comes to mind, but beyond that, one could argue that reading and re-reading a script made from an interview can continue to create just as many new meanings as can having a look and a second/third/fourth look at a photo. The difference between interviewing and photography that I can see is that interviewing offers the potential for a much more fixed, rigourous process, whereas the use of photography, to a large extent, is itself a commitment to embrace a research method that involves the participant much more in the process.

Regardless of these structural aspects, there might be something to the use of photographs to find out more about students’ thinking. Consider school culture. When you ask a student to write down feedback, like in a survey, this structured written form is similar to what students experience in other parts of school and there may be strong psychological aspects at play governing their answers. However, exit cards are casual and quick, often on 3×5 cards which is not specifically how class tasks are done – which may cause them to open up a bit further. So, if you ask students to send you a digital photo with a description as a way of answering a question (of course, if this is logistically possible in your context), this could provide you with different information that you would have otherwise received using a different format.

References

Donoghue, D. O. (2007). “James always hangs out here”: making space for place in studying masculinities at school. Visual Studies, 22(1), 62–73. doi:10.1080/14725860601167218

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.