Binaries
Binaries… it is interesting that this week’s introduction started with this exclusionary concept of binaries – one end of the spectrum or the other, as far apart as possible. The idea of binaries as a way in which we see the world was introduced to me in our last class on teaching mathematics for social and ecological justice. Ideas around this have been rolling around in my head since. I notice these ideas around binaries, almost like “stops” that make me pause and consider. Where, why and how did these seemingly competing ideas come from? Last week, while doing the readings, I began making a list of binaries I was coming across. Perhaps I did this to take the ideas off my working memory load, but also so I can remember the many ways our world is divided or considered this way. So, I stopped when the introduction for this week began with a discussion of binaries. It brings me back to perspectives as I was discussing last week. If we see and understand things in a binary way, we miss the interrelated, connectedness of things, ideas, people. We miss opportunities for growth and learning. As Snow worried, “we (will) lack the flexibility of thinking and acting that is needed to solve big world problems” (Introduction, EDCP 553, Week4).
One stop for me in the introduction this week was this pondering by Dr. Gerofsky, “it is worth asking ourselves why contemporary mainstream culture in places like Canada and the US is quick to separate people into ‘math people’ and ‘arts people’, and to look askance at work that bridges these ‘two cultures’." The answer to this question is not simple or easy, it is big and complicated, but I think it is related to the matrix of domination (D'Ignazio & Klein, 2020): the structural domain with laws and policies as well as educational institutions that privilege some paths and people over others, the disciplinary domain that bureaucratically implements and enforces exclusionary binaries, the hegemonic domain in which culture develops and supports ‘oppressive’ ideas, and the interpersonal domain, in which individuals experience narrow pathways to define who they are.
The Bridges mathematics/arts group is a beacon of light, providing an example of how we can counter divisive binaries with hopefulness, grace and acceptance while maintaining high standards of excellence. One stop for me in the article by Fenyvesi, “Bridges: A world community for mathematical art,” was the following statement about Reza Sarhangi, “Bridges was begun by a many-sided individual” (Fenyvesi, 2016, p. 37). Many sided, multi-modal, multidisciplinary, polyphonic… all ways of being and describing that fight against the binary, including the binary of openness versus academic legitimacy. In speaking about the potential of the Bridges organization, Fenyvesi says, “today, as changes in the world bring about unseen alterations in the structure of knowledge, any form of research, learning, or creativity capable of heightening awareness toward interlocking systems possesses untold value” (p.44), interlocking… not dividing.
a) Dylan Thomas & Doris Schattschneider (2011) Dylan Thomas: Coast Salish artist, Journal of Mathematics and the Arts, 5:4, 199-211, DOI: 10.1080/17513472.2011.625346
The article I am reflecting on this week is on Dylan Thomas: Coast Salish artist by Dylan Thomas and Doris Schattschneider. Through reading the other articles on Bridges, I came to learn that Schattschneider is an active member of the Bridges community (as is Dr. Gerofsky!).
Dylan Thomas (Qwul’thilum) is from the Lyackson First Nation from Valdes Island. Thomas did not consider mathematics to be a part of his world beyond completing his high school math courses, until he began to study the work of Escher and recognized the possibilities of tessellation in Coast Salish design. As an apprentice of Rande Cook, Salish art became a focus for Thomas who states, “the mentor-apprentice relationship is very important to all Northwest Coast arts because it is the only way that our traditional arts have survived” (Thomas, 2011, p. 202). Thomas cites Susan Point and her use of geometric symmetry in Salish art as an influence.
Thomas' art is rich with mathematics, symbolism, history, culture and meaning. One of his works that particularly stood out to me was "Salmon Spirits" which speaks to the depletion of salmon due to climate change and “depicts the overcrowding of salmon in the spirit world” (p. 204).
In this article, we hear two voices. Dylan writes about his art and Schattschneider then writes about the mathematics in Dylan’s art. It is an engaging interplay between the two voices and two levels of understanding. Dylan concludes the discussion with this inspiring statement, “Mathematics and especially geometry have been a big part of my art and because of that, a big part of my life. Mathematics has become a huge inspiration to me, especially the way in which nature uses geometry so beautifully. I plan to continue to study the mathematical side of art to see where it takes me in the future” (p. 210).
How can we take Dylan’s story, the work of others such as Vi Hart (those music videos were amazing!), the Dancing Euclidean proofs from last week and the work of Bridges, to inspire students and give them permission and opportunities to let go off the art/mathematics binary?
The Bridges Math and Art conference definitely gives us a starting place to be inspired. With my little ones, I was especially interested in the Family Day public workshops, which reminded me of the Virtual Family Math Fair that we contributed to last February. Mahima and I hosted a session for preschooler, titled “Tik Tok Inspired Pattern Dance Party.”
What I am considering myself, is can we incorporate art and math in a seamless, connected way, rather than as an occasional ‘fun’ activity that we add to our teaching? How can we help students to learn mathematics through art? Should we? How can we bring families onboard so that parents do not perpetuate the ‘math person/ non-math person’ binary with their children?
For the activity this week, I looked at the Bridges 2013 gallery. The art pieces I choose to interact with are photography pieces by Mohammad Yavari Rad titled “Waves -1” and “Waves -2”.
I began by investigating and learning more about different types of waves. This was an interesting site for younger students with lots of information about all sorts of different kinds of waves. https://www.mathsisfun.com/physics/waves-introduction.html
There is so much mathematical language and so many mathematical ideas that can be approached through a study of waves including how waves are measured – frequency, wavelength, and amplitude. Waves are found in water, sound, movement of the earth (earthquakes) etc. I learned about the connections between waves, circles, and triangles, and the simplest equation to represent at wave (y-Sin(x). The mathematics of waves is deep!
Throughout the week, I went to a couple of different bodies of water and took some videos/photos of waves. Here are some of my favourites.
After spending too long trying to unsuccessfully upload the video here, I'm going to instead include a YouTube link so you can view the video.
Rock Drop on Pond: Traverse Waves
I love that the art of photography is about different ways that you can see the world, while looking at the same objects… seems like the same can be said for mathematics.
Just for fun... Check out this Public Media Art Wave in Seoul, Korea. Wave in Seoul, Korea. If you scroll down, you can see a 1 minute video of the wave. Not a strong connection to the topic this week but I came across it and thought it was fun to see.
Joy, I find the question about math and art a difficult one to engage with, so I was caught by your comment in your second group of questions: "Should we?"
ReplyDeleteI don't think it's commonplace enough for this question to be asked in educational circles. It's very easy to get caught up in the excitement of trying something new, so we fail to stop and consider whether we should even be trying whatever it is.
That being said, I think that YES, we should absolutely be seeking to break down these binaries. When you look at traditional schools, they are are divided, separated, very specific departments that teach specific things. I find that my colleagues are often "claiming" topics and literature as their own, because if something is done in one class, we couldn't possibly do it in another!
The question then arises: when is this seen in the "real world"? I've yet to come into a situation in which I was required to use math, math, and only math! Rather, I'm encouraged, and EXPECTED, to be able to think critically and creatively, providing solutions to problems that don't just result in a mathematical equation, but an experience around that equation.
Too frequently we lump students into STEM or Humanities. Speaking from experience, as I'm a Theology major, Math minor for my undergrad, melding the two can lead to very interesting experiences that we might not otherwise have the opportunities to encounter!
This is a long-winded way of saying: I think this is really important, and we need to figure out how to do it authentically, rather than sticking math and art together just to be flashy and cool.
I agree Fiona, that we need to figure out how to do it authentically. When I read about your thoughts on how subjects/topics are divided and claimed, it makes me thing that the issue we are talking about is bigger than art and mathematics... it is about how we envision and deliver education. Breaking down the binaries in our own thinking and places is a way to start.
ReplyDeleteDylan Thomas’s art is fascinating, but what I find more amazing is that even though his artwork involves important math concepts his formal knowledge of math was not extraordinary when he started creating his first work. As stated by Doris Schattschneider, Dylan’s knowledge of school math and interest in tessellations was similar to that of M.C. Escher. I read somewhere that Escher enjoyed geometry, but his performance in school math, like algebra, was poor. Here, I am not thinking in terms of how teaching and learning arts and math is dealt in binaries. I wonder how some people with seemingly ordinary mathematical skills at school can visualize math in a different light, with phenomenal results, later in professional life. Perhaps similar cases are in the field of arts. Whether true or a myth, Elvis Presley’s music teacher told him he could not sing. And, in the field of literature, many famous writers, according to the assessment by their teachers at school, were not expected to do well. For example, Roald Dahl’s English teacher in his school report wrote: “I have never met anybody who so persistently writes words meaning the exact opposite of what is intended.”(Wikipedia). What are the reasons that some people strive for excellence and pursue their passion, while others in apparently similar conditions do not?
ReplyDeleteYears ago, I had a copy of a publication coauthored by Doris Schattscneider, titled M.C. Escher’s Kaleidocycles. I used to show the class some fantastic models made of the cardboard nets that came with the book. That was after they had learned about basic forms of symmetries and types of tessellations. They were able to produce some interesting posters. But that was it. I never saw one that would go beyond the completion of the assigned project. The big question for me is: what can a teacher do to inspire and motivate the students to be the best they can be? How much of the student success depends on teachers? How is it that some people excel even though they did not have excellent conditions and learning support at the beginning of their journey?
Wow, You have asked some big questions here, Zaman! I don’t think there is an easy answer to what can a teacher do to inspire and motivate students but I do think it all starts with relationship. Teachers need to create a space and a place in their classroom where students feel comfortable to be who they are… That means we need to provide students with different ways to represent their learning. We need to help students see the bigger picture and the beauty of the mathematics in the world. To not get stuck on the marks on the paper but to experience the dance!
ReplyDeleteYou asked why some people strive for excellence and pursue their passion, while others in apparently similar conditions do not. The make-up of each learner is so different, so conditions in which one learner thrive may differ from conditions in which another learner thrives. This is part of what make teaching so complex and why education is changing and evolving. There is no one size fits all solution. Perhaps that’s why this course involves embodied learning, and outdoor learning and the arts… quite a buffet of learning opportunities!
I’m not sure how much student success depends on teachers but I know that a teacher can make all the difference in the world to a child. Reminds me of that quote… “the best teachers are those who show you where to look but don’t tell you what to see”.
Wow! What a great post and wonderful group discussion! Joy, Fiona and Zaman, thank you for raising deep questions about such important questions about cultural binaries, ways of integrating math and art pedagogies (and Fiona, math and theology as well!), and how to inspire students to want to take up important inquiries even after they leave school. Amazing discussion, and I will watch where this goes in your upcoming work! Joy, thanks for a great post that sparked it all, and for your beautiful waves videos. I was entranced watching the ripples on the pond start, and then gradually calm, leaving that beautiful reflection of the tree.
ReplyDelete