I have been spending the last few days asking people questions around how you experience creating art/mathematical art, how does doing art/mathematical art change the way you look at the world and if art could help students reconnect with being curious and asking questions to satisfy their own curiosity. I think that answering the question myself could be a good way to end this conference.
How did I feel when I created my poem? How did I live the experience?
I was happy to have to dedicate time to write a mathematical poem for the conference. I have always enjoyed poetry, and I used to write poems more in the past years. Although I knew I would dread the moment I would have to share my poem, because I had never really shared any of my poems before.
I decided to create a poem that was meaningful to me and my students. I like mathematical arts because it allows me to be whole when doing mathematics and doing it with meaning. The process of writing it went smoothly and I can say that I reached a state of flow when I would not see the time fly. Unlike many presenters this week, I am not obsessed with mathematical poems, but that might be because my obsession is about teaching mathematics. I think that it is normal that not everyone develops an obsession with mathematical art.
What struck me the most is how proud I was for pushing myself to do something completely out of my comfort zone. It was already challenging to send my poem to Sarah, reading it in front of an audience was terrifying! But I did it, and now I feel more resilient; I feel like I am stronger in a way that I know I can overcome challenges and difficulties.
This sense of resilience, confidence, and strength is exactly what my students would benefit from. I feel like art could give them an ‘easier’ (with less pressure) entryway to challenge themselves, notice that they can overcome difficulties, and hopefully give them the confidence to start tackling problems more easily.
How does my interest in mathematics and arts change the way I see the world?
The dualistic worldview defines ‘pure’ and ‘true’ knowledge as knowledge only coming from the realm of thoughts. It thus separates the mind from the rest of what makes us human beings (body, heart, and soul). I never enjoyed mathematics that seemed meaningless and did not seem beautiful or mystical to me. I think that the dualistic worldview hegemonic in mathematics is narrowing ones’ perspective of the world. I like having interests in both domains, because I can build on their strengths. I know I have the critical and mathematical knowledge required to ask questions when something seems wrong. And I also know I can use different mediums of communication (arts) to convey my message. I feel that having an interest in the arts makes me more inclined to appreciate the beauty of mathematics. And being so good at finding patterns makes me more inclined to appreciate how an artist decides to convey a message. Finally, I think that having interest in arts makes me more empathic toward people, and I can use that empathy more easily within mathematics.
Noemi, I really appreciated that you ended your conference reflections by asking yourself the same questions you have been asking others and I thought it would be a great way to respond to your post.
ReplyDeleteOne of the most surprising experiences for me at Bridges was participating in the reading of Tom Petsinis’s Euler’s Vision. I played the imaginary number, i. At first, what worried me wasn’t the acting. It was that I had always believed that to play a character well, I needed to understand that character deeply enough to know how they would respond. In previous acting experiences, I have even kept character journals to help me get inside a character’s head. But how was I supposed to develop that kind of relationship with an imaginary number? The only way forward was to start learning. Participating in the play pushed me to explore mathematical ideas that I didn’t understand and wasn’t particularly comfortable with. I certainly can’t claim expertise in Euler's ideas, but I can claim the beginnings of knowledge that I didn’t have before. I didn’t have to know enough to participate. Participating helped me know more.
I experienced something similar when I wrote and shared my mathematical poem. I loved the constraints of the form. Rather than limiting my creativity, the constraints gave it somewhere to go. There was something surprisingly enjoyable about having to work within those boundaries. It makes me think that I might return to Bridges through writing and poetry, although there are still so many other possibilities I want to explore.
Your question about how mathematics and art have changed the way I see the world is a much bigger one. I came into this work knowing that mathematics was not my strongest area. I am leaving with the realization that mathematics is everywhere. I see angles and fractals everywhere. I see possibilities for mathematics through movement—I even created a dance for my students to understand pi. I notice mathematics in everyday decisions. But I think the bigger change is this: I’m not just seeing mathematics; I’m seeing mathematics differently.
This change in perspective makes me think about my students. I hear “I’m not a math person” differently now. Perhaps we are all mathematical thinkers, but we don’t always recognize ourselves that way because we have been given such narrow ideas about what mathematics looks like.
This is where I think your question about art and curiosity connects with my own thinking about access. I didn’t engage with everything at Bridges. Sometimes I didn’t have enough knowledge. Sometimes the presentation didn’t draw me in. Sometimes I simply had to work to bring myself back to the conversation. If that was true for me, then I can’t expect one mathematical doorway to work for every student.
Perhaps my responsibility is to keep creating ways for students to enter the mathematics—to notice, wonder, make, move, write, play, and talk before they necessarily have all the mathematical language or confidence they need.
Maybe that is my biggest takeaway from Bridges: we don’t always have to know enough before we begin. Sometimes beginning is what helps us know more. Perhaps that is part of how we help students see themselves as mathematical thinkers.
@Noemie
ReplyDeleteI love the idea of answering these inquiry questions yourself. Thank you for sharing the poem The Power of a Round Dance with us with its rhythm you stomped out while reciting that gave it a very unique presentation during open mic! I have a couple of wonders about this that would extend to our students if done with them:
1) Would our students too build resilience, confidence and strength simply by participating? Does it take the extra step of processing the effort and outcome for our students to notice how the experience has affected them? (You mentioned “notice that [our students] can overcome difficulties”)
2) I think you touched on something really interesting by mentioning that students could challenge themselves with mathematical art. This pushing of the self is something I haven’t given much attention to until this past year and reading about flow in a 1988 paper by Csikszentmihalyi. Do we need to encourage our students to push the limits when creating, or encourage them to play/explore by giving them time and space? Will they enter a state of flow trying to overcome self-imposed challenges at the brink of their skill set as you did?
I understand your need for the connection between thoughts, body, heart and soul; I think it is to our detriment when we attempt to isolate experiences to various realms. I keep thinking back to my students and their claims (or rather rejection) of their identity of not being artistic, being too self-critical over their drawings, being too self-conscious to dance or move their body out of a sport context. They are artists in their own way and based on their priorities of their age and desire to not stand out (read as “fit in”), how can we tap into a medium that speaks to them specifically. There isn’t one right answer for this, but I think the solution will require time (limited-resource) and flexibility across a semester – perhaps in the form of an inquiry project. The benefit of developing empathy toward others through understanding symbolic or visual representations in art using pattern recognition of mathematics adds more vocabulary to our meaning-making narratives.
Thank you for the thoughts!
References:
Csikszentmihalyi, M. (1988). The flow experience and its significance for human psychology. In M. Csikszentmihalyi & I. S. Csikszentmihalyi (Eds.), Optimal Experience (1st ed., pp. 15–35). Cambridge University Press. https://doi.org/10.1017/CBO9780511621956.002