Starting off my post with a fibble about my journey on August 4th-5th. The poetic form is based on the first 8 digits of the golden ratio: 1.6180339
Pack.
Westjet steals our prep time.
Call.
Eight hours forty minutes on phone.
Re-booked flight.
Reunite.
Thankful we arrived in Ireland.
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I arrived at the mathematical art gallery absolutely floored with the pieces displayed. Here's a small glimpse:
Today, we started with a plenary talk by Nick Sayers on Math-Art with Meaning. I particularly loved his emphasis on meaning which he gave the examples of poetry, societal relevance, ambiguity, universality and transcendence. Sayers uses math as a medium, not the message itself. This was my first stop. I believe that my most successful lessons have been when I've used math as a means of developing an idea (ie. graphing function art, angles, shapes and geometry) instead of as an abstract end in itself learning it for the sake of learning it. Before i dig into planning my future units, I will need to remember this brief and powerful idea of "math as medium, not as message". This is impactful because when it is used as a tool to work something into existence through a means of self-expression, then the creator feels the utility and importance of the tool - especially when it improves the quality of their life.
Sayers foreshadowed aside ties in with his final inquiry question for us: What is the meaning of your math-art? Art for the sake of art was lost to me until a few days ago, when I read through Saad Mneimneh's presentation proceedings about "The Poetry of Math" and the thoughts that arise when we engage with poetry in the same way as a mathematical formula regardless of the creators original meaning. When the process itself brings about new thought pathways that become the keys to meaning-making for the individual, the making of the art (not necessarily the art itself) becomes meaningful to the creator. This would infer that the world is full of human-slop (not AI-slop) and that not all art is meaningful to everyone (or anyone), but the process of making it helped to transform the creator themself. Mneimneh reiterated that, "meaning is in the journey and the process" during the Q&A period.
Throughout each of Sayers' math-art pieces, he demonstrates his positionality and intersectionality as mathematician, artist, eco-activist, father, programmer, and pro-cyclist. This brings me to my second stop: Find the intersection where all your passions, values, and skills meet. Sayers has found a unique niche where each of these pieces of his being unite and mutually strengthen each other while contributing to the betterment of society. I think this is one of the prime functions that teachers are capable of due to our unique positions of constantly and rigorously introducing new ideas, tools and experiences to our students. I keep thinking about helping students develop a relationship (and making-meaning) with others and their environments, but I keep forgetting that they need to be able to develop the strongest relationship with their own self through noticing, recognizing, and reflecting.
Our second plenary talk was with Dave Whyte on Bees + Bombs, his webpage is https://beesandbombs.com/ where he highlights his journey in developing short looping geometric animations (gifs). Listening to his journey of growth as an artist, mathematician and programmer was very inspiring as it required observation, experimentation, excitement, reiteration, and playfulness. My third stop came when he introduced a simple idea that the symbol for nothing is 0, and the symbol for everything is ♾️... so everything is nothing with a twist. This cheekily became one of his frequently used tools in his bag of tricks but the concept is profound. I visualize the twist being the flip of a zero from the numerator to a denominator. I imagine it like a mindset going from a thought of scarcity to one of gratitude. It is a really appealing metaphor of life for me.
During the Q&A, someone asked about Whyte's creative process: he jokingly declares that he thinks things, writes them down, and then creates them... but there's so much more than that. Whyte has a vague idea about the kind of effect that would be visually attractive to him, then he experiments and tries many things. Sometime he comes up with something that he absolutely loves, an intricate visual pattern with hidden seams. Sometimes he comes up with nothing and throws it away. This brings me to my four stop of the day: Both Sayers and Whyte have exceptionally explorative (or playful) attitudes towards creative projects. McClellan helped me to connect this idea even with the talks from Aug. 5th of which I was absent. She said each presenter was extremely playful and wouldn't stop tinkering and reiterating and exploring and tweaking just for fun or out of curiosity! These examples have solidified my belief that playfulness is one of the most important qualities of a successful creator and mathematician.
I attended six more presentations today. Surprisingly my fifth stop is the most important things I've learned have come from the Q&A sections regarding the artists preferences or creative processes. This makes me want to come to the next presentations with some pre-written generic questions all related to their creative process, or meaning-making because, as stated in stop one, the creation of the art is most transformative for the artist themself! So who better to report out on it than them of what they learned?
An example of this was during Kerry Mitchell's presentation on Creating Art with Space-filling Curves. He mentioned his favourite part of creating these pieces (ie. Fig 11 below) is that the Hilbert curve is subtly embedded in this abstract artwork, it doesn't jump out at you but you have to work to reveal it. I appreciate Mitchell's response as I feel the same way about my artwork. I subtly embed or hide easter eggs in my artwork so that it has layers of meaning for those who engage with it. There's a saying for this: "if you know, you know" abbreviated "IYKYK" online. When digging or revealing new layers within artwork, it re-ignites a viewer's interest and helps them further develop an expectation for success and discovery that motivates them to keep exploring/digging. The same happens in mathematics!
This reminds me of Aharoni's (2014) discussion of an unexpected twist in poetry (and mathematics) where one level of meaning is made while the details of a poem or story are read until the unexpected twist occurs that forces the reader to take all that accumulated data at once and re-interpreting it with a new meaning giving the reader a sensation of transcendent beauty (Su & Jackson, 2020) - giving the reader a glimpse into a larger truth by comprehending a great deal all at once.
That's all for now!
References:
Su, F. & Jackson, C. (2020). Mathematics for human flourishing. Yale University Press.
Whyte, D. (2026) Bees & Bombs: My Gifs. Proceedings of Bridges 2026: Mathematics and
the Arts. 2-2.
“I believe that my most successful lessons have been when I've used math as a means of developing an idea (ie. graphing function art, angles, shapes and geometry) instead of as an abstract end in itself learning it for the sake of learning it.”
ReplyDeleteThis connects to an interesting idea Anton Bakker and Tom Verhoeff shared with me. They said that in school, we spend most of our time teaching answers to questions students did not even know they have. For example, I teach how to use analytic geometry to find the distance between two points, but my students never asked me: is there another way to find length without using a ruler? Thus, students are used to absorbing what we think they should know. And our curriculum is so dense, that we have little time to explore the different ideas in it, but also to foster our students’ creativity and desire to be curious. How can students learn who they are, the intersection where all their passions, values, and skills meet, if they do not have time to pursue their own interest?
Even if we are confined by the curriculum, there is always a way to smoothen its rigid structure to leave a little space for what we believe is important for our students. But how nice would it be if our students would have time to discover themselves throughout their school days.
Olly, your blog post touches on many exciting facets explored during the Bridges conference. One that immediately resonated with me was the idea that meaning occurs in the making of the art, and not necessarily in the art itself. It made me think about why people create, explore, and play, and the important role these experiences play in our learning. This idea also made me think about how the act of making can broaden our ways of seeing and thinking. King and McCall (2024) found that engaging in artmaking expanded students’ worldviews and challenged their previous ways of thinking, reminding me that perhaps one of the most important outcomes of creating is not the thing we make, but the new perspectives we develop along the way.
ReplyDeleteAs an educator, this is a key takeaway from the conference. Getting my students to playfully see themselves as creators who can take ideas and create art, new ideas, poems, or gain new curiosities connects beautifully with the idea that mathematics is indeed playful and can be artful.
This also connects to your profound recognition that this kind of work demands that students develop their sense of self as they notice, recognize, and reflect. This is where I think the demanding work lies with primary students: they are still beginning to understand who they are as creators, thinkers, and learners.
References:
King, C. R. P., & McCall, M. (2024). How the fine arts create the finest students: A design thinking study. Higher Education Quarterly, 78, 1162–1174. https://doi.org/10.1111/hequ.12521
I'm not sure why my reference spaced so oddly.
ReplyDelete