Today started with a plenary talk from Amy Alznauer on Why We Tell Stories. Her main argument was that we tell stories because our lives are stories, and we have questions of which we long for answers. The stories themselves are simply vehicles for council: my first stop. Alznauer introduced a quote from Walter Benjamin: "Council is less an answer to a question than a proposal concerning the continuation of a story which is just unfolding." This makes sense and connects with my experiences and discussion with Coast Salish educators on the topic of parenting; stories are often told as a means of council rather than prescriptive commands that lead to power-struggles. The stories then become a vehicle for self-reflection and introspection; the same story may be told many times with the child pulling a new message from it due to their developing experiences in life. A story becomes a way for a teller to process occurrences of cause and effect, making clearer for themselves relations in time.
My second stop was when Alznauer brought up the idea (through quotes of Edward Shils, Wendell Berry and Doris Schattscheider) of being at the centre and alternatively (or simultaneously) at the periphery. Each location comes with benefits. As math artists, mathematics is at the periphery of fine art, and art is at the periphery of mathematics. The peripheral relation promotes beneficial qualities of engaging in generative (genius) power as an originator, with freedom and passion of a lover/amateur, with the wonder of a child. Perhaps this is why cross-curricular interdisciplinary projects offer such exciting opportunities; just by engaging simultaneously in two different disciplines, you get to access all the benefits of peripheral qualities.
My third stop was when Alznauer mentioned the tombstone of Lucy Joan Slater which read Computer Pioneer. Alznauer stated that Lucy was homeschooled and that it was a huge benefit to her as she was able to have the time to pursue whatever interested her. This connects with thoughts that I've been having about the rapid pace of 21st century life, time-pressures of government curriculum and the school system, and focused downtime for hobbies (aka boredom that leads to discovery). As Hannah Fry stated in a youtube short, "Time [pressure] - the killer of all things good." to which I absolutely agree. I'm not sure if "fear" is the right word that accompanies time-pressures, but I certainly have made many choices in my classroom out of "fear" (linguistically, perhaps literally) that I will run out of time - condensing instructions for important activities, cutting activities short ruining experiences, reducing exploration, or skipping concepts to name a few. The uninterrupted free mind that can take the time to obsess and wander and pursue imaginative ideas really makes all the difference to a creative (not just creative but generative) individual. I now wonder how I can structure my classroom to have more of this uninterrupted free time where they can pursue what interests them in mathematics, then choose how they wish to represent it... perhaps in more of a Montessori style such that students may have agency to explore several concepts all at once and spend the most time on what is most challenging to them.
My fourth stop came from Clare Moriarty on Semiotics, Ease and Elegance: Oliver Byrne's Elements of Euclid. Moriarty drove home the fact that Byrne was obsessed with accessibility of mathematics trying to build in many ways/systems for understanding and accessing knowledge. Byrne therefore used red, yellow, blue and black in his print on Elements of Euclid freeing up mental space for geometrical reasoning by rendering each shape/angle/object/ etc in colour, then referencing it in colour during the proofs. This connects deeply with me as a math educator and - before that - a tutor trying to explain or draw things in ways that allowed my students to grasp the concepts. This monumental effort of printing a coloured book in the 1800s that tanked the printing company shows the kind of dedication (obsession) Byrne had in trying to make math accessible.
On the topic of making math more accessible, my fifth stop came during Gary Lester's talk on Art as Math Representation: A practice-based Investigation of Cognition and Pedagogy. Lester wanted to investigate why the notion of "I'm not a math's person" was socially acceptable leading him to develop an art-based sculptural approach with embedded mathematical concepts as a way to invite discussion. Lester found that the same scupture presented a very different message to very different audiences with their interpretation largely reflected by the background knowledge they brought in to the experience. Lester reminded us that when teachers teach what they already know, they fail to communicate complex mathematical ideas from the viewpoint of a novice using their vocabulary and their experiences from which to scaffold. So, how can we extract a math concept's core idea and introduce them from the viewpoint of the novice? Lester finished with two more leading questions that are thought provoking: What are the differing cognitive processes taking place between experts and novices? And, can artistic forms be used as avenue for greater engagement? This becomes another point of entry towards accessibility of complex math ideas.
Quick aside: On Aug 8th (the following day) I had the pleasure of meeting up with Georgina Ryan in the art gallery as I wanted to have a discussion with her about the differences between her findings and that of Gary Lester's. Ryan has created a website called Threaded Theorems in which she shares unique self-made embroidery patterns of advanced mathematical ideas as an accessible entry point for women to become introduced and curious.
Where Lester's findings showed that people only cognitively engage with art at the level of their background prior knowledge, separately Ryan's idea feels like a hopeful attempt to introduce and advance mathematical knowledge. These two ideas work together and become driven by curiosity. In the beginning, embroidery enthusiasts would only engage with the artistic qualities of the math ideas, but then find out more about their embroidered concepts through inquiry. I believe as long as we don't let the curious walk away and miss out on an opportunity to engage, then this could be a strong point of entry in education.
A dramatic reading by Susan Gerofsky (e), Kristie McClellan (i), Eveline Pye (pi), Oliver Podwysocki (+), Jim Wolper (1), Lisa Lajeunesse (=), Britt Kaufmann (0), and Tom Petsinis (Euler)
References:
Alznauer, A. (2026) Lunar Music, Lost Notebooks, Pentagons, and Paralysis: How the Hidden Stories of Amateurs – of Those Who Love – Offer Vital Counsel to Both Mathematicians and Artists. Proceedings of Bridges 2026: Mathematics and the Arts. 3-3.
Gerofsky, S., Nicol, C., Li, Z., Leung, A., and Omonade, C. (2026) Artists Re-Storying Their Relationship with Math and Art. Proceedings of Bridges 2026: Mathematics and the Arts. 427–434.
Lester, G. (2026) Art as Mathematical Representation: A Practice-Based Investigation of Cognition and Pedagogy. Proceedings of Bridges 2026: Mathematics and the Arts. 553–556.
Moriarty, C. M. (2026) Semiotics, Ease, and Elegance: Oliver Byrne’s Elements of Euclid. Proceedings of Bridges 2026: Mathematics and the Arts. 1–1
Mneimneh, S. (2026) The Poetry of Math. Proceedings of Bridges 2026: Mathematics and the Arts. 419–426.
Ryan, G. (2026) Threaded Theorems: Hand Embroidery as Mathematics Outreach. Proceedings of Bridges 2026: Mathematics and the Arts. 541–544.
“Lester reminded us that when teachers teach what they already know, they fail to communicate complex mathematical ideas from the viewpoint of a novice using their vocabulary and their experiences from which to scaffold.”
ReplyDeleteThis was also a stop moment for me. I think it might even have been an aha moment. I always knew that my students did not know all the math that I knew and I had to review basic concepts before teaching, but I never thought about it as my students might not have the underlying understanding/skill behind some of the concepts I teach. I think having this presentation right after Marta Kopyt’s made it click. In her presentation, Marta Kopyt (2026) showed some of the books she wrote, one being about points. And she said something along that points is just an idea, but we can play with it.
If I take both ideas together in my teaching practice, my students struggle with developing a deep understanding of analytic geometry and functions. I think it might come from the fact that they do not understand the idea of points. There is nothing in their cultural referent that could help them make sense of the idea of points. Then if I try to teach functions and analytic geometry taking in consideration they have a strong understanding of the idea of points, it is to be expected that few will be able to connect those new concepts to something they know, as Gary Lester (2026) would say. I am eager to try some art activity inspired by Marta Kopt’s book to help my students understand better what is a point.
References
Kopyt, M. (2026, August 7th). Talking about mathematics through books [Conference presentation]. Bridges 2026, Galway, Ireland.
Lester, G. (2026, August 7th). Art as a mathematical representation: A practice-based investigation of cognition and pedagogy. [Conference presentation]. Bridges 2026, Galway, Ireland.
Olly, your post left me with several ideas to keep turning over. Looking up the Collatz conjecture and trying it out made me wonder if there are mathematical problems I could introduce to my Grade 3 students at the beginning of the year with the idea that we could work toward them all year. I’m not sure yet what problems would be both challenging and accessible to the group, but it feels like a germ of an idea. It would bring some aliveness to the world of mathematics, and that’s not something students always understand or see. I’m not sure I’ve always appreciated it either. I love the idea of students having a mathematical question that they can return to, wonder about, test, represent, and perhaps never completely “finish.”
ReplyDeleteDuring Lester’s talk, I was struck by the idea that perspective can shift when we are open to looking at things in new and fresh ways. I was also reminded that as our knowledge grows, our perspective changes. This seems particularly important to remember when teaching a new mathematical concept. I think about something as seemingly simple as skip counting by 5. I have taught the pattern of 5, 10, 15, 20… and thought it would take two minutes to teach and for students to learn. But when I try to approach it from a novice perspective, I can see how much might actually be going on. A student might be able to recite the sequence without understanding why the numbers change by 5, why they alternate between ending in 5 and 0, or how skip counting connects to equal groups and multiplication. What feels like an obvious pattern to an experienced mathematician may not be obvious at all to a child encountering it for the first time.
This makes me think about the importance of accessibility. Approaching mathematics from a novice perspective means asking myself not only, “How do I teach this?” but also, “How might a child access this idea?” During David Reimann’s talk, I was struck by his use of LEGO to move mathematical ideas out of the routine of paper and pencil and give them a physical form that invites exploration (Reimann, 2026). I could see adapting some of these ideas with LEGO in my own classroom—not simply because students enjoy building, but because construction could make mathematical relationships and structures visible in ways that allow students with different levels of mathematical understanding to enter the same problem. Perhaps a child can build an idea before they can explain it, see a pattern before they have the language to describe it, or manipulate something that would otherwise remain abstract.
This makes me think about how important it is to approach teaching with fresh eyes—to try to temporarily forget what I already know and wonder what the concept might look like to someone who doesn’t yet have the underlying ideas. The more mathematics I know, the harder it can sometimes be to remember what it feels like not to know it. Perhaps part of becoming a more responsive mathematics teacher is learning to notice those invisible barriers and finding multiple ways into an idea. Lester’s reminder to consider the novice perspective feels like an important invitation to slow down, notice what I am assuming students already understand, and make space for more students to find their way into the mathematics.
Reference
Reimann, D. A. (2026). Using LEGO® elements to communicate mathematical concepts. Bridges 2026 Conference Proceedings, 549–552.