In Bridges Stockholm 2018, Torrence (2019) provides a descriptive account of the 21st Bridges Conference, an international gathering dedicated to exploring connections between mathematics, art, music, architecture, education, and culture. Held at the National Museum of Science and Technology in Stockholm, the conference is presented as an immersive, multi-day experience that extended well beyond traditional academic presentations. Torrence highlights a wide range of activities, including keynote lectures, peer-reviewed paper sessions, workshops, juried art exhibitions, mathematical performances, poetry readings, film screenings, and a public Family Day that invited children and community members into mathematical play. Particular attention is given to the Mathematical Garden and public-facing events, which positioned mathematics as embodied, visual, and accessible rather than abstract and exclusive. Overall, the article portrays Bridges as a space where mathematics is experienced as a creative, communal, and interdisciplinary practice, emphasizing participation, aesthetic engagement, and informal learning alongside scholarly exchange.
Reflections:
One moment that made me pause was the description of Marjorie Rice: “Marjorie Rice, a woman with no mathematical training beyond high school, wrote to Martin Gardner in 1976 claiming she had found a new pentagonal tiling” (Torrence, 2019, p.706). What struck me was that her ability to discover a new geometric pattern did not require any advanced formal training. Instead, it seemed to come from sustained curiosity and a willingness to explore. This made me wonder whether school mathematics, with its emphasis on procedures, memorization, and technical accuracy, might actually prevent some learners from engaging more deeply with mathematical ideas. I found myself asking whether such experiences could have discouraged Rice from pursuing further formal mathematics, and more broadly, how many students may lose opportunities to experience mathematics as something creative and joyful.
Another moment that stood out to me was the description of Colm Mulcahy’s performance: “Despite having one arm in a cast, Colm performed several card tricks, and explained how he used mathematics in each” (Torrence, 2019, p.707). This reminded me that mathematics can be playful. Play is often dismissed as a distraction from serious learning, yet it can create the conditions for deep exploration—echoing Einstein’s idea that play is the highest form of research. Mulcahy’s performance shows mathematics unfolding through surprise, experimentation, and curiosity rather than formal explanation. In this moment, mathematics is not something to be delivered, but something to be experienced. This made me reflect on how playful inquiry can shift students from following rules to actively making sense of ideas.
This perspective is further reinforced by the artwork of Roger Antonsen presented at the 2018 Bridges Conference. Antonsen describes exploring card shuffling by visualizing permutations through code, motivated by the question, “What if I make invisible structures visible?” His process highlights mathematics as experimentation—playing with ideas to see what emerges. For me, this example captured the freedom to wonder that is often missing from school mathematics. It reminded me that mathematical understanding can grow through exploration and creativity, not just through applying known methods.
Together, these examples prompted me to reflect on my own role as a mathematics teacher. If mathematics thrives on curiosity, play, and “what if” questions, then the way I structure classroom norms matters deeply.
Antonsen, R. (2018). Six perfect in-shuffles with 125 cards and five piles [Digital print]. Bridges Mathematical Art Galleries. https://gallery.bridgesmathart.org/exhibitions/2018-bridges-conference/rantonse-ge
Discussion Questions:
How can teachers balance open-ended exploration with curricular expectations and assessment requirements?
Discussion Questions:
What kinds of classroom norms would need to change for play and experimentation to be taken seriously as mathematical work?
How can teachers balance open-ended exploration with curricular expectations and assessment requirements?
Hi Amy, many thanks for sharing this reflection. Below, I have copied the passages I found especially noteworthy, and in a way they also seem to address your first question!
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Amazing!
"Mulcahy’s performance shows mathematics unfolding through surprise, experimentation, and curiosity rather than formal explanation."
Gives a lot to think about for our math pedagogies!
"For me, this example captured the freedom to wonder that is often missing from school mathematics."
Yes the idea of self-discovery is often so underrated in math pedagogy!
Hi Amy, thanks for your insightful reflection and discussion questions! I think for play and exploration to be taken seriously in the classroom, it must be integrated regularly and not treated as "extra" or "additional". Often, when we incorporate play into the classroom, we try to get our students to buy in by telling them we're playing games, it's going to be fun, etc. and the students assume that means no true "work". Somehow, we must find a way to integrate play into the classroom while simultaneously maintaining the high rigour and expectations of any other lesson.
ReplyDeleteAdditionally, balancing open-ended exploration with curricular and assessment expectations can be incredibly difficult. If the exploration activities in class do not have a direct tie to the summative assessment (which may be mandatory at the end of a unit), and students do not have notes or examples from the activity to further study for that assessment, it can be difficult to ensure the exploration be taken as seriously. In scenarios like this, we must work alongside the constraints of the institution by combining exploration activities alongside more traditional practices.
Great connections with our role as teachers. We’ll be discussing this today!
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