"As members of a collective undertaking, Bridges participants experienced the joy of creating a colorful and unique mathematical art community in which layperson and expert worked side-by-side as equal partners" (p. 35). This quote opened my heart wide open as someone who often feels inadequate when encountering the mathematical concepts behind the art featured in Bridges exhibitions. I've never considered myself a mathematician. But this quote suggests that one person alone doesn't need to know everything to participate in and contribute to meaningful mathematical work. What strikes me most is the emphasis on community—not just collaboration, but genuine partnership where everyone's contribution matters. This idea that I don't have to be an expert challenges traditional academic hierarchies, and opens up an exciting way of thinking about mathematics. This model of equal partnership changes what it means to be a math person. The article describes how Bridges creates "a rich community" (p. 37) where hundreds of people from different disciplines and backgrounds come together not just to present papers, but to build giant sculptures, perform plays, create music, and explore together. Imagine how many more people would be willing to engage in math if what's required isn't expertise, but rather curiosity and a willingness to be what Francis Su (2020) calls a "math explorer."
Schattschneider observed that at Bridges, “mathematics creates art,” “mathematics is art,” and “mathematics renders artistic images” (p. 36). After eighteen years of conferences, however, the Bridges community came to see that the inverses are equally true: art creates mathematics, art is mathematics, and artistic images render mathematics. A fascinating example is the Spidron system, introduced by Hungarian designer Dániel Erdély as an art project in Bridges exhibitions. When mathematicians noticed its interesting geometric properties, the artwork became recognized as generating new mathematical insights. This reframes mathematics from something fixed and rigid into something living and generative. Thinking about this bridge between the two opens up a whole new world. Math isn't just what I thought it was—formulas, calculations, precise measurements. It's so much bigger than that, and that's exactly what drew me to this program. There's beauty in math that can be experienced when we dig deeper into concepts and connections beyond what is on the page and in a textbook.
The idea of approaching math problems as an art project makes me think I would have embraced them far more than a page of problems from a textbook. This raises an important question: how can I break the cycle? I know I need to teach my primary students foundational skills—counting, addition, and number sense—yet I also want them to experience math as creative exploration. What if learning to count could happen through creating tessellations—is this really too ambitious for young learners? How can foundational skills coexist with creativity and art? The Bridges model suggests that art-based math opportunities don't diminish foundational learning—they can enhance it. My wonder is this: How do we balance teaching essential mathematical skills with the open-ended, exploratory approach that Bridges embodies? Can we truly do both, or will one always compromise the other?
Fenyvesi, K. (2016). Bridges: A World Community for Mathematical Art. The Mathematical Intelligencer, 38(2), 35–45. https://doi.org/10.1007/s00283-016-9630-9
I really appreciated your focus on the bidirectional relationship between math and art—using mathematics to create art, but also seeing mathematics emerge from art itself. Like you, I find it much easier to look at art and notice the mathematics within it than to intentionally create art using mathematical principles. I think that difficulty speaks to how deeply many of us have been trained to see math and art as separate domains.
ReplyDeleteYour question about balance really resonated with me. I wonder if part of the answer lies in being intentional about foundations without letting them become a barrier to creativity. Sometimes that might mean starting with concrete materials—like counters or blocks—without art being the primary focus, but then intentionally creating space for artistic exploration to emerge once students have a foothold. In that sense, art doesn’t replace foundational learning; it grows out of it.
I was also thinking about Indigenous ways of knowing, where mathematics, art, land, and community are inherently relational rather than separate disciplines. Practices such as beading, weaving, and patterning are not “applications” of mathematics after the fact, but living expressions of mathematical thinking—symmetry, repetition, proportionality, and spatial reasoning—embedded within cultural practice. I was reminded of work by Dylan Thomas, whose explorations of symmetry, circles, and geometric forms reflect this holistic way of knowing. Using these contexts invites students to ask, What mathematical ideas are present here? rather than positioning math as something imposed afterward.
Perhaps the balance you’re describing isn’t linear, but circular: noticing math in lived practices, creating and reflecting, naming the mathematical ideas that emerge, and then returning to those ideas with deeper intention and scaffolding. That cycle feels aligned with both the Bridges philosophy and Indigenous ways of knowing—and feels especially powerful for primary classrooms.
I also felt energized by the idea that you don’t need to be an “expert”! That emphasis on curiosity and partnership resonates so strongly! It challenges the usual hierarchies and inspires for what math can be!
ReplyDeleteI’m also fascinated by your point about art creating mathematics. The Spidron example is such a vivid illustration that these ideas can emerge from artistic exploration, not only from textbooks. It reminds me of how we can discover through making, whether it’s drawing, origami, or even dance, and those discoveries can be mathematically rich without feeling like “traditional math.”
I think it’s possible to do both a balance of skills and open-ended. Unfortunately, though, I find I often am bouncing between the parameters of them both as I adjust and correct course, between the students who look bored, to the students who did not do well on their quiz, to looking at how they’re performing during vertical whiteboards. Foundational skills can be inside open-ended, exploratory projects, which helps take some of the pressure off myself! I like that students are practicing these skills while engaging creatively. Sometimes that does mean adding structure and narrowing the project scope to ensure these content pieces are met, like when they designed a video game, they could only use cylinders and rectangular prisms. I find my own success is usually made or broken in my ability to scaffold the math within the creative task. It's hard to provide enough structure to ensure the essential skills are present, but the students still have freedom to explore, try multiple solutions, and see how math comes out “naturally” from their making. I find I unfortunately have much less time for complete open ended, other than a 20-minute exploration every few classes.