The applause ends. The chair asks if there are questions in the room. We hear a quiet “I wonder if…”. Then, it’s followed by another “have you tried to flatten your sculpture in a 2D dimension?, “I wonder if there is always the same length of the path in different paths…”, “and I wonder if there is always the same number of double edges!” The room is not quiet at all anymore. People start debating and sharing their ideas. The talk is over. It is time to go, but I am stuck. On my left side, people are counting the number of double edges present on the sculpture in German. On my right side, people are deeply engaged in a discussion around the symmetry of the sculpture in English. I, myself, is thinking in French about how I could bring those sculptures in my classroom. This is the potential of mathematical art.
My colleague is joining me on this trip and today told me: “I like that you know it’s a room full of mathematicians when they keep asking questions starting with I wonder if…and they just keep circling their ideas to each other.” She predicted the scene I would witness a couple of hours later.
The potential of mathematical art is its ability to bring people all around the world to wonder about mathematics, its beauty, and its potential; what other things are there that we cannot see just yet?
Tom Verhoeff and I talked about curiosity and its importance in mathematics. He told me: “We need to learn how to ask questions, but we need to learn that some questions are more relevant than others to pursue.” Mathematical arts have the potential to bring people to ask questions about what else is out there. But it also has the potential of bringing people in a state of flow so intense they can dedicate their life to answering a question. In the talks I have seen today, all had one thing in common: a desire to push limits. We can see it when Ayliann says that she can spend hours drawing her work. We can see it in the work of Koos Verhoeff, Anton Bakker, and Tom Verhoeff trying to solve a puzzle for 10 years, we can see it in Rinus Roelofs looking at so many polyhedra and their rotations, etc.
In brief, mathematical art can make people curious about mathematical ideas and make them want to challenge themselves into solving hard problems.
How interesting!
ReplyDeleteThat conclusion to Verhoeff's interview where some questions are weighted more heavily than others due to relevance is significant. This is meaningful to me as it is a practice I always model and teach in the classroom warning my students daily that the action of questioning requires courage - courage to stand out and be vulnerable, courage to show your level of comprehension and engagement, courage to learn something new and not understand it right away, and courage to ask for clarification, to name a few.
The unifying nature of sharing wonders and have it contagiously become the wonder of others without judgement is magical.
Pursuit of the unknown requires questioning, courage, and persistence in finding points of entry (like what we learned by Mason et al., 1982), as long as we can find another point of entry, our pursuit can continue unrelenting for decades like your presenters talked about. I suspect that this process is cyclical in that the learning of something unknown would lead to wonders, then attack in points of entry to determine something else unknown which motivates the next cycle. Unfortunately and fortunately, the process requires an injection of energy/action that is motivated by curiosity and playfulness before each cycle so as long as that continues, the flow can go on. That connects with Dave Whyte and Nick Sayers attitudes towards their artful pursuits where they found their niche.
Thanks for sparking these thoughts with your post!
Noemi, your post captured the essence of the Bridges conference beautifully. I too was struck by the joy found in each room that seemed to grow from a constant sense of wonder and questioning. I think it captured my attention precisely because it is what I want for my students. Amy Alznauer and I spoke about the importance of helping children find their obsession and run with it—asking questions, experimenting, and following their curiosity. It gives so much more freedom to mathematics than I had considered during my own school years. I keep coming back to wondering how I can give young students a taste of that kind of mathematical freedom to wonder and play in meaningful ways.
ReplyDeleteAs you wrote, Tom Verhoeff stated the importance of recognizing which questions are most relevant to pursue. This made me think about how important it is to begin teaching what a question is in kindergarten and to layer that understanding year after year, so that students begin to recognize what makes a question worth pursuing. In fact, the saying, “There’s no such thing as a stupid question,” is one I don't entirely agree with. Though the sentiment is encouraging and reminds people to speak up, you only need to sit in a primary classroom to reconsider the saying. In Grade 3, I am often reminding my students what a question actually is, as they love to comment rather than ask questions after a presentation: “I like rainbows, too.”
In mathematical dialogue, students need opportunities to become active thinkers—to notice, wonder, connect ideas, and then share. Perhaps part of mathematical freedom is not simply giving students permission to ask questions but helping them develop the knowledge and confidence to recognize which questions might take them somewhere interesting.