Recently I was invited to give a keynote presentation to the participants at an international workshop on the topic of mathematical thinking. I accepted the invitation with quite a fair deal of excitement: I was looking forward to spending a week with a group of distinguished and emerging scholars, and having intelligent conversations about a topic that has been very close to my heart for a long time.
The group of workshop participants was very diverse. There were quite a few graduate students and postdoctoral fellows, a strong group of mathematicians, a significant number of researchers involved in mathematical education, as well as teaching practitioners, administrators and academics from other fields, including cognitive science and computing science.
Among the keynote speakers was a couple of academics from the United States whose contribution to the workshop was a presentation connecting mathematics to dance. He was a dancer and choreographer who pioneered the teaching and promoting of mathematics through dance, and she was a mathematician who implemented dance in the teaching of some of her undergraduate math courses and also did research about the outcomes.
Their session was scheduled in two parts. The first part was a demonstration of one of the activities that they perform with students in the class or with general audiences interested in learning more about their work. The second part was a presentation about their research on how the use of dance as a way of communicating mathematical concepts helps students better understand a particular topic and in general improves their attitude towards mathematics.
For the first part, all workshop participants were invited to the local concert hall. We had for ourselves the whole floor of a beautiful 80-year-old theater designed in the Spanish Baroque style.
After assuring us that no previous dance experience was required, the workshop moderators invited everyone to stretch and perform a series of simple movements. It was obvious that both of them were very good at managing this kind of audience. They were patient and encouraging, they would repeat their instructions and invite questions to clarify possible misunderstandings.
Still, since this was my first time in a situation like this and even though I was determined to do my best, almost immediately I felt uncomfortable with what I was doing. I was not sure if I could hear the complete instructions and if I understood and followed them fully. Since I didn’t want to stick out as ignorant, asking for clarification in front of everyone seemed out of the question. Looking around gave me an impression that everyone else was enjoying themselves. To me it seemed obvious: I was the only one who didn’t understand what our instructors said. The only comfort was that I had smartly positioned myself at the edge of the room, so nobody could really see what I was doing or not doing.
Well, this relative comfort didn’t last long. The next instruction was that we find a partner and continue working in pairs. But I was lucky! Right beside me was a colleague that I had met at a conference a few years back and who I knew as a very thoughtful and caring person. And indeed, during this segment of the workshop, she tried hard to help me to do exactly what we were asked to. For example, one of the exercises was that one person would take a certain body position and the other person was supposed to mirror it. When my colleague realized that I was too slow in connecting what I was told to do and what I was actually doing with my arms and legs, she simplified the whole sequence of exercises by giving me even more precise instructions and making the body movements more elementary. “Thank you,” I thought.
Then came the instructions that we make groups of three or four! My partner and I were joined by a distinguished scholar whose books and work have shaped both her particular field of research and her national government’s policies in math education. It turned out that she was also an experienced dancer.
During the first group exercise, the smile disappeared from her face. She was, I felt, really disappointed with my lack of body coordination. I was quite sure that I could see in her eyes that the verdict was: “You are dumb!” Oh, how I wished to be somewhere else at that moment. My other colleague sensed the awkwardness of the situation and suggested that, for our task, our “dance” was supposed to mimic the geometrical notion of translation, that I be in the middle and that she would be in the back to cover my “mistakes.” The slight head nod by our partner convinced me that she too wanted to be somewhere else.
When the workshop moderators brought us all back together it became clear that each group had actually performed at least one of the four basic types of symmetry for planar patterns: translation, rotation, reflection and glide reflection. Very neat!
The following Monday morning I was back in front of my calculus class. Still jetlagged, I was looking at my students and thinking: What else do I need to do to reach out to those of you who need more of my time, attention and support to fully grasp what we are talking about and to develop your skills and talents to the best of your abilities? The feeling of being treated as a dumb student for a moment will, I hope, make me a better teacher from now on.
Veselin Jungic is a 3M National Teaching Fellow and a professor in the department of mathematics at Simon Fraser University.