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.
About the last paragraph, where you’re asking yourself “What else do I need to do …” My provocation: why is it that YOU need to do more? Don’t forget that, in your dancing experience, it was your *peer* and not your instructor who took you out of your misery 🙂 and made your experience worthwhile.
So here is my question. Why is it that students expect so much help from us (their instructors), and yet so many are unwilling to help (or work with) their peers?
Routinely, students tell me that they reach out to me because they do not know anyone in class. In spite of my frequent words of encouragement that they should introduce themselves to their neighbours, talk to them, discuss my math questions in class when I suggest that they do, a majority of students remain frozen in their seats. (Needless to say, this is not just my experience.)
The moment I assign homework, there are hands in the air – concerned students asking me “When are YOU going to post solutions?” Why is it impossible that a group of 4-5 students organize themselves, solve the assignment together and post in on a web page that they created? Other students can comment, point at possible errors, and together they can create an A+ assignment!! (Imagine the benefits of doing that.)
Students suggest that I do podcasts of my lecture. These days when a phone can easily record videos, why don’t a group of students (I’d be very happy to assist) offer to record my lectures and post them on Youtube? As an added benefit, they could annotate the lectures, and/or make comments or append with a few extra practice questions, or link to online resources (again, great learning experience!)
Why do students ask me if I am going to organize a review session for them before a test?
I am teaching very large first- and second-year classes, perhaps the situation is different in smaller classes. But I doubt. Answer, anyone?
Veso, this is a wonderful article that elegantly describes how simply shifting our perspective can help us all be more Inclusive. Aren’t we all students, peers and instructors in our various roles in Life? Thank you for sharing your enlightening experience with us. Shared on LinkedIn.
Excellent post, Miro. We seem to have bred a generation of students who decline to accept responsibility for their own learning. In some cases, we have even promoted their actively finding ways to avoid doing so. Where would they get the motivation to do so, let alone learn to do so, given the society we live in?
Growing up, they were not allowed to receive failing grades and were not held to deadlines/due dates for assignments. High schools allow students to wait until the last possible day to turn in any work even if no need for accommodation has been demonstrated formally or informally. How does this benefit the student, who receives no feedback on opportunity for improvement throughout the semester?
The high school curriculum, in response to universities’ criticisms that high school graduates were unprepared for university, evolved to focus more on designer courses (e.g., computer programming and modelling, statistics, philosophy) than simply focusing on teaching their students how to learn, read/interpret assignments/questions and communicate effectively.
Good grief, if you don’t give students a ‘rubric’, breaking down exactly how grades will be allocated to specific components of an assignment, they have a conniption fit. What happened to reading the assignment outline and thinking critically about what you’re being asked to do? That would be a good starting point, given that the function of a university education is to develop critical, independent thought, no? How does one demonstrate independent, critical thought when one follows someone else’s recipe for desired grade achievement?
Our students protest paying 1/10 of the cost of their post-secondary education even though they claim a university degree is the only way to assure their own future careers and fiscal well-being. Although relying on the degree for a satisfying career, they fail to inform themselves about the function of a university education vs a college or trade school education (let alone the job market), then blame the government (and baby boomers) when they are unable to find work upon graduation.
In Ottawa, a particular medical clinic employs university students to staff the front desk. It is common knowledge that those students print off doctor’s notes for students for the purposes of academic accommodations, without the doctors having seen the individual. Instructional and administrative staff at the universities and colleges openly acknowledge this fact. None of the universities or colleges in Ottawa take any action to address these fake “doctor’s notes”. Certainly, Ottawa is not the only place where falsified documentation for accommodation takes place. It would be a simple fix. A top level administrator could simply send out a notice to physicians listed on the College of Physicians & Surgeons’ website that this problem has come to their attention and respectfully remind the physicians of their legal obligations to ensure that accurate documentation within their practices.
Universities ploddingly go along with it all, making excuses for students and accommodating these demands because it is easier to do so than to hold grown adults, who have been socialized to be excuse-making, government-blaming, egocentric dilettantes, accountable for their own development. Maybe if academics stopped playing the victim card on behalf of everyone (intersectionality scholars, I’m looking at you), we could address some of this. For heaven’s sake, our universities need to get better legal teams, pay their insurance policies, take a stance on this nonsense and fight these fights.
Thank you for sharing this Dr. Jungic! I was in your class two years ago, during my first semester at SFU. It’s difficult to transition from small classrooms to large impersonal lecture halls; it’s intimidating and takes some adjustment. I remember that during the first week of class you met with each of your students during office hours. In retrospect, I wanted to thank you for taking the time to get to know your students. Your enthusiasm for teaching not only made learning in the course easier, it also made my experience entering university more positive.