Students as Performance Mathematicians

George Gadanidis, Faculty of Education, UWO
February 14, 2008

What if we take the view (as an elementary school teacher noted) that mathematics “can be discussed with your family and friends just like you would a favourite book or new movie”? (Gadanidis, Hughes & Borba, in press).

Such a view – which is rather uncommon in our culture, where mathematical ideas are rarely shared or discussed outside of mathematics classrooms or communities of mathematicians – leads us to consider parallels between the arts and mathematics: between what makes for “a favourite book or movie” and what makes for “a favourite math idea or activity”. It also leads us to look to the performing arts to understand students’ repertoires for organising and expressing the mathematical ideas they seek to communicate to one another and to their worlds outside of the classroom.

I am working on this view of mathematics in collaboration with Marcelo Borba (Sao Paulo State University), Susan Gerofsky (UBC), Cornelia Hoogland (UWO), and Janette Hughes (UOIT).

The idea of “students as performance mathematicians” is new in mathematics education. It offers a fresh perspective on what school mathematics might be and how students might experience the subject. Some mathematical films do exist (like the 1960’s short films produced by filmmaker René Jodoin at the National Film Board of Canada: Spheres (Jodoin, 1969), Dance Squared (Jodoin, 1961) and Notes on a Triangle (Jodoin, 1966)) and some mathematical songs are used in schools (like Zero, My Hero by Schoolhouse Rock (Schoolhouse Rock, 1973)). There do exist popular movies about mathematicians, such as Good Will Hunting and A Beautiful Mind, but these movies are not performances of mathematics but rather of the social adventures of mathematicians. Some examples of student “artistic” mathematical performances can be found on the Web, such as images of geometric art (typically using tessellations) and student-produced mathematical videos are starting to appear on the Web (on YouTube, for example). We have also created a variety of mathematical performances: see http://www.edu.uwo.ca/mpc/performances.html. For the most part, however, it is fair to say that the idea of students creating mathematical performances as a way of communicating their ideas within the classroom and to the world beyond is new. In today’s mathematics classrooms “mathematical performance” is associated with testing and standards, and not with students’ artistic experiences and expressions of mathematics.

A performance model we have used to analyze mathematics experience (Gadanidis & Borba, in press; Gadanidis, Hughes & Borba, in press) is one developed by Boorstin (1990) for analyzing movies. Boorstin suggests that we get three distinct pleasures from watching a movie, which I paraphrase to suit our mathematics context: (1) the pleasure of experiencing the new, the wonderful and the surprising in mathematics; (2) the pleasure of experiencing emotional mathematical moments (either our own, or vicariously those of others); and (3) the visceral pleasure of sensing mathematical beauty.

We are not suggesting that every mathematics experience needs to be seen as a performance, although some would argue that performance is unavoidable – we are always performing – because “(w)e inhabit a performance-based, dramaturgical culture” (Denzin, 2003, p. x). What we are saying is that seeing mathematics education through a performative lens may help us to: (1) make better decisions about which mathematics is worthy of student attention (at the moment, references to mathematical surprise, emotional mathematical moments, and mathematical beauty would be rare finds in a mathematics curriculum document); and (2) find new ways of students sharing mathematics with the world beyond the confines of their classrooms. It can also start of process of disrupting common conceptions of what it means to do, learn and teach mathematics

The latest project we are developing (Gadanidis (PI), Gerofsky, and Jardine with Hughes and Craven), is that of a Mathematics Performance Contest (see http://mathfest.ca). This Contest is sponsored by the Fields Institute, the Faculty of Education at UWO and the Canadian Mathematical Society. The Festival invites grades 4-6 students and teachers (and others too) from across Canada to submit performances via a Web portal we have developed. See for example the performance submitted by a grade 5 student where a Triangle sings “I lost my head ... now I’m a trapezoid”. Student performances will be adjudicated by a committee of public figures (Susan Aglukark, Tracy Bone, Douglas Coupland, Bob Hallett and Jay Ingram), mathematicians and mathematics educators organized by the Fields Institute.

Acknowledgement
This research has been funded by a grant by the Social Sciences and Humanities Research Council of Canada.

References
Boorstin, J. (1990). The Hollywood Eye: What Makes Movies Work. NY: Harper Collins Publishers.
Denzin, N.K. (2003). Performance ethnography: Critical pedagogy and the politics of culture. Thousand Oaks, California: Sage Publications.
Gadanidis, G. & Borba, M. (in press). Our lives as performance mathematicians. For the Learning of Mathematics.
Gadanidis, G., Hughes, J. & Borba, M. (in press). Students as performance mathematicians. Mathematics Teaching in the Middle School.
Jodoin, R. (1961). Dance squared (animated film). Montreal: National Film Board of Canada.
Jodoin, R. (1966). Notes on a triangle (animated film). Montreal: National Film Board of Canada.
Jodoin, R. (1969). Spheres (animated film). Montreal: National Film Board of Canada.
Schoolhouse Rock (1973). Zero, My Hero (song).

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