# Students as Performance Mathematicians (SSHRC Research Project)

**Funding**

Funded by SSHRC (2008-2011).

**Team**

George Gadanidis (UWO), Marcelo Borba (UNESP, Brazil), Susan Gerofsky (UBC), Cornelia Hoogland (UWO), and Janette Hughes (UOIT).

Research Assistants: Ricardo Scucuglia (UWO), Sarah Tolley (UOIT), Natasha Wiebe (UWO)

- Rio Claro Festival (summer 2009)
- Shapes Project 2009
- A Research Performance (June 2009)
- Big Ideas Across Grades 2-8 (2009)
- Area and perimeter (grade 2)
- Do parallel lines meet? (grade 2)
- Odd numbers hiding in squares (grade 2 + grade 7)
- Story-based math projects (grade 2)

- Alderville First Nation project (2008)

**Related Projects**

**Research Goals **

We ground our research in contemporary performance theory and on a view that media are not neutral and serve to disrupt and reorganize human thinking (Borba & Villareal, 2005). Our research seeks to explore students’ ways of knowing and communicating that might make mathematics a subject that can be discussed outside of classrooms or communities of mathematicians (as one might with a good book or a favourite movie). Our research also seeks to do this using the multimodal and read/write affordances of new media.

The research objective is to explore the concept of students as “performance mathematicians”. The initial research questions are:

- how might classroom mathematical ideas and experiences be structured to increase their performative potential?
- how might (a) performance arts methods and (b) digital communication affordances (like the multimodal nature of new media and the read/write capabilities of wikis) be used by students for organizing and expressing the mathematical ideas they seek to communicate to one another and to the wider world?

We intend to create a parallel between the classroom focus on performance and the methods and methodology of our research, by relying on performance ethnography methods (Denzin, 2003, 2006; Dicks, Mason, Coffey & Atkinson, 2005; Madison, 2006; McCall, 2000).

**Students as Performance Mathematicians? **

The construct of “students as performance mathematicians” rests on the following ideas: (1) mathematics is an aesthetic, human experience (Sinclair, 2001; Sinclair, Pimm & Higginson, 2006; Upitis, Phillips & Higginson, 1997); (2) narrative is a fundamental vehicle for understanding and communicating meaning (Bruner, 1986, 1990, 1996); (3) engaging students’ imaginations is a key element of learning (Egan, 1997a, 1997b; Greene, 1995); (4) the interpretative perspective of theatre studies offers a valuable lens for analysing the quality of the mathematics teaching and learning experience (Rodd, 2003); (5) performance can be used as a vehicle for disrupting and reconfiguring traditional power and authority structures in education (Boal, 1985; Pineau, 2005); (6) technology itself is an actor in the mathematics learning process (Borba & Villareal, 2005; Levy, 1997).

The labelling of students as “mathematicians” is not uncommon in the mathematics literature (for example: Fuis & Huinker, 2000; Fosnot & Dolk, 2001a, 2001b; Ginsburg, 2002; Papert, 1980; Sharp & Hoiberg, 2001; Upitis, Phillips & Higginson, 1997). However, until recently (Gadanidis & Borba, 2008; Gadanidis, Hughes & Borba, forthcoming), it has been quite uncommon to label students as “performance mathematicians”. Our work contrasts with the view of “mathematical performance” as associated with testing and standards and “digital mathematics” as associated with mathematical simulations or eLearning, rather than with students’ aesthetic experiences and artistic expressions of mathematics.

**Recent Publications**

- Gadanidis, G., Hughes, J. & Borba, M. (2008). Students as performance mathematicians.
*Mathematics Teaching in the Middle School 14*(3), 168-176*.* - Gadanidis, G., Gerofsky, S. & Hughes, J. (2008). A celebration of mathematics.
*Ontario Mathematics Gazette, 47*(1), 13-20*.* - Gadanidis, G. & Borba, M. (2008). Our lives as performance mathematicians.
*For the Learning of Mathematics 28*(1), 44-51*.* - Gadanidis, G. (2008). A Lust for Mathematics.
*Canadian Mathematical Society Notes*. - Gadanidis, G. & Hughes, J. (2008). Performing Mathematics: A Guide for Teachers and Students.
- Borba, M. (2007). Humans with media: A performance collective in the classroom? In Gadanidis, G. & Hoogland, C. (Eds.)
*Proceedings of Digital Mathematical Performance: A Fields Institute Symposium*, 15-21. - Gerofsky, S. (2007). Performance Space & Time. In Gadanidis, G. & Hoogland, C. (Eds.) (2007).
*Digital Mathematical Performance.*Proceedings of a Fields Institute Symposium, Faculty of Education, University of Western Ontario. - Gadanidis, G. & Hoogland, C. (Eds.) (2007).
*Digital Mathematical Performance.*Proceedings of a Fields Institute Symposium, Faculty of Education, University of Western Ontario.

**Recent Performances **

- Gadanidis, G. (August 2009). I Love Math concert by Joy of X.
*University of Ontario Institute of Technology.* - Gadanidis, G. (Feb 2009). Tell me a Good Math Story: Math through the Arts Lens. Keynote address at the
*Durham Gifted Conference.* - Gadanidis, G., Gerofsky, S. & Jardine, R. (2008). Math Performance Festival.
- Gadanidis, G. & Sinclair, N. (2008). Imagine This!
- Gadanidis, G. (May 2008). Students as Performance Mathematicians. Keynote address at the
*New Brunswick Teachers' Association Annual Conference.* - Gadanidis, G. (Feb 2008). Mathematical Performance. Keynote address at the
*OAME Leadership Conference.* - Gerofsky, S. et al. (2008). Building a Geometric Sculpture.
- Gerofsky, S. (2007). On Mathematical Performance.
- Borba, M. & Scucuglia, R. (2007). The Waiter.
- Gadanidis, G. (August 2007). Math Concert.
*University of Ontario Institute of Technology.*

**References**

- Boal, A. (1985).
*Theatre of the Oppressed.*New York: Theater Communications Group.

- Borba, M.C. & Villarreal, M.E. (2005).
*Humans-with-Media and the Reorganization of Mathematical Thinking*New York: Springer. - Bruner, J.S. (1986)
*Actual minds, possible worlds*.Cambridge, MA.: Harvard University Press. - Bruner, J.S. (1990)
*Acts of Meaning*.London: Harvard University Press. - Bruner, J.S. (1996).
*The Culture of Education*. Cambridge, MA: Harvard University Press. - Denzin, N.K. (2003).
*Performance ethnography: Critical pedagogy and the politics of culture.*Thousand Oaks, California: Sage Publications. - Denzin, N.K. (2006a). The politics and ethics of performance pedagogy: Toward a pedagogy of hope. In D.S. Madison & J. Hamera, (Eds.)
*The Sage Handbook of Performance Studies.*Thousand Oaks, California: Sage Publications, pp. 325-338. - Denzin, N. K. (2006b). Pedagogy, performance, and autoethnography.
*Text and Performance Quarterly*26(4), 333-338. - Dicks, B, Mason, B., Coffey, A & Atkinson, P.(2005).
*Qualitative research and hypermedia: Ethnography for the digital age.*London: Sage Publications. - Egan, K. (1997a). The arts as the basics of education.
*Childhood Education**73*(6): 341-345. - Egan. K. (1997b).
*The educated mind: How cognitive tools shape our understanding.*Chicago: University of Chicago Press.

- Fosnot, C.T. & Dolk, M. (2001a).
*Young Mathematicians at Work: Constructing Multiplication and Division.*Portsmouth, NH: Heinemann.

- Fosnot, C.T. & Dolk, M. (2001b).
*Young Mathematicians at Work:*Constructing Number Sense, Addition and Subtraction*.*Portsmouth, NH: Heinemann.

- Fuis, D. & Huinker, D. (2000). Children as mathematicians.
*Teaching Children Mathematics 6*(6), 341-342.

- Gadanidis, G. & Borba, M. (2008). Our lives as performance mathematicians.
*For the Learning of Mathematics 28*(1), 44-51*.* - Gadanidis, G., Hughes, J, & Borba, M. (forthcoming). Students as Performance Mathematicians.
*Mathematics Teaching in the Middle School.*

- Madison, D.S. (2006). Staging fieldwork/performing human rights. In D.S. Madison & J. Hamera, (Eds.)
*The Sage Handbook of Performance Studies.*Thousand Oaks, California: Sage Publications, pp. 397-418.

- McCall, M. (2000). Performance ethnography: A brief history and some advice. In N. Denzin & Y. Lincoln, (Eds.),
*Handbook of Qualitative Research (pp. 421-433).*Thousand Oaks, CA: Sage Publications.

- Papert, S. (1980). Mindstorms: Children, Computers, and Powerful Ideas. New York: Basic Books.

- Pineau, E.L. (2005). Teaching is performance: Reconceptualizing a problematic metaphor. In Alexander, B.K., G.L. Anderson & B.P. Gallegos (Eds.),
*Performance Theories in Education: Power, Pedagogy, and the Politics of Identity.*Mahwah, N.J.: Lawrence Erlbaum.

- Rodd, M. (2003). Witness as participation: The lecture theatre as site for mathematical awe and wonder.
*For the**Learning of Mathematics*23(1), 39-43.

- Sharp, J.M. & Hoiberg, K.B. (2001). And then there was Luke: The geometric thinking of a young mathematician.
*Teaching Children Mathematics 7*(7), 432-439.

- Sinclair, N. (2001). The aesthetic is relevant.
*For the Learning of Mathematics*,*21*(1). 25-32.

- Sinclair, N., Pimm, D. & Higginson, W. (Eds). (2006)
*Mathematics and the aesthetic: Modern approaches to an ancient affinity*. NY: Springer-Verlag.

- Upitis, R., Phillips, E. & Higginson, W. (1997).
*Creative Mathematics: Exploring Children's Understanding.*London: Routledge.