# Maths and Open-space Learning Case Study

**Project Leader, Dr Dave Wood, Principal Teaching Fellow, Warwick Mathematics Institute**

**Context**

Because Maths was a new venture, beginning in the academic year 2010/11, it provided an ideal opportunity for us to consider a more general strategy for introducing OSL to departments that have not encountered it before.

One might have the impression that a partnership between OSL and Maths is a perfect fit, since OSL is a pedagogy which reflects on spatial relations and the permutations of physical movement, and Maths is a discipline which encourages collaborative work in communal spaces. There were nonetheless potential barriers to this collaboration, including the conventions of teaching Maths via large lectures and small tutorial groups; and a persistent doubt about whether an experiential pedagogy could intervene effectively in a subject which deals in high levels of abstraction.

Our initial strategy for overcoming these barriers was twofold: we decided to hold an interdisciplinary OSL and Maths event using the Student Ensemble, and to approach a Teaching Fellow within the Maths department to act as a liaison with the OSL project. This approach was based on our experience with long standing projects in Chemistry, Philosophy and the Warwick Business School. Without a committed partner within the academic department concerned –someone who is willing to co-conceive the workshops with OSL practitioners– it is difficult to sustain a meaningful teaching practice. We felt equally that an event designed to attract mathematicians to the OSL venues, introduce the interdisciplinary ethos and trail some OSL workshop activities was vital to build confidence for such a novel partnership.

## Method

An ideal opportunity to pursue this strategy arrived in the person of Dr Stephen Abbott, Middlebury College and a visiting Research Fellow at the University of Cambridge. Although by profession a mathematician, Stephen was researching the thematic and formal representations of Maths in the theatre. After contacting him it became obvious that his work looking at theatre pieces about mathematicians or mathematical discoveries could provide a basis for OSL activity. Using the trained actors from the Ensemble to dramatise excerpts from those plays Stephen was researching we presented a kind of interdisciplinary and pedagogical conundrum: Can these theatrical works be used to teach Maths; and can these open rehearsal spaces be further used to formally explore mathematical problems?

**Maths and Drama Interdisciplinary Event**

*How Does a Theorem Act? a* talk by Stephen Abbot and the Student Ensemble.

Plays performed and discussed: *Arcadia* by Tom Stoppard; *Proof *by David Auburn; *Lovesong of the Electric Bear* by Snoo Wilson; *A Disappearing Number *co-written and devised by Théâtre de Complicité company and directed and conceived by Simon McBurney.

*Interactive Workshop*

This workshop comprised three major parts:

1) Permutations by Owen Daniel (undergraduate, Mathematics)

Owen began discussing the relation between magic and Mathematics before delivering a card trick. It was the trick of 'unshuffling' a pack. Then the students became the cards -wearing red and yellow t-shirts for ease of identification - and he attempted a human (un)shuffle. By keeping track of certain cards/people using the whiteboards we were able to trace the permutations and understand why it was that the position of the cards was predictable after a certain number of movements. This led to further consideration of pattern and permutation.

2) Game Theory by Dave Wood

David divided the group into hawks and doves: the students mingled birdlike until, on his say so, they stopped and partnered with the person closest to them. They scored points according to their bird-identities (hawks beat doves; doves and doves come out even; hawks and hawks fight, only one coming out on top). After a few rounds the students recorded their scores and swapped identities -hawks became doves and vice versa. Then finally David distributed new identities to each of the students irrespective of their previous incarnation. The accumulated scores from the three rounds show the mathematics behind the fluctuations in animal population as well as indicating mathematical ways to think about strategy.

3) Plenary session by Jonathan Heron and Barry Sheils

## Findings

Three major overlapping interests emerged:

- Using the space to give undergraduates an opportunity to explore and experience mathematical ideas in an embodied way: here we could consider the efficacy of providing a workshop on a mathematical topics such as ‘Game theory’ or ‘permutations’
- Using the space to consider teaching Maths at secondary or primary level (for those in Education): here, again, workshop ideas could be explored in the open-spaces using non-mathematicians or UG mathematicians as ‘students’
- Exploring more experimental interdisciplinary links between physical theatre, dance and Maths

The variety and value of the ideas expressed in the plenary session were hugely promising. They proved there was a pre-existing commitment among those who attended to embodied work in Maths, but that such work had not yet found its home in the University.

The result of this discussion was a successful proposal to IATL under the ‘Pedagogic intervention’ rubric to hold a series of OSL workshops for 2^{nd} year mathematicians on the theme of abstraction. The beginning of the second year is a key time for many students who struggle with the introduction of new mathematical concepts – especially abstraction. An effectively planned OSL session, or series of sessions, could be successful in orienting those who have fallen behind in lectures and tutorials.

IATL Pedagogic Intervention application