Mathematics as Story

• A symposium on Mathematics through the lenses of Art and Technology
• Friday June 13 to Sunday June15, 2003, Faculty of Education, University of Western Ontario
• Sponsored by:
  • The Fields Institute for Research in Mathematical Sciences
  • The Faculty of Education, University of Western Ontario

Description

The Symposium brings together mathematics educators, mathematicians, artists, literary scholars, anthropologists and computer scientists to explore the metaphor 'mathematics as story'. Story - at the heart of the arts - is composed of aesthetic elements. Roger Schank, working in the field of AI, confirms the age-old suggestion that human cognition is story-based. That is, we think in terms of stories, we understand the world in terms of stories, we learn by living and accommodating new stories, and we define ourselves through the stories we tell ourselves.

Our primary interest is not on story as a narrative to be told to others (although this could play a role) but rather on story as experienced by doing, learning and teaching mathematics.

We further Dissanayake's notions of the basis of art by applying them to the art or "story" of mathematics. Dissanayake explains such focus in terms of "elaboration", in that something that has been made special is more likely to attract and engage our attention and the attention of others. We are also concerned with Boyd's notion of both the individual and communal forms of attention that focusing on cognitive problems facilitates.

Our goal is to address the nature of mathematical experiences and what makes for a good mathematics story by bringing together mathematics experts and experts on art and story processes. We hope to identify the aesthetic and see where and how it fits within, and enhances, mathematical stories.

We are also interested in how recent online technologies affect the mathematics story. For example, do online interactive applets that allow for the exploration of mathematics relationships add a new dimension to the mathematics experienced? What design principles - what story principles - potentially offer a better mathematics story?

Participation

The keynote addresses are open to the academic community.

Symposium deliberations are limited to registered/invited participants.

Product

A Monograph will be compiled that will include contributed papers (or summaries of the papers) and proceedings of the Symposium.

Symposium Agenda

We are extremely fortunate to have Ellen Dissanayake, Rena Upitis and Brian Boyd as keynote speakers. They will also join us for the Symposium deliberations.

Friday June 13

• 5:00-7:00 - Registration
• 7:00-7:30 - Introductions
• 7:30-8:30 pm - Invited lecture #1, Ellen Dissanayake, Visiting Scholar, Walter Chapin Simpson Center for the Humanities, University of Washington
• 8:30-9:00 pm - Questions/discussion
• Title: AESTHETICS AND UNCERTAINTY IN HUMAN EVOLUTION
• Abstract: Living with uncertainty has been part of the burden humans bear for possessing such large, versatile brains. Other animals exist, as far as we can tell, in a more or less continuing present, with little if any active memory of the past or anticipation of the future. But humans recall and predict, worry and suppose. Quick wits and lavish imaginations make us aware of life's uncertainties and possibilities, and we actively seek to forestall misfortune and to assure good outcomes to our ventures. Coping with uncertainty has made us into storytellers as well as problemsolvers, fantasizers as well as pragmatists. Indeed, there is evidence to suggest that the arts -- ways of shaping and elaborating experience -- may have arisen, as much as practical intelligence, as means of dealing with uncertainty. My talk will explore this possibility, as well as some of the ways in which the arts are inextricably entangled with the most fundamental endowments of human psychobiology.
• Bio: Scholar-writer-speaker Ellen Dissanayake is known nationally and internationally for her provocative claim that humans, both as individuals and societies, actually need -- biologically require -- the arts. Using insights drawn from fifteen years of living and working in non-Western countries (Sri Lanka, India, Nigeria, and Papua New Guinea, where she taught at the National Arts School), she has developed a unique perspective that considers artmaking to be a normal, natural, and necessary component of our evolved nature as humans. Her books -- What is Art For? (1988), Homo Aestheticus: Where Art Comes From and Why (1992), and Art and Intimacy: How the Arts Began (2000) -- provide firm cross-cultural, historical, prehistorical, and developmental evidence that humans are biologically prepared to make and respond to the arts.
• 9:00 pm - reception

Saturday June 14

• 9:00-10:00 - Invited lecture #2 - Rena Upitis, Professor of Arts Education at Queen's University, Kingston, Ontario
• 10:00-10:30 pm - Questions/discussion
  • Title: LEARNING IN AND THROUGH THE ARTS
  • Abstract: The reported benefits of an education rich in the arts include greater motivation to learn, lower school drop-out rates, and higher achievement in other subjects. However, it is exceedingly difficult to establish cause and effect relationships between arts experiences and other outcomes, because it is hard to isolate the effects of the arts from other variables that affect learning. Further, such approaches also run the danger of failing to acknowledge the unique qualities of arts experiences. The research that will be described during this keynote extends the existing literature by comparing a school-wide arts education approach to two other types of schools: schools with a technology initiative, and 'regular' schools without a specific school-wide curriculum focus. Students' views and activities both in and out of school were considered, as were socioeconomic factors. At the end of three years, students in the arts schools scored significantly higher on tests of computation than students in the other two types of schools. There were no differences in other mathematics measures (e.g., geometry) nor in language and writing scores. It was also found that music lessons and reading for pleasure outside of school were significant contributing factors for achievement after the effects of SES and the arts program were taken into account. Other activities-such as playing videogames on a daily basis-were negatively associated with achievement measures. The data supported the conclusion that involvement in the arts contributed to engagement in learning-emotionally, physically, cognitively, and socially. .
  • Bio: Rena Upitis has taught courses on music and mathematics curriculum methods, integrated arts and technology, and research methodologies. She is co-author of Creative Mathematics: Exploring Children's Understanding (1997, Routledge). A recent research project was with the Electronic Games for Education in Mathematics and Science (E-GEMS) group where she contributed to the development and field-testing of computer games. Rena is now involved in the SSHRC funded project called Teacher Transformation Through the Arts as well as serving as a Principal Co-investigator (with Katharine Smithrim) on a national research project on Learning Through the Arts.
• 10:30-12:00 - "mathematics as story" working groups
• 1:30-3:30 - brief presentations and working group discussions
• 3:30-4:30 - Invited lecture #3 - Brian Boyd, University Distinguished Professor in the Department of English, University of Auckland, New Zealand
• 4:30-5:00 - Questions/discussion
  • Title: ART, STORY, MAUS, MATH
  • Abstract: An evolutionary explanation for art needs to discern the function of the behaviors we call art. I propose one that may seem obvious but has not been proposed in the evolutionary literature: art is an adaptation for creativity that has evolved from the importance for an ultrasocial species of catching, or catching up with, the attention of others. Our attention can naturally be efficiently caught by appeals to human cognitive preferences. Other kinds of creativity, such as that of mathematics, science or technology, are difficult to advance against a resistant, non-human world, but in art the route to success follows rather than cuts across human preferences. By developing our habits of manipulating actuality by turning it around freely in the much larger space of possibility, art seeds all forms of human creativity. Because story appeals to one of the strongest human cognitive preferences, for strategic social information, it can easily command wide attention for hours at a stretch. In this, it is quite unlike mathematics. Yet in terms of creative problem-solving, in terms of imagining precise ways of exploring the possible beyond the actual, and in terms of the understanding of space and number that are a prerequisite even to social cognition, mathematics and story have much in common. Art Spiegelman's comic about his parents' surviving Auschwitz, the greatest of all comics, shows his creative problem-solving at many levels, often making the most of our intuitive reading of space, shape, position, distance, proportion, and our capacity to see the same entity in multiple ways at once, to reduce its individuality and yet simultaneously reaffirm it. Perhaps this kind of creativity may have something to suggest to those focused on the creativity of mathematics.
  • Bio: Brian Boyd is best known for his work on Vladimir Nabokov, including the award-winning biography Vladimir Nabokov: The Russian Years and Vladimir Nabokov: The American Years (Princeton, 1990, 1991). Recently he has begun to focus on the relationship between art and science and between creativity and discovery, partly because of Nabokov's work as a lepidopterist (he has edited Nabokov's Butterflies, Beacon, 2000) and partly because of his long-standing interest in philosopher of science Karl Popper (a close friend and an inspiration to art historian Ernst Gombrich), whose biography he is writing. He is currently working on an attempt to explain fiction from an evolutionary and cognitive point of view.
• 6:00 pm - Symposium Dinner

Sunday June 15

• 9:00-12:00 - "mathematics as story" working groups
• 1:30-5:00 - creating a research agenda

Other Dates

Friday May 16

• Date for submitting papers/responses to Discussion Paper (in rtf format)
• Approximately 2 pages - may be longer if a participant wishes to add more detail
• The purpose is to identify interests and directions for Symposium discussions; and to create a starting point for the Mathematics as Story monograph

Friday May 23

• Submitted papers/responses will be compiled and circulated electronically to all participants

June 13-15

• Mathematics as Story symposium

September

• Working group leaders submit proceedings
• Participants may submit papers or reflections

November

• A draft copy of the Monograph will be circulated electronically to all participants for comment

February

• The Monograph will be published and a copy will be mailed to each participant

Travel Information

• The Symposium will be hosted at the University of Western Ontario Althouse Faculty of Education.
• For more travel directions, please see http://communications.uwo.ca/western/about_directions.html
• Faculty of Education main switchboard 519 661-2111 ext 88651
• Taxi from Airport A taxi from the airport to Essex Hall is about $25.
• If you are driving, parking is available at the Faculty of Education (see blue path on map below) at a cost of $4 per entry.
• Checker Cabs 659-0400
• Robert Q. Airbus travels from the Pearson Airport in Toronto to London, On. If you wish to go to the University, get off at the Wharncliffe main station and take a cab straight north on Wharncliffe which becomes Western Road. Get off at either Essex Hall (on your right at the corner of Western and Sarnia Roads) or at the Faculty of Education on your left just before that same intersection. Approximately $77.00 round trip per adult fare. http://www.robertq.com/Airbus/ Robert Q. Airbus phone 673-6804
• VIA Rail’s station in is downtown London. If you wish to go to the University, take a cab on York west to Wharncliffe , which, heading north, becomes Western Road. Get off at either Essex Hall (on your right at the corner of Western and Sarnia Roads) or at the Faculty of Education on your left just before that same intersection. Costs vary. http://www.viarail.ca/en_index.html VIA Rail phone 672-5722

Contact

For more information please contact:

• George Gadanidis (ggadanid@uwo.ca), Faculty of Education, University of Western Ontario
• Cornelia Hoogland (chooglan@uwo.ca), Faculty of Education, University of Western Ontario
• Kamran Sedig (sedig@uwo.ca), Department. of Computer Science (Faculty of Science) and Faculty of Information and Media Studies, University of Western Ontario