Mathematics as Story
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
The keynote addresses are open to the academic community.
Symposium deliberations are limited to registered/invited participants.
A Monograph will be compiled that will include contributed papers (or
summaries of the papers) and proceedings of the Symposium.
We are extremely fortunate to have Ellen Dissanayake, Rena Upitis and
Brian Boyd as keynote speakers. They will also join us for the Symposium
Friday June 13
- 5:00-7:00 - Registration
- 7:00-7:30 - Introductions
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
- 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
- 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
- Invited lecture #3 - Brian Boyd, University Distinguished
Professor in the Department of English, University of Auckland, New
- 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
- 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
Friday May 16
- Date for submitting papers/responses to Discussion Paper (in rtf
- 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
Friday May 23
- Submitted papers/responses will be compiled and circulated electronically
to all participants
- Mathematics as Story symposium
- Working group leaders submit proceedings
- Participants may submit papers or reflections
- A draft copy of the Monograph will be circulated electronically to
all participants for comment
- The Monograph will be published and a copy will be mailed to each
- 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
- 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
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