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THE FIELDS
INSTITUTE
FOR RESEARCH IN MATHEMATICAL SCIENCES
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Fields Cognitive Science
Network:
for the Empirical and Interdisciplinary Study of the
Nature of Mathematics
Co-directors
Marcel Danesi (Anthropology, University of Toronto)
Rafael Núñez (Cognitive Science, UC San
Diego)
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Overview
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In contemporary academia the question of the nature
of mathematics, and how it is learned, has been addressed primarily
within the confines of the philosophy of mathematics (for example,
as a formal logical process) and mathematics proper (for instance,
metamathematics), with little, or no input from other scientific
disciplines. In the context of current intellectual developments,
this is arguably an unnecessarily narrow approach to the investigation
of this significant phenomenon of human cognition and culture.
During the last four decades, substantial theoretical and scientific
advancements have been made in the study of human thought and
its relationship with language, culture, history, as well as
with its biological underpinnings. These advancements have been
made through a variety of methods in a broad set of disciplines,
from the cognitive sciences (neuroscience, psychology, linguistics,
anthropology, etc.) to semiotics, history and archaeology.
Building on some of the developments in these fields, scholarly
proposals have been made in the last decade or so to address
the question of the nature of mathematics as an empirical question
subject to methodological investigations of an interdisciplinary
nature, involving hypothesis testing and appropriate theoretical
interpretations (see Where Mathematics Comes From, Lakoff &
Núñez, 2000; The Way We Think, Fauconnier &
Turner, 2002). In these proposals, there is the claim that mathematics
is a unique type of human conceptual system, which is sustained
by specific neural activity and bodily functions; it is brought
forth via the recruitment of everyday cognitive mechanisms that
make human imagination, abstraction, and notation-making processes
possible. Data and new results in this domain have been collected
gradually and published in a variety of peer-reviewed academic
documents. Among others, these new results have profound implications
for the teaching and learning of mathematics.
While there is some awareness of the importance of giving education
a rigorous foundation in cognitive science, little has been
done to develop programs based on this science or to raise the
standards of evidence in evaluating the effects of educational
interventions. The time has come for gathering empirical data
and testing these new ideas, with the purpose of informing,
on scientific grounds, how to teach mathematics efficiently
and meaningfully in a cognitive-friendly fashion. The implementation
and changes should affect not only young students, but also
teachers, educators, and administrators, who generally are poorly
trained in subjects involving the working of the human mind
and brain.
In the past few years a growing community of scholars has been
gathering to discuss findings in this new interdisciplinary
area of investigation, holding a workshop at Case Western Reserve
University in 2009 organized by Professor James Alexander (Mathematics)
and Professor Mark Turner (Cognitive Science), and most recently,
meeting at a workshop organized by Professor Marcel Danesi (University
of Toronto) and sponsored by the Fields Institute for Research
in Mathematical Sciences in Toronto. The time is now ripe for
fostering the exchanges of many of these scholars, along with
their students, collaborators, and projects, in an institutionalized
manner. Since the Fields Institute is in a unique position to
grant the credibility that this institutionalized effort requires,
we have formed this Network to pursue the relevant objectives.
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The primary
aims of the Network are as follows:
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(1) to address the very question of the cognitive
nature of mathematics itself (i.e., not just the history and
practice of this discipline, but rather, as a genuine conceptual
system with a specific inferential organization);
(2) to analyze and help facilitate the testing of ideas about
how children and adults learn mathematics;
(3) to advocate for higher standards of evidence in education
so that school systems won't adopt mathematics programs unless
they are based on rigorously tested sound scientific principles;
(4) to carry (1) through (3) out primarily via the use of empirical
methods;
(5) to utilize methods and theoretical frameworks derived form
a variety of disciplines in the academic world, from cognitive
science to linguistics and anthropology; this would make the
mode of inquiry of the network truly unique among disciplines
investigating mathematics;
(6) to gather and disseminate ideas that have broad implications
for society by hosting conferences and workshops;
(7) to put out relevant position papers and publications, making
these known to both the academic community and the larger circle
of interested parties. |
Coordinators
at the University of Toronto
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Bockarova, Mariana
Compagnone, Vanessa
Costa, Stacy
Kim, Susanna
Maida-Nicol, Sara
Subhan, Aamir |
Members
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Aage-Brandt, Per (Cognitive Science, Case Western
Reserve, USA)
Alexander, James (Mathematics, Case Western Reserve)
Anderson, Myrdene (Anthropology, Purdue, USA)
Ansari, Daniel (Cognitive Neuroscience, University of Western
Ontario, Canada)
Bockarova, Mariana (Psychology, Harvard University, USA)
Butterworth, Brian (Institute of Cognitive Neuroscience &
Dept. Psychology, University College London, UK)
Davis, Chandler (Mathematics, University of Toronto, Canada)
De Beule, Joachim (Artificial Intelligence, University of Brussels,
Belgium)
Deely, John (Philosophy, University of St. Thomas, Houston,
USA)
Delmonte, Rodolfo (Linguistics, Ca' Foscari University, Italy)
Devlin, Keith (Mathematics, Stanford University, USA)
Edwards, Laurie (Mathematics Education, St. Mary's College of
California, USA)
Fauconnier, Gilles (Cognitive Science, University of California,
San Diego)
Ferreirós, José (Philosophy of Mathematics, University
of Seville, Spain)
Fias, Wim (Experimental Psychology, Ghent University, Belgium)
Fischer, Martin (Cognitive Science, University of Potsdam, Germany)
Goldin-Meadow, Susan (Psychology, University of Chicago, USA)
Gowers, William Timothy (Mathematics, University of Cambridge,
UK)
Hersh, Reuben (Mathematics, The University of New Mexico, USA)
Hofstadter, Douglas (Cognitive Science, Indiana University)
Isabelli, Christina L. (Hispanic Studies, Illinois Wesleyan,
USA)
Kari, Lila (Computer Science - University of Western Ontario,
Canada)
Kauffmann, Louis (Mathematics, Univ. of Illinois at Chicago,
USA)
Kiryushchenko, Vitaly (St. Petersburg State School of Economics,
Russia)
Kotsopoulos, Donna (Mathematics Education, Wilfrid Laurier University,
Canada)
Kull, Kalevi (Biosemiotics, University of Tartu, Estonia)
Lakoff, George (Linguistics Department, University of California,
Berkeley)
Logan, Robert K. (Physics, University of Toronto, Canada)
Mancosu, Paolo (Philosophy of Mathematics, University of California,
Berkeley, USA)
Marcus, Solomon (Mathematics, University of Bucharest, Romania)
Marghetis, Tyler (Cognitive Science, University of California
San Diego, USA)
Martinovic, Dragana (Education, University of Windsor, Canada)
Matsuzawa, Tetsuro (Cognitive Primatology, University of Kyoto,
Japan)
Mighton, John (Mathematics, University of Toronto)
Neuman, Yair (Department of Education, University of the Negev,
Israel)
Nuessel, Frank (Linguistics, University of Louisville, USA)
Robson, Eleanor (History of Mathematics (Mesopotamia), University
of Cambridge, UK)
Roth, Wolf-Michael (Faculty of Education, University of Victoria,
Canada)
Shorser, Lindsey (Mathematics, University of Toronto, Canada)
Tanaka-Ishii, Kumiko (Department of Creative Informatics, University
of Tokyo, Japan)
Thurston, William P. (Mathematics, Cornell University, USA)
Turner, Mark (Cognitive Science, Case Western Reserve University)
Vedovelli, Massimo (Linguistics, Università per Stranieri
di Siena, Italy)
Whiteley, Walter (Mathematics, York University, Canada) |
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