April 25, 2014

THE FIELDS INSTITUTE FOR RESEARCH IN MATHEMATICAL SCIENCES

Fields Cognitive Science Network:
Empirical Study of Mathematics
and How it is Learned

Co-directors
Marcel Danesi (Anthropology, UToronto)
Dragana Martinovic (Mathematics Education, UWindsor)
Rafael Núñez (Cognitive Science, UC San Diego)
  Aims of the Network Executive Board Coordinators at the University of Toronto Members
To receive updates on activities in Cognitive Science Network subscribe to our mailing list at www.fields.utoronto.ca/maillist

Overview

  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.

The primary aims of the Network are as follows:

  (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.

Executive Board

 

Alexander, James (Mathematics, Case Western Reserve)
Lakoff, George (Linguistics Department, University of California, Berkeley)
Mighton, John (Mathematics, University of Toronto)
Turner, Mark (Cognitive Science, Case Western Reserve University)

Coordinators at the University of Toronto

 
Project Director Co-ordinator
Bockarova, Mariana Costa, Stacy
Assistants  
Bojeczko, Lydia
Bryers, Lorraine
Clivio, Caterina
Colaguori, Robert
Compagnone, Vanessa
Kim, Susanna
Khurshid, Akbar
Maida-Nicol, Sara
Mann, Alison
McElcheran, Pat
Nagra, Kuljeet
Subhan, Aamir
Willsey, Elizabeth
Yorgiadis, Nikki
Xavier, Alexa
 

Members

  Aage-Brandt, Per (Cognitive Science, Case Western Reserve, USA)
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)
Candia, Victor (Experimental Psychology, Neuroscience; Collegium Helveticum, Switzerland)
Cobley, Paul (London Met University)
D’Ambrosio, Ubiratan (São Paolo, Brazil)
Davies, E. Brian (Mathematics, Kings College, London)
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)
Koedinger, Kenneth R. (Carnegie Mellon University)
Kotsopoulos, Donna (Mathematics Education, Wilfrid Laurier University, Canada)
Kull, Kalevi (Biosemiotics, University of Tartu, Estonia)
LeFevre, Jo-Anne (Carlton University)
Lerman, Stephen (Centre for Research in Education at London South Bank University)
Logan, Robert K. (Physics, University of Toronto, Canada)
Loric, Miroslav (McMaster University)
Machenry, Trueman (Mathematics and Statistics, York University)
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 (Mathematics Education, University of Windsor, Canada)
Walsh Matthews, Stéphanie (Ryerson)
Matsuzawa, Tetsuro (Cognitive Primatology, University of Kyoto, Japan)
Neuman, Yair (Department of Education, University of the Negev, Israel)
Nuessel, Frank (Linguistics, University of Louisville, USA)
Radford, Luis (Laurentian University)
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)
Thomas, Kevin (York University)
Vedovelli, Massimo (Linguistics, Università per Stranieri di Siena, Italy)
Whiteley, Walter (Mathematics, York University, Canada)
Zhang, Jun (University of Michigan)

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