FIELDS INSTITUTE Cognitive Science Network

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
			Passed Members
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Network Activities

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
Bigliardi, Victoria Bryers, Lorraine Chandrasegaram, Ruby Clivio, Caterina Colaguori, Robert Compagnone, Vanessa Khurshid, Akbar	Maida-Nicol, Sara McElcheran, Pat Nagra, Kuljeet Palangi, Roozbeh Subhan, Aamir Yorgiadis, Nikki

Members

Aage-Brandt, Per (Cognitive Science, Case Western Reserve, USA)
Anderson, Myrdene (Anthropology, Purdue, USA)
Ansari, Daniel (Cognitive Neuroscience, University of Western Ontario, Canada)
Barbeau, Edward (Mathematics, University of Toronto)
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 (Media & Performing Arts, Middlesex University, London, UK)
D’Ambrosio, Ubiratan (Mathematics Education, Universidade Bandeirantes de São Paolo/URBAN, Brazil)
Davies, E. Brian (Mathematics, Kings 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)
Dehaene, Stanislas (Unité Inserm-CEA de NeuroImagerie Cognitive, France)
Delmonte, Rodolfo (Linguistics, Ca' Foscari University, Italy)
Devlin, Keith (Mathematics, Stanford University, USA)
Edwards, Laurie (Mathematics Education, St. Mary's College of California, USA)
Eichholtz, Ruth (Mathematics, The York School, Canada)
Fauconnier, Gilles (Cognitive Science, University of California, San Diego, USA)
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)
Herbst, Behnaz (Mathematics, TDSB, Canada)
Hersh, Reuben (Mathematics, The University of New Mexico, USA)
Hofstadter, Douglas (Cognitive Science, Indiana University, USA)
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 (Philosophy of Language, St. Petersburg State School of Economics, Russia)
Koedinger, Kenneth R. (Human Computer Interaction and Psychology Carnegie Mellon University, USA)
Kotsopoulos, Donna (Mathematics Education, Wilfrid Laurier University, Canada)
Kull, Kalevi (Biosemiotics, University of Tartu, Estonia)
LeFevre, Jo-Anne (Institute of Cognitive Science, Carlton University, Canada)
Lerman, Stephen (Centre for Research in Education at London South Bank University, UK)
Logan, Robert K. (Physics, University of Toronto, Canada)
Lovric, Miroslav (Mathematics, McMaster University, Canada)
Machenry, Trueman (Mathematics and Statistics, York University, Canada)
Mancosu, Paolo (Philosophy of Mathematics, University of California, Berkeley, USA)
Marghetis, Tyler (Cognitive Science, University of California San Diego, USA)
Martinovic, Dragana (Mathematics Education, University of Windsor, Canada)
Walsh Matthews, Stéphanie (Languages, Literatures, and Cultures, Ryerson University, Canada)
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)
Pierce, Sandra (Simcoe County District School Board, Canada)
Radford, Luis (Sciences de l'education, Laurentian University, Canada)
Robson, Eleanor (History of Mathematics (Mesopotamia), University of Cambridge, UK)
Roth, Wolf-Michael (Faculty of Education, University of Victoria, Canada)
Sfard, Anna (Education, University of Haifa, Israel)
Shorser, Lindsey (Mathematics, University of Toronto, Canada)
Tall, David (Centre for Education Studies, University of Warwick, UK)
Tanaka-Ishii, Kumiko (Department of Creative Informatics, University of Tokyo, Japan)
Thomas, Kevin (Education, York University, Canada)
Vedovelli, Massimo (Linguistics, Università per Stranieri di Siena, Italy)
Vinner, Shlomo (Science, Hebrew University, Israel)
Whiteley, Walter (Mathematics, York University, Canada)
Zhang, Yun (Mathematical Psychology, University of Michigan, USA)

Passed Members

Marcus, Solomon ( 1925-2016) (Mathematics, University of Bucharest, Romania)

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