Fields Cognitive Science Network

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.