Enacting Enactivism: Exploring the potential for a theory of mathematical cognition to enhance classroom practice (11w2177)

Arriving in Banff, Alberta Friday, November 4 and departing Sunday November 6, 2011


Lyndon Martin (York University)

Lynn McGarvey (University of Alberta)

(University of Calgary)


The "Enacting Enactivism: Exploring the potential for a theory of mathematical cognition to enhance classroom practice" workshop will be hosted at The Banff International Research Station.

Constructivism (however defined) has undoubtedly become a major theoretical influence in contemporary mathematics education. Although constructivism began as a theory of learning, it has progressively expanded its influence, in particular becoming what might be seen as a theory of teaching. However, in recent years a new (and renewed) theoretical way of thinking about knowing has emerged. Broadly termed 'enactivism', this framing prompts a reorientation to the collective body, both in terms of what is known and of who is doing the knowing. Within enactivism then, the teacher is not seen as a facilitator or a guide but as being 'structurally coupled' with the learners, and hence an authentic, full, and genuine participant in students' learning. rnrnQuestions remain about what enactivism means concretely in practice, for mathematical teaching and learning. We need to know more about what such 'authentic participation' might mean for the classroom teacher of mathematics and what the implications for such a view of learning might be for his or her classroom practices. How does such a view affect the teaching dynamic? What liberties and constraints does this afford in the classroom? What kinds of organizational structures, tasks, and student groups do such an understanding prompt and what are their effects? In what ways does the fact that the teacher needs to be pro-active and participative in the learning environment enable him or her new actions that the constructivist facilitator would restrain from doing? In what ways is the fact that the teacher is complicit in, and part of, students' learning afford or constrain actions, as well as provoke ethical issues? In what ways does the requirement for the teacher to be active in the learning process affect his or her decisions and actions? What does being an authentic and genuinely participative teacher mean? There is a vital future for enactivism in research in mathematics education concerning the asking and answering of these questions about teaching. The proposed workshop will be the first systematic step towards such a research agenda.rn

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the US National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnologí255a (CONACYT).