Being mathematical : an exploration of epistemological implications of embodied cognition

Abstract

In this thesis I explore epistemological implications of embodied cognition in the hope of developing my apprehension of what it means to think mathematically. I allow my understanding of embodied cognition to emerge in stages, early in the piece laying contrasts against which it may be set, infolding elements to the purpose of qualitatively interpreting data as my thesis finds form. I use the language of autopoiesis to frame an understanding of change in the context of an individual’s learning and also within broader constructs, such as in mathematics classrooms. I recognise dualisms and set them aside in an attempt to reread what it means to think mathematically.Research from a variety of fields constitutes one part of my data, the second part being a selection of experiences drawn from mathematics classes I have taught. In balancing the two, I find that an embodied account contributes a means of interpreting mathematical experience wherein received boundaries, such as between you and me, and categories, such as "number", are not globally robust, and intentionality pervades and shapes the worlds we create.The perspective that embodiment affords my apprehension of mathematical thinking is consistent with a formulation in which judgements of what is good are aligned in part with a kind of aesthetic, whereby being moral is founded in innate dispositions. The question of what one is to do with an embodied epistemology is therefore focused on a consideration of how I am to orient myself to teaching mathematics.Throughout all of this, the locus of my attention remains within the classroom, fixed upon the goal of eliciting perspective and on developing skill in interpreting experience; on becoming a tactful teacher, sensitive to the tacit language of the body.