Bodily experience and mathematical conceptions: from classical views to a phenomenological reconceptualization

Abstract

Mathematical concepts and conceptions have been theorized as abstractions from-and therefore transcending-bodily and embodied experience. In this contribution, we re-theorize mathematical conceptions by building on recent philosophical work in dialectical phenomenology. Accordingly, a conception exists only in, through, and as of the experiences that the individual realizes it. To exemplify our reconceptualization of mathematical conceptions, we draw on an episode from a study in a second-grade classroom where the students learned about three-dimensional geometrical objects.

How Multimodality Works in Mathematical Activity: Young Children Graphing Motion

“…Streeck & Mehus, 2005). Microethnography is increasingly recognised as a suitable research methodology thanks to the notable interest in the study of gestures in mathematics learning Nemirovsky & Ferrara, 2009;Radford, 2009;Roth, 2009). …”

“…Radford (2009) discussed why gestures matter from a cultural perspective, by sketching the sensuous cognition view that "thinking does not occur solely in the head but also in and through a sophisticated semiotic coordination of speech, body, gestures, symbols and tools" (p. 111, emphasis in the original). Roth (2009) proposes the phenomenological stance that mathematical concepts are not abstractions transcending bodily activity, but emerge "in and through experience, never consisting in anything else but activated prior experiences (embodied bodily traces thereof)" (p. 188).…”

The relationality in/of teacher–student communication

“…Research in the embodied nature of mathematical cognition (e.g., Davis et al 1996;Lakoff and Nunez 2000;Roth 2011) also informed our reflections on being-in-the-know-with and its relationship with languaging (Maheux and Roth 2011;Roth and Thom 2009). Embodied cognition first helps us to recognize how mathematical activity emerges from early bodily experiences shaped by social interaction in such a manner that they become an integral part of our living bodies rather than product of a conscious intellect.…”

“…Classroom conversations have since become of increasing interest to mathematics educators (e.g., Brown 2001;Pimm 1987;Zevenbergen 2000) with a growing interest in the fine-grain semiotic analysis of teachers' and students' utterances as well as gestures, body orientations and movements, intonation, rhythm, or sound, all of which constitute integral parts of mathematical thinking (e.g., Bautista and Roth 2012a, b;Radford et al 2008, Bussi andMariotti 2008). The importance of the collective aspect of communication also runs through the work of scholars who study language in classroom mathematics talk (e.g., Barwell 2012;Roth and Thom 2009;Sfard 2008;van Oers 2001).…”

Hands that See, Hands that Speak: Investigating Relationships Between Sensory Activity, Forms of Communicating and Mathematical Cognition

“…In this viewpoint, understanding anything-something immediately perceivable by our sensory apparatus or something that only manifests itself only through semiotic sign systems-involves activating and reliving, that is, simulating, any part of the previous experiences that have come to be allied with it. In this sense, when we come across any object, or a representation of an object, the plurality of perceptions associated with it are reactivated, leading Roth and Thom (2009) to suggest that we experience a single instance associated with any concept as its whole.…”