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Body of Knowledge: Practicing Mathematics in Instrumented Fields of Promoted Action

  • Author(s): Trninic, Dragan
  • Advisor(s): Abrahamson, Dor
  • et al.
Abstract

A central issue in education in general, and mathematics education in particular, is the relationship between skills and concepts, between performing procedures and understanding content. This dissertation draws on recent research on the embodiment of cognition to cast doubt on the accepted separation of bodily practice and mental understanding. What are the implications of embodiment perspectives for designing mathematics learning environments? Can conceptual understanding sprout from procedural fluency? To answer these questions, I partook in two interrelated strands of research: (1) investigating pedagogical traditions of explicitly embodied disciplines; and (2) implementing and analyzing embodied-interaction mathematics designs. The first strand involves immersive ethnographic investigations of pedagogical practices in surfing and martial arts, corroborated via interviews and archival research. It focuses on enactive artifacts, or disciplinary routines through which students develops a felt sense as grounding for disciplinary concepts. This felt sense, I argue, cannot be taught directly via demonstration or verbal instruction. Instead, it must be personally experienced via practice. The second strand involves video analysis of task-based interviews situated in technology-enabled motion-sensitive learning environments. In the focal design, students who have not formally studied the mathematical concept of proportion first learn to enact a dynamical bimanual coordination, in which they move their hands proportionally, and only later signify this felt sense mathematically using symbolic artifacts interpolated into the problem space. I claim that conceptual understandings can sprout from practicing mathematics in instrumented fields of promoted action. Therein, practice serves as a form of exploration rather than drill. Ultimately, I argue for an account of learning across disciplines as explorative problem solving, where students find themselves moving in new ways and, upon appropriating available disciplinary frames of reference, recognize in their own actions its disciplinary significance. Regardless of the discipline, one’s body of knowledge is built through the labor of practice.

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