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Embodied Interaction as Designed Mediation of Conceptual Performance

Part of the Mathematics Education in the Digital Era book series (MEDE,volume 1)

Abstract

Can conceptual understanding emerge from embodied interaction? We believe the answer is affirmative, provided that individuals engaged in embodied-interaction activity enjoy structured opportunities to describe their physical actions using instruments, language, and forms pertaining to the targeted concept. In this chapter, we draw on existing literature on embodiment and artifacts to coin and elaborate on the construct of an embodied artifact—a cognitive product of rehearsed performance such as, for example, an arabesque penchée in dance or a flying sidekick in martial arts. We argue that embodied artifacts may encapsulate or “package” cultural knowledge for entry into disciplinary competence not only in explicitly embodied domains, such as dance or martial arts, but also implicitly embodied domains, such as mathematics. Furthermore, we offer that current motion-sensitive cyber-technologies may enable the engineering of precisely the type of learning environments capable of leveraging embodied artifacts as both means of learning and means for studying how learning occurs. We demonstrate one such environment, the Mathematical Imagery Trainer for Proportion (MIT–P), engineered in the context of a design-based research study investigating the mediated emergence of mathematical notions from embodied-interaction instructional activities. In particular, we discuss innovative features of the MIT–P in terms of the technological artifact as well as its user experience. We predict that embodied interaction will become a focus of design for and research on mathematical learning.

Keywords

  • Embodied interaction
  • Sociocultural theory
  • Educational technology
  • Learning sciences
  • Mathematics
  • Proportion
  • Embodied artifact

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Notes

  1. 1.

    We invite the reader to compare our “embodied artifact” with the construct of “organizational routines” (Feldman & Pentland, 2003). Though organizational routines share commonalities with embodied artifacts in terms of constituting structured procedures, our construct serves particular interests both in the embodiment of knowledge and in learning from an artifact-mediated perspective.

  2. 2.

    By naming this sequence with a phrase commonly used in the context of this particular cultural practice, we are anticipating that it will be signified as a “chunked” performance.

  3. 3.

    Esther Gokhale (2008) argues that embodied artifacts, such as those found in traditional dances, serve to encapsulate and preserve traditional physiological knowledge, not unlike how a recipe may preserve traditional (tacit) nutritional knowledge.

  4. 4.

    As the mathematician G. H. Hardy famously stated, not without pride: “I have never done anything ‘useful’.”

  5. 5.

    That said, these studies date back to American pragmatism in relatively recent times (see Chemero, 2009) and Buddhist psychologies many centuries before that (Varela, Thompson, & Rosch, 1991).

  6. 6.

    It is telling that the most popular workshop at the CHI 2011 conference on Human-Computer Interaction was titled “Embodied Interaction”—and yet the idea of that very workshop was considered untenable in the previous years at the same venue.

  7. 7.

    See http://www.youtube.com/watch?v=n9xVC76PlWc for a video.

  8. 8.

    Students initially worked with a 1:2 ratio, though the protocol included 1:3, 2:3 ratios and beyond. These more challenging scenarios were introduced only after a student displayed confidence with a 1:2 ratio.

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Acknowledgments

The notion of an embodied artifact originates in Abrahamson’s earlier publications on the Mathematical Imagery Trainer. We gratefully appreciate Mira-Lisa Katz for her comments on an earlier draft. This research was supported by a UC Berkeley Committee on Research Faculty Research Grant and an Institute of Education Sciences pre-doctoral Research Training grant R305B090026.

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Trninic, D., Abrahamson, D. (2013). Embodied Interaction as Designed Mediation of Conceptual Performance. In: Martinovic, D., Freiman, V., Karadag, Z. (eds) Visual Mathematics and Cyberlearning. Mathematics Education in the Digital Era, vol 1. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-2321-4_5

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