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Title: A Tempest in a Teapot Is but a Drop in the Ocean: Action-Objects in Analogical Mathematical Reasoning
Authors: Abrahamson, Dor
Issue Date: Jun-2010
Publisher: International Society of the Learning Sciences (ISLS)
Citation: Abrahamson, D. (2010). A Tempest in a Teapot Is but a Drop in the Ocean: Action-Objects in Analogical Mathematical Reasoning. In Gomez, K., Lyons, L., & Radinsky, J. (Eds.), Learning in the Disciplines: Proceedings of the 9th International Conference of the Learning Sciences (ICLS 2010) - Volume 1, Full Papers (pp. 492-499). Chicago IL: International Society of the Learning Sciences.
Abstract: We discuss a brief transcribed excerpt from a task-based interview with Li, an 11.5-year-old participant in a design-based research study of probabilistic cognition pertaining to the binomial. We investigate whether and how Li made sense of the behavior of an unfamiliar computer-based artifact--the diminishing proportional impact of successive random samples on the overall shape of a dynamically accumulating outcome distribution. Li constructed two informal analogical situations as multimodal discursive means of concretizing, elaborating, and communicating his emerging understanding of the artifact's behavior. These non-routine utterances shifted the discourse to an explicitly embodied, imagistic space bearing unique affordances for negotiated epistemic syntheses of phenomenological and technological constructions of quantitative relations. Microgenetic analysis suggests that Li's presymbolic notion was not a static magnitude but an intensive-quantity "actionobject"; he subsequently unpacked this dynamical "a/b" qualia into its constitutive "a" and "b" elements. We reflect on implications of this counter-curricular sequence for educational design.
Appears in Collections:ICLS 2010

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