"An algebraic sandbox: gounding symbolic math in perceptual-motor interaction," a talk by Robert Goldstone, Indiana University

 

"An algebraic sandbox: gounding symbolic math in perceptual-motor interaction," a talk by Robert Goldstone, Indiana University

Sage 4101

February 5, 2014 12:00 PM - 1:30 PM

Much of the power of mathematics comes from its generality and ability to unify prime face dissimilar domains.  By one account, analytic thought in math and science requires developing deep construals of phenomena that run counter to untutored perceptions.  This approach draws an opposition between superficial perception and principled understanding.  In this talk, I advocate the converse strategy of grounding mathematical reasoning in perception and action.  I will describe empirical evidence for perception and action changes that accompany learning in mathematics. Sophisticated performance can be achieved not only by ignoring perceptual features in favor of deep conceptual features, but also by adapting perceptual processing so as to conform with and support formally sanctioned responses.  These “Rigged Up Perception-Action Systems” (RUPAS) offer a promising strategy for achieving educational reform.

Based on the theoretical foundation of RUPAS, we have designed and implemented virtual, interactive sandboxes for students to explore algebra.  One implementation of this system, Algebra Touch for Ipads, has the goal of educating students’ perceptions of algebraic notation so that the perceptual groupings and spatial transformations that they spontaneously form conform to formally sanctioned operations.  For example, we want students to naturally perceive that the Xs from (6*X)/(3*X) = Y can be cancelled out, but the Xs from (6+X)/(3+X) = 4 cannot.  In addition to increasing students’ algebraic fluency and ideally also their underlying conceptual understanding of mathematics, these systems have proven to be an effective platform for exploring science of learning issues related to scaffolding, distributed cognition, and embodied cognition.

 

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