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SUMMARY:Mathematical Reasoning as a Literally Physical Symbol System -  Pr
 ofessor Robert Goldstone  Chancellor's Professor of Psychological and Brai
 n Sciences  Indiana University\, Department of Psychological and Brain Sci
 ence
DTSTART:20120612T153000Z
DTEND:20120612T170000Z
UID:TALK38582@talks.cam.ac.uk
CONTACT:Araceli Hopkins
DESCRIPTION:Much of the power of mathematics comes from its generality and
  ability to unify prime face dissimilar domains.  The same combinatorics f
 ormula applies to sealing wax\, cabbages\, and kings with no customization
  needed\, or even permitted.  By one account\, analytic thought in math an
 d science requires developing deep construals of phenomena that run counte
 r to untutored perceptions.  This approach draws an opposition between sup
 erficial perception and principled understanding.  In this talk\, I advoca
 te the converse strategy of grounding mathematical reasoning in perception
  and action.  I will describe empirical evidence for perceptual changes th
 at accompany learning in mathematics.  In arithmetic and algebraic reasoni
 ng\, we find that proficiency involves executing spatially explicit transf
 ormations to notational elements.  People learn to attend mathematical ope
 rations in the order in which they should be executed\, and the extent to 
 which students employ their perceptual attention in this manner is positiv
 ely correlated with their mathematical experience.  People produce mathema
 tical notations that they are good at reading.  Perceptual and attentional
  processes are tailored to fit mathematical requirements.  Thus\, for reas
 oning in mathematics (and science\, but that’s another talk)\, relativel
 y sophisticated performance can be achieved not only by ignoring perceptua
 l features in favor of deep conceptual features\, but also by adapting per
 ceptual processing so as to conform with and support formally sanctioned r
 esponses.  These “Rigged Up Perceptual Systems” (RUPS) offer a promisi
 ng strategy for achieving educational reform.
LOCATION:Faculty of Education\, 184 Hills Road\, Cambridge\, CB2 8PQ\, (Rm
  G09 Mary Allan Building))
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