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Explaining Apparent Infant Numerical Competence in Terms of Object Representation Tony J. Simon

Explaining Apparent Infant Numerical Competence in Terms of Object Representation Tony J. Simon Neuroscience Center National Institute on Drug Abuse Bethesda, MD 20983 USA tjsimon@mindspring.com. The Innate Numerical Competence Claim.

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Explaining Apparent Infant Numerical Competence in Terms of Object Representation Tony J. Simon

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  1. Explaining Apparent Infant Numerical • Competence in Terms of Object Representation • Tony J. Simon • Neuroscience Center • National Institute on Drug Abuse • Bethesda, MD 20983 USA • tjsimon@mindspring.com

  2. The Innate Numerical Competence Claim • “Humans innately possess the capacity to perform simple arithmetical calculations......... Infants possess true numerical concepts: they have access to the ordering of numerical relationships between small numbers. They can calculate the results of simple arithmetical operations of small numbers of items” Wynn (1992).

  3. The Task

  4. 13 12 1+1=1 11 2-1=2 "Addition" 10 "Subtraction" 9 8 1+1=2 2-1=1 7 6 1 object 2 objects Number of Objects Remaining Simon et al. (1995) Replication of Wynn (1992)

  5. The Identity Condition

  6. Object Representation Theory • Simon (1997) “Non-Numerical” Account • 4 documented infant competencies sufficient for observed behavior. • Object Individuation (perceive/represent unitary objects) • Physical Reasoning (object permanence) • Abstract Representation (spatiotemporal object coding) • Memory (object/event comparison) • If OR Theory is right it must demonstrate 2 things: • infants, like those in the studies, must possess these abilities • these abilities are sufficient to generate the observed behavior • topic of this presentation

  7. The INFANT Model • Simon (1998) clear replication by INFANT of all key findings • Built in ACT-R 3, models Simon et al. (1995) study • Individuation/Representation • Object-File” token created for each visible entity • spatial rep’n (location, motion, support) by separate events in task • Memory • Same Object-File encodes record of hidden/removed object

  8. INFANT - The Model • Physical Reasoning • Create spatiotemporal prediction for Memory Object-Files • implements object permanence • Verify predictions for “unhidden”: entities • 1-to-1 Object File match - Memory with new Physical O.F. • Spatial/Object searches for disappearance/reappearance outcomes • Time to execute actions affected by activation of objects in memory • activation grows & decays with #/frequency of processing events

  9. INFANT - All Conditions

  10. The Strange Case of “Magical Appearance” • Wynn & Chiang (1998) report a gap in infants’ object knowledge • LT not longer when an object impossibly appears than possible case • conclude infants must be unable to detect/understand this violation

  11. Object Representation Failure in MA, Or Not? • OR predicts babies will detect MA impossibility • obviously, 1-1=1 will be processed just like 2-1=2 • shouldn’t that produce wrong data - longer LT for impossible task? • INFANT does respond to impossible MA outcome like other tasks • there is no failure of impossibility detection or object representation • yet looking times are just like Wynn & Chiang data!

  12. INFANT vs Wynn & Chiang (1998) • INFANT reproduces Wynn & Chiang’s habituation results:

  13. INFANT vs Wynn & Chiang (1998) • … and all the condition comparisons!

  14. Object Representation Failure, Or Not? • So why isn’t impossible MA looking time longer than possible EA? • In 2-1=2 vs 2-1=1 procedure is identical until outcome • extra actions needed to resolve violation create longer looking time • But 1-1=1 (MA) gets compared to 1+0=1 (EA), not to 1-1=0 (ED)! • the single object in MA is processed very differently from that in EA • LT differences due to task comparison, not failure of MA detection • different actions & activations during tasks create similar LTs

  15. OR Theory Explains the Puzzle • The original “number” experiments compare identical tasks • The magical appearance experiment compares different tasks • The object in MA (1-1=1) has high activation - actions execute quickly • The object in EA (1+0=1) has low activation - actions execute slowly • different number of actions required by different tasks take same time • Infants aren’t failing to detect MA violation, they treat it like experts • object representation is stronger in MA relative to EA, not faulty! • Only a detailed process theory like OR can explain the puzzle • looking time just describes, does not explain behavior

  16. So, Where Do Numerical Abilities Come From? • Numerical ability foundations: 4 early-developing infant competencies • When presented with particular tasks they compute representations & generate behavior that appears, but is not, numerical (Clever Hans). • Object Representation Theory is coherent, parsimonious account: • explains all existing data, resolves puzzling inconsistencies • based on existing, documented, human infant competencies • foundation for construction of domain-specific numerical competence • consistent with neural development trajectory (Simon, in press)

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