Transcript Slide

Explaining Apparent Infant Numerical
Competence in Terms of Object Representation
Tony J. Simon
Neuroscience Center
National Institute on Drug Abuse
Bethesda, MD 20983 USA
[email protected]
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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).
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Initial transf ormation
The Task
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Test trial outcomes
Possible
Arithmetically Impossible ( Wynn)
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Simon et al. (1995) Replication of Wynn (1992)
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1+1=1
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21=2
"Addition"
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"Subtraction"
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8
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1+1=2
21=1
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1 object
2 objects
Number of Objects Remaining
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The Identity Condition
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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
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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
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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
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INFANT - All Conditions
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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
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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!
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INFANT vs Wynn & Chiang (1998)
INFANT reproduces Wynn & Chiang’s habituation results:
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INFANT vs Wynn & Chiang (1998)
… and all the condition comparisons!
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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
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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
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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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