understanding number discriminate –based on number and nothing else categorize –generalize...
TRANSCRIPT
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Understanding Number
• Discriminate– based on number and nothing else
• Categorize– generalize across situations – label
• Conceptualize– serial learning (1, 2, 3, 4…)
• transitive inference• Scanning in pigeons vs. chimps
– operations (2 + 1 =3)
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Early Counting Experiments
• Clever Hans– answers math questions
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Clever Hans
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Early Counting Experiments
• Clever Hans– answers math questions
• Spontaneous Counting– not impressive
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Early Counting Experiments
• Clever Hans– answers math questions
• Spontaneous Counting- not impressive
• Mechner (1958)– press lever “X’ times– pigeons can tell the difference between 45 and 50 pecks– time passed and not number?
• Other examples of responding based on counts which seem to generalize
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Generalize AcrossModalities
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Discriminate Number (not Time)
• Acquisition
– RRRN
– NRRRN
R = RewardN = Nonreward
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Categorize (Generalize)
• Acquisition
– CPPN
– PPN
• Shift
– PCCN
– CCN
P = Pellets
N = Nonreward
C = Corn Pops
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Categorize (Label)
Answers Correctly:“How many blocks?”
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Not Subitization
• Perceptual not cognitive
• Estimating small quantities at a glance without counting
• Hard with similar distractors
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How Many?
Squares Ovals
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Conceptualize (Serial Learning)
• Transitive inference
• Simultaneous chaining
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Three-Item Transitive Inference
Train A > B B > C
Test A > C
But…………..A is 100% reinforced and C is 0%
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Five-Item Transitive Inference
Train A > B B > C C > D D > E
Test B > D
But…………the are alternatives!
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Successful “Species”
Children Monkeys Pigeons Fish “Inebriated” University Students
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Why?
• Fewer unreinforced responses directed at B because its partner A is always reinforced (Disappointment Hypothesis)
• B reminds you of A and C, D reminds you of C and E. A and C have much more strength than D and E (Value Transfer Hypothesis).
• So, transitive inference does not imply the learning of a mental sequence
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Simultaneous Chaining
Ordered Series of Responses
A-B-C-D-E
Response Chain: Each response serves as a discriminative stimulus
Serial Representation: Mental chunking
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Serial Order Learning
• Simultaneous Chaining Task– All stimuli appear simultaneously in random locations
– Press numbers or objects in a specified order
– Stimuli disappear when pressed and trial finishes with reinforcement
– Trial immediately ends if a mistake is made
• Tests Trials With Missing Items – Mental Line?
– S-R sequence?
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Pigeons (Test Trials)
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Chimpanzees (Test Trials)
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(Brannon & Terrace, 1998)
Basic paradigm: Touching stimuli in numerical order produces a reward.
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Primates Rosencrantz and Macduff
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Test with novel stimuli
About 75% correct
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Number Operations
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Sheba
• Taught to look in three different locations and choose a number for the total, 0+2+1=3
• Maybe just counting not adding?
• Numbers always added to less or equal to 4
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But can’t do2+2.
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Nonverbal Counting Models