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Unformatted text preview: PSYC 103
Winter 2011
Lecture 18
Number
Review session Tuesday Feb. 22 @ 8:00 PM Pepper canyon hall 109 Serial order
Terrace et al. (1997)  Animals construct a spatial representation of 4 slots, in serial order
 Different spatial representations can be integrated… 2 Counting Clever hans Numerical competence
Upper end of capability:
• Concept of number: property of all sets with ‘n’ items, Increasing complexity absolute, not relative; may include mathematical properties.
(x + y = n )
• Counting: a sensitivity to the number of things in a set; attachment of ordered labels (“numerons”: in arabic notation
“1”, “2”, “3”)
• Subitizing: immediate apprehension of small numbers of
items without counting
Lower end of capability:
• Numerosity discrimination: discrimination among sets based on how many items they contain (e.g. many vs. few)
Perceptual matching: Snapshot of training stimulus remembered: test patterns
compared to this. Good match = response Relative numerosity discrimination
Honig & Stewart (1989)
 Required pigeons to discriminate 36 red dots (+) from 36 blue dots ()
 Then tested with patterns of various proportions of red and blue dots
 Direct relationship between proportion of red dots and the rate of responding to that pattern
 Not absolute number of dots – same effect revealed when tested with patterns composed of 16 dots Adapted from Honig & Stewart, 1989. 5 Relative numerosity discrimination
from Honig & Stewart, 1989 Relative numerosity generalization gradients for a group of pigeons who were
tested with patterns containing either 16 or 36 elements Counting & Absolute number
Counting Responses
Rumbaugh & Washburn (1993) 
 Trained a chimpanzee to move a cursor with a joystick
 Arabic numeral presented (1, 2, 3 etc.)
 Arrays of rectangles presented: chimp required to delete the
number of rectangles = Arabic number, which it did (eventually!) Counting Sequential Stimuli
Meck & Church (1983)
Rats rewarded for pressing:
 Left lever after 2 pulses of noise
 Right lever after 8 pulses of noise
 Discrimination solved with ease Breukelaar & DalrympleAlford (1998)
 Replicated Meck & Church’s experiment
 Varied the duration of bursts from trial to trial
 Problem could not be solved by timing
7 Counting Control for time (duration)
Control for number • Rats are sensitive to time
and number
Are time and number coded
together? Counting: Time vs number Case 1 Case 2 Conditional time/number discrimination with flashing colored keys:
• if Green, then peck left for 2 flashes, right for 8 flashes, regardless of duration
• if Red, then peck left for 2 sec, right for 8 sec, regardless of number of flashes
• Test with 28 pulses over 4 sec (counting), or 4 pulses lasting 28 sec (timing) Timing at chance counting at chance Counting sequential stimuli This drop shows
that they are
counting rewards Rats count small numbers of feeding and transfer this count across food types
• food pellets ➔ cocoa puffs™
• can count on RR’R’N sequences too Counting simultaneous stimuli
Brannon & Terrace, 2000 Sketches of two possible
arrangements of the stimuli used in
an experiment to study counting in
monkeys. Subjects were required to
touch the four arrays in each panel
in ascending order of the number of
dots they contained • Monkeys presented with arrays of patterns
• Each pattern contained 1, 2, 3 or 4 objects
• Patterns had to be touched in order (1 then 2 etc.) for reward.
Position of objects
Shape of objects
Orientation of objects Varied from trial to trial  Monkeys solved the problem and generalized to novel objects
 Zorina & Smirnova (1996) conducted similar study with crows Number
The representation of number
 Nominal scale: numbers act as labels (e.g. numbers on a footballer’s shirt)
 Ordinal scale: items can be rank ordered – items in higher rank have more objects than
lower rank item
 Interval scale: as an ordinal scale, but also interval between any two adjacent points is
the same
Experiment by Brannon & Terrace may confirm animal’s appreciation of nominal scales
But,
On test trials with patterns comprising 4 and 5 objects, 4 was pressed before 5. More than
a label?
However,
Monkeys trained to press patterns in reverse (4, 3, 2, 1) order when tested with 4 and 5,
did not press 5 then 4 12 Number
Numerical symbols
Can animals use different symbols to refer to different quantities? Boysen & Berntson (1989)
 Showed a chimp (Sheba) different Arabic numerals from 04
 Tray in front of numerals contained number of food items (04)
 Rewarded for choosing Arabic numeral that = number of food items
 Learning transferred to novel items
Pepperberg (1994)
 African grey parrot (Alex) trained to respond (verbally) to questions 13 Alex Can correctly label novel arrays of items up to 6.
Can tell how many items of a certain type are in larger array.
Is he subitizing? Counting?
Pepperberg (2006)
 Alex shown two inverted cups, both of which concealed nuts
 Shown objects in turn and asked “How many nut total?”
 Correctly responded more than would be expected by chance Counting in chimp (Sheba)
1.
2.
3.
4. Boysen Match numbers of gum drops to numbers of tokens on cards
Match Arabic numerals (on cards) to numbers of gum drops
Choose correctly sized array when shown numeral & vise versa (up to 6
or 8 items)
Sheba can count the total number of hidden objects & add the numerals
on hidden cards! Adding and subtracting
Rhesus macaques “looking time” (habituation/dishabituation) Adding and subtracting 56 mo old infants ...
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This note was uploaded on 03/24/2012 for the course PSYC 103 taught by Professor Pearlberg during the Spring '07 term at UCSD.
 Spring '07
 Pearlberg
 Psychology

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