Learning - Number Flashcards
What abilities are involved in numerical competence?
Relative numerosity discrimination (lots and few)
Absolute number discrimination
Ability to count
Ability to do arithmetic
What is relative numerosity discrimination
Ability to discriminate between sets of items on the basis of the relative number of items that they contain.
Emmerton, Lohmann, Niemann (1997) - Relative numerosity discriminations in pigeons
Trained pigeons to discriminate between few (1-2) and many (6-7)
Reversed colours to ensure pigeons weren’t just judging based on light
Responded approporiately (transfer of concept) to new numbers (3,4,5)
What is the concept of absolute number
Number not intrinsically related to what you’re counting - 4 apples and 4 cars have something in common
Koehler - Jakob and absolute number
Jakob the raven coud choose pot with 5 spots from an array even when size of spots varied 50-fold
Size of dots varied to rule out other explanations
Matsuzawa (1985) - Ai and absolute number
Ai the chimp had to select six response keys (labelled 1-6) when shown arrays of red pencils with 1-6 pencils per array
Over 90% accuracy
No necessarily same as counting
What is the perceptual matching problem?
Animals could be learning about specific perceptual patterns - learning patterns not numbers
Why did Matsuzawa argue that Ai did not use perceptul matching?
Ai could transfer ability to other types of objects - not just pencils
What other factors is number often confounded with?
Time - for items presented serially
Space - for items presented simultaneously
How did Pepperberg (1994) attempt to overcome the problem of perceptual matching?
Used the same array but varied the colours
Asked how many of certain colour
What is subitising?
o The perception at a glance of the number of items present, without counting them successively; the maximum number of items that can be counted in this way is five
What is the relationship between RT and counting?
If counting, RT should increase with increasing number
How is it argued that subitising differs to counting?
The original claim was that subitizing is different from counting because there is little increase in reaction time per item for low numbers of items
When dealing with numbers bigger than six, you have to count each one, and because it takes a finite amount of time to count each item the RT increases with number of items
What is implied about counting low numbers?
Do not need to count displays of five items or less - number is immediately perceived
What evidence is there against subitising?
There is a RT effect of display size with displays of less than five items - takens longer to perceive oneness than twoness
Suggests we are counting even with small displays
Meck and Church (1983) - Rats and noise
Serially presented items
Rats trained with two signals – 2 or 8 pulses of white noise
- After 2 were rewarded for left lever response
- After 8 were rewarded for right lever response
Each pulse = 0.5 seconds
- 2 pulse lasted 2 seconds
- 8 pulse lasted 8 seconds
Responding to number or time?
Meck and Church (1983) - Rats and noise - second test
Devised test in which both stimuli lasted 4 seconds
- If rats were responding on the basis of stimulus duration, this task should be impossible
Rats continued to respond correctly – responding to number not time
Also respond correctly to light - evidence against perceptual matching
Davis and Bradford (1986) Rats and food
Access to a plank with food pellets on it
Experimenter nearby talking to rat
Each rat had designated number of pellets to eat – if he ate more the experimenter shouted ‘no’ or clapped loudly
When they ate the right number or fewer than the target they were rewarded by praise and petting (and a little more food)
Got it right even when no longer rewarded for correct responses
Also transferred response to sunflower seeds rather than pellets
What does counting involve?
Counting involves mapping numerosity (the property of the display corresponding to number – e.g. two items) onto a label that represents that numerosity
How do humans and animals differ in the labels they use for number?
We usually use number words or symbols as labels for number, but presumably animals use nonverbal labels, which we can call numerons
What three principles are involved in counting?
One to one principle
Stable order principle
Cardinal principle
What is the one to one principle?
Each item is assigned only one numeron
What is the stable order principle?
Numerons must always be assigned in the same order
What is the cardinal principle?
The final numeron assigned applies to the whole display
What do the three principles of counting imply knowledge about?
Order of labels (numerons)
How these labels are ordered in relation to quantity - ordinal scale
The size of the difference between each item is the same - interval scale
Biro and Matsuzawa (2000) Ai and numbers
Ai trained to touch Arabic numerals in ascending order
Some argued this is just rote learning of a particular stimulus-response sequence
No requirement to know anything about the quantitive relation between numbers
Brannon and Terrace (2000)
CHimps trained to order arrays of 1-4 items in ascending, descending, or random order
Could learn ascending or descending but not random
Tested with novel displays of 5-9 items
Chimp taught ascending could generalise to higher numbers
Chimp taught descending needed further training
Implies limited understanding of the ordering of quantities
Alex the parrot - Pepperberg (2000)
What number green?
- Knew about naming quantities and identifying numbers but not about applying numbers to quantities
What colour bigger?
- Performance above chance from beginning - could relate written numbers with quantities
- Not just rote learning
What is the ability to do arithmetic?
To perform the operations of addition, subtraction, etc.
What does true mathematical competence allow for?
Allows operations to be generalised to new situations in a way that implies a concept of number
Boysen and Berntson (1989) Sheba, arithmetic
Chimp called Sheba trained to label arrays with counters and with Arabic numerals
Performed well when items swapped for everyday objects
Extensive training for numbers 0-4
Final test - had to find oranges in any of three hiding places and pick Arabic numeral that represented sum of all oranges that were hidden
Could argue she memorised all ways of adding 0-4 to a total of 4
Also performed accurately when experimenters hid cards with numbers written on them rather than oranges
Implies understanding of interval scale
What is the problem with competence?
Sometimes animals are more competent than they appear
Is experiment designed in a way that allows animal to perform to its best ability
Boysen and Bertson (1995) Competence and performance
Chimp A given choose between two amount of candy, whichever it chose was given to chimp B and chimp A got the other amount
Chimp should choose smaller quantity - could only solve task when candy swapped for numerals
Motivation critical to performance
