Learning - Number

Question 1

What abilities are involved in numerical competence?

Answer 1

Relative numerosity discrimination (lots and few)
Absolute number discrimination
Ability to count
Ability to do arithmetic

Question 2

What is relative numerosity discrimination

Answer 2

Ability to discriminate between sets of items on the basis of the relative number of items that they contain.

Question 3

Emmerton, Lohmann, Niemann (1997) - Relative numerosity discriminations in pigeons

Answer 3

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)

Question 4

What is the concept of absolute number

Answer 4

Number not intrinsically related to what you’re counting - 4 apples and 4 cars have something in common

Question 5

Koehler - Jakob and absolute number

Answer 5

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

Question 6

Matsuzawa (1985) - Ai and absolute number

Answer 6

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

Question 7

What is the perceptual matching problem?

Answer 7

Animals could be learning about specific perceptual patterns - learning patterns not numbers

Question 8

Why did Matsuzawa argue that Ai did not use perceptul matching?

Answer 8

Ai could transfer ability to other types of objects - not just pencils

Question 9

What other factors is number often confounded with?

Answer 9

Time - for items presented serially

Space - for items presented simultaneously

Question 10

How did Pepperberg (1994) attempt to overcome the problem of perceptual matching?

Answer 10

Used the same array but varied the colours

Asked how many of certain colour

Question 11

What is subitising?

Answer 11

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

Question 12

What is the relationship between RT and counting?

Answer 12

If counting, RT should increase with increasing number

Question 13

How is it argued that subitising differs to counting?

Answer 13

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

Question 14

What is implied about counting low numbers?

Answer 14

Do not need to count displays of five items or less - number is immediately perceived

Question 15

What evidence is there against subitising?

Answer 15

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

Question 16

Meck and Church (1983) - Rats and noise

Answer 16

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?

Question 17

Meck and Church (1983) - Rats and noise - second test

Answer 17

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

Question 18

Davis and Bradford (1986) Rats and food

Answer 18

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

Question 19

What does counting involve?

Answer 19

Counting involves mapping numerosity (the property of the display corresponding to number – e.g. two items) onto a label that represents that numerosity

Question 20

How do humans and animals differ in the labels they use for number?

Answer 20

We usually use number words or symbols as labels for number, but presumably animals use nonverbal labels, which we can call numerons

Question 21

What three principles are involved in counting?

Answer 21

One to one principle
Stable order principle
Cardinal principle

Question 22

What is the one to one principle?

Answer 22

Each item is assigned only one numeron

Question 23

What is the stable order principle?

Answer 23

Numerons must always be assigned in the same order

Question 24

What is the cardinal principle?

Answer 24

The final numeron assigned applies to the whole display

Question 25

What do the three principles of counting imply knowledge about?

Answer 25

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

Question 26

Biro and Matsuzawa (2000) Ai and numbers

Answer 26

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

Question 27

Brannon and Terrace (2000)

Answer 27

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

Question 28

Alex the parrot - Pepperberg (2000)

Answer 28

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

Question 29

What is the ability to do arithmetic?

Answer 29

To perform the operations of addition, subtraction, etc.

Question 30

What does true mathematical competence allow for?

Answer 30

Allows operations to be generalised to new situations in a way that implies a concept of number

Question 31

Boysen and Berntson (1989) Sheba, arithmetic

Answer 31

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

Question 32

What is the problem with competence?

Answer 32

Sometimes animals are more competent than they appear

Is experiment designed in a way that allows animal to perform to its best ability

Question 33

Boysen and Bertson (1995) Competence and performance

Answer 33

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