Numbers

Question 1

What abilities are involved in numerical competence?

Answer 1

1. Relative numerosity discrimination
   
   2. Concept of absolute number
   3. Ability to count
   4. Ability to do Arithmetic

Question 2

Emmerton, Lohmann & Niemann (1997)

Answer 2

trained pigeons to discriminate between “few” (1/2 items) and “many (6/7 items)

cannot tell if its light and dark discrimination

Question 3

Relative numerosity discrimination

Answer 3

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

Question 4

Concept of absolute number

Answer 4

understanding that 4 bananas and 4 elephants have something in common…
… i.e. number is not intrinsically related to what you are counting

Question 5

Matsuzawa (1985)

Answer 5

trained a chimp called Ai to select one of six response keys (labelled 1-6) when shown arrays of red pencils, with 1-6 pencils per array. She achieved more than 90% accuracy.

Question 6

Problems and solution to Matsuzawa (1985)

Answer 6

• But this is not necessarily the same as counting…
• Animals could be learning about specific perceptual pattern
  
  • Perceptual matching
    ○ .. although Ai could transfer her ability to arrays of items other than pencils

Matsuzawa argued no: Ai could transfer her ability to arrays of different types of item

Question 7

Meck and Church (1983): Serial presentation

Answer 7

• Rats trained with two signals, of 2 or 8 pulses of white noise.
• 2 pulses –> reward for responding on the left lever
• 8 pulses –> reward for responding on the right lever:
• Solved task; but were animals responding on basis of total time, rather than number of pulses?

Question 8

Davis & Bradford (1986)

Answer 8

• 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 also a little more food)
• got it right even when no longer rewarded for correct responses
  transferred to sunflower seeds

Question 9

Meck and Church (1983) follow up

Answer 9

• To investigate this, they devised a test in which both stimuli lasted 4 seconds
• If the animals were responding on the basis of stimulus duration, this is impossible; but they continued to respond correctly.
• Rats also tested with pulses of light – and continued to respond appropriately
• This is more evidence against perceptual matching

Question 10

Gelman & Gallistel (1978)

Answer 10

argued that counting involves mapping numerosity (the number in the display – e.g. two items) onto a label that represents that numerosity

Question 11

The process of counting involves three principles:
according to German & Gallistel (1978)

Answer 11

i) one-to-one principle: each item is assigned only one numeron

ii) stable-order principle: numerons must always be assigned in the same order

iii) cardinal principle: the final numeron assigned applies to the whole display

Question 12

Representation of number in chimp? Biro & Matsuzawa 2000

Answer 12

Ai trained to touch arabic numerals in ascending order

• Or is it just rote learning of a particular stimulus-response sequence… – no requirement to know anything about the quantitative relation between numbers?

Question 13

Brannon & Terrace, 2000

Answer 13

• Chimps (Benedict, Rosencrantz & MacDuff) trained to order
• arrays of 1-4 items in ascending, descending, or random order
• They could learn ascending and descending orders, but not the arbitrary order 1-3-2-4

Question 14

Maths in the chimpanzee? Boysen & Berntson, 1989

Answer 14

• A chimp called Sheba was trained to label arrays with counters, and then with arabic numerals:

In the final test a number of oranges were hidden in the lab, in any of three hiding places. Sheba had to find all the oranges, and then pick the arabic numeral that represented the sum of all the oranges that were hidden. After 12 training sessions (of around 20 trials per session) she was performing at about 85% correct.

Question 15

(Boysen & Bertson,1995)

Answer 15

chimp A was given a choice between two amounts of candy. Whichever chimp A chose was given to a second chimp, B, and chimp A got to eat the unchosen one.
- In chimp A’s interest to choose the smaller quantity, so it could eat the larger quantity. Completely unable to solve this task

Question 16

give an example of absolute number discrimination?

Answer 16

understanding that 4 and 5 are different things

Question 17

do animals have the ability to do relative numerosity discrimination, according to Emmerton, Lohmann & Riemann (1997)?

Answer 17

yes - pigeons able to discriminate between “few” (1/2 items) and “many” (6/7 items)

Question 18

what is a criticism of Emmerton, Lohmann & Riemann (1997) study into relative numerosity discrimination?

Answer 18

are the pigeons responding on the feature of the display (light = few, dark = many) and ignoring the number?

Question 19

in Emmerton, Lohmann & Riemann (1997) study into relative numerosity discrimination, when the spots were switched to light colours and the keys to dark colours, did this influence how the pigeons responded?

Answer 19

no - pigeons still responded the same as they had before, must be responding on the basis of the number of dots on the keys = must discriminate many vs few arrays

Question 20

do animals show a concept of an absolute number, according to Koehler?

Answer 20

yes - Jakob the raven could choose a pot with 5 spots from an array, even when size of spots varied 50-fold

Question 21

did Meck & Church (1983) provide evidence for or against perceptual matching?

Answer 21

against

Question 22

how many subjects were there in Brannon & Terrace (2000) study into the representation of number in the chimpanzee?

Answer 22

only 3 - not very reliable

Question 23

one-to-one principle

Answer 23

each item is only assigned one numeron

Question 24

stable-order principle

Answer 24

numerons must always be assigned in the same order

Question 25

cardinal principle

Answer 25

the final numeron assigned applies to the whole display i.e 5 means 5 numbers displayed if other 2 principles followed