Numbers

Question 1

Comparative Psychology:
Compare different species in doing certain things
This leads us to assume if animals can do things the same/ differently to what us humans do.

Question 2

What are the 4 abilities that are involved in numerical competence?

Answer 2

1) Relative numerosity discrimination many v few, more v less

2) Absolute number discrimination 4 v 5

3) Ability to count 1 2 3 4

4) Ability to do arithmetic calculations 1 + 2 =

Question 2

The ability to discriminate between sets of items on the basis of the relative number of items that they contain is known as?

Answer 2

Relative numerosity discrimination many v few, more v less

Study:
trained pigeons to discriminate between “few” (1/2 items) and “many” (6/7 items). But birds may be ignoring number, and instead using some other feature of the display such as:

LIGHT=few
DARK=many

Then did the same experiments but with opposite key displays:
various light keys with dark display

Found that birds still responded to the correct amount of keys=
evidence that birds have relative numerosity discrimination

Question 2

The ability in understanding that despite differing appearances, 4 bananas and 4 elephants have something in common is known as?

Answer 2

Absolute number discrimination

i.e. number is not intrinsically related to what you are counting
it’s an abstract thing unrelated to physical characteristics

Study:
Bird examples:
Jakob the raven could choose a pot with five spots from an array, even when size of spots varied 50-fold
He could tell 5 apart from all other numbers

Primate examples: Chimp called Ai had to select one of six response keys (labelled 1-6) when shown arrays of red pencils, with 1-6 pencils per array. Achieved > 90% accuracy.

But this is not the same as counting!
Animals could be learning about specific perceptual pattern perceptual matching

Question 2

Perceptual matching (animals could be learning about specific perceptual pattern) can be mixed up and perceived as…

Answer 2

Absolute number discrimination
This number 4 is different from that number 5

e.g. four objects have more in common with each other
than arrays of e.g. 2 or 7

Question 2

How do you test for Absolute number discrimination?

Answer 2

Pepperberg, 1994
same array – bird must count different components
bird responds with speaking the number when asked how many green blocks

Question 3

What is the perceptual matching problem?

Answer 3

Often confused with Absolute number discrimination (4 v 5)

Often number is confounded with other factors such as:
Time (for items presented serially) and
Space (for items presented simultaneously)

Animals use other cues such as
Duration of how much display is taken up
e.g. smaller number of items also takes up less space. =<1
May be the the size of the display controls the response, not number.

Question 3

The size of the difference between each item is the same
eg. 4-3 = 3-2 is known as which type of scale?

Answer 3

Interval scale

Question 3

Good numerical competence involves what other knowledge besides counting?

Answer 3

Order (ordinal scale)
-how these labels are ordered in relation to quantity

Interval (interval scale)
-the size of the difference between each item is the same

Question 4

Testing for counting:

Meck and Church (1983): 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 rewarded for right lever response

Each pulse 0.5 sec –’2 pulse’ lasted for 2 seconds,
‘8 pulse’ for eight seconds.

But unsure of whether animals responded on the basis of the total time, rather than the number of pulses.
What was done in response to this problem?

Answer 4

To investigate this, they devised a test in which both stimuli lasted
4 seconds: so that the overall stimulus was exactly the same duration

If rats were responding on the basis of stimulus duration,
this task should be impossible but they responded correctly showing evidence against perceptual matching.

you can also can make animals respond a fixed number of times – no array involved.

Question 5

Study:
Representation of number in chimps measuring if animals can learn numbers in the right sequence?

Chimp Ai trained to touch Arabic numerals in ascending order:

Answer 5

Found, yes they can learn sequences
However, it may be learning of a particular stimulus-response sequence… – no requirement to know anything about the quantitative relation between numbers.

Question 5

Ability to count

Which ability of numerical competence involves mapping
numerosity (the number in the display – e.g. two items) onto
a label that represents that numerosity.

We usually use number words (one, two) or symbols (1, 2)
as labels, but animals must use nonverbal labels. What are these nonverbal labels known as?

Answer 5

Numerons

Question 5

The process of counting involves which three principles?

Answer 5

One-to-one principle: each item is assigned only one numeron
eg. 3 and 4 cannot have the same symbol

Stable-order principle: numerons must always be assigned in
the same order
eg. cannot be 1, 3, 2 has to be 1,2,3

Cardinal principle: the final numeron assigned applies to the
whole display
eg. 1, 2, 3 3 must represent the whole sequence

Question 5

Representation of number in the chimpanzees:

Chimps were trained to order arrays of 1-4 items in ascending, descending, or random/ arbitrary order
order.

What were the findings on their abilities to complete each other?

Answer 5

They could learn ascending and descending orders,
but, NOT the arbitrary (random) order 1-3-2-4

Question 6

The ability to understand addition, subtraction etc. To some extent this can be done by rote learning (e.g. times tables). Still, true mathematical competence would allow these operations to be generalised to new situations in a way that implies a concept of number, is known as which numerical ability?

Answer 6

Ability to do arithmetic

Question 6

Representation of number in the chimpanzees:
After being tested to order arrays of 1-4 items in ascending, descending, or random/ arbitrary order, they were then tested with novel displays of 5-9 items:

ascending should go 5 6 7 8
descending should go 8 7 6 5
arbitrary should go 5 7 6 8

What were the new findings?

Answer 6

The chimp taught an ascending order could generalize immediately to the higher numbers, but the one who taught a descending order needed further training.

(arbitrary chimp never learned in the first place)

Evidence for learning number representations but implies (limited) understanding of the ordering of quantities.

Question 6

Time tables is an example of which type of learning?

Answer 6

rote learning

Question 7

Maths in chimps:
A chimp called Sheba was trained to label arrays with counters and then with Arabic numerals. She also performed well when items were swapped for everyday objects.

She was given extensive training with numbers 0-4

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.

She could also perform accurately when the experimenters hid
cards with numbers written on them, rather than oranges, performing above chance right away.’

This implies chimps can have an understanding of which scale?

Answer 7

implies an understanding of the interval scale
– if she understood only bigger than she would have chosen 4 as often as 3

Question 7

Evidence that bees can count:

Bees trained that sucrose reward would be at 1st, 2nd, 3rd, 4th or 5th landmark; distance between landmarks varied on each trial
in training.

Tested without reward

in Experiment 1 on same landmarks (yellow stripes)

in Experiment 2 on different landmarks (yellow discs)

in Experiment 3 could only see one landmark at a time (yellow and grey baffles both grey on the back); all trained with 3 landmarks.

Found bees can count to which number?

Answer 7

4

Even when transferred to novel items

Question 8

If the experimental design is not done properly, we can undermine animals’ ability, thus animals can underperform during numerical competence tasks.

Answer 8

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