Numbers Flashcards
Numbers is a type of
Comparative psychology
Associative learning works in all animals – and it is clever!
Doesn’t just glue things that occur together – sensitive to correlations – can track causal relationships
…and in man they can do complex stuff: connectionist networks – language, pattern recognition
but can associations do everything? or are there other learning mechanisms involved?
What abilities are involved in numerical competence?
1) Relative numerosity discrimination
2) Absolute number discrimination
3) Ability to count
4) Ability to do arithmetic
Relative numerosity discrimination
Ability to discriminate between sets of
items on the basis of the relative number
of items that they contain.
First to try was Koehler c. 1913
Emmerton, Lohmann & Niemann 1997
trained pigeons
to discriminate
between “few”
(1/2 items)
and “many”
(6/7 items)
.. but are the birds ignoring number, and instead using some other feature of the display?
Concept of absolute number
understanding that 4 bananas and 4 elephants have something in common…
… i.e. number is not intrinsically related to what you are counting
Koehler again…
Jakob the raven could choose
a pot with five spots from an array, even when
size of spots varied 50-fold
Matsuzawa (1985):
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.
Perceptual matching
But this is not necessarily the same as counting….
Animals could be learning about specific perceptual pattern
perceptual matching problem again…
often number is confounded with other factors such as time
(for items presented serially) and space (for items presented
simultaneously). Are animals using number or these other cues?
e.g. smaller number of items also takes up less space.
Is it the size of the display controls the response, not number ??
Pepperberg, 1994
with visual arrays there is always going to be something like this.. so hard to rule out but people have tried in various ways
Are the animals subitising?
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 ”
If you are counting then RT should increase with every item
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
whereas 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
This implies that you do not need to count displays of five items
or less – the number is perceived immediately
But is this true?
However, there is an effect of
display size with
displays of
less than five items – it takes
longer to perceive “twoness”
than “oneness”, and so on
This suggests that even with
small displays we are using a
counting process
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 were animals responding on the basis of the total time,
rather than number of pulses?
To investigate this, they devised a test in which both stimuli lasted
4 seconds:
If rats were responding on the basis of stimulus duration,
this task should be impossible
but they continued to respond correctly
Church & Meck, 1984
The rats were also tested with pulses of light -- and continued to respond appropriately (Church & Meck, 1984).
This is more evidence against perceptual matching
Can you think of any other confounds?
.. or can make animal respond a fixed number
of times – no array involved
