Lecture 3 - Learning by Number Flashcards
What does comparative psychology ask?
How do animals do these things
Is it the same way humans do them
Need to do analysis tasks to ask these questions
Learn more about our abilities too
What is associative learning
Works in all animals
Doesn’t just glue things that occur together - sensitive correlations
Track causal relationship
Connectionist networks - language, pattern recognition
What abilities are involved in numerical competence
- Relative numerosity discrimination
- Absolute number discrimination
- Ability to count
- Ability to do arithmetic
What is relative numerosity discrimination
Ability discrimination between sets of items on basis of relative number items they contain
Discriminate many from few
Who was the first person to research Relative Numerosity Discrimination
Koehler 1913
Given raised dots
Choose which fewer dots
Especially good with pigeons
Outline Emmerton, Lohmann and Niemann 1997 study on relative numerosity discrimination
Trained pigeons to discriminate between few and many items
Discriminated between few and many pictures in box.
Pecked red button when few items. Pecked green button when menu items. Face value present
Criticism of Emmerton, Lohmann and Niemann 1997
Birds are ignoring numbers, and instead using another feature of display
Don’t have to pay attention to number dots on screen
Rule this out by inversing display
Generalise responses
What is the concept of absolute number
Understand that 4 bananas and 4 elephants have something in common
I.e. number is not intrinsically related to what you are counting
Outline Koehlers concept of absolute number
Jakob the raven could choose a pot with 5 spots from array, even when size spot varied 50 fold
Outline Matsuzawa 1985 concept of absolute number
Chimp called Ai had to select 1 of 6 responses keys (labelled 1-6) when shown array of red pencils, with 1-6 pencils per array
Achieved greater 90% accuracy
Criticism of Matsuzawa 1985 concept of absolute number
Not necessarily same as counting. Animals could be learning about specific perceptual pattern - perceptual matching (look similar nothing to do with number)
Matsuzawa counter argument to criticism
Ai could transfer her ability to arrays of different types of items
What is the perceptual matching problem
Number confounded with other factors such as time (items presented serially) and space (items presented simultaneously)
Are animals using these cues?
Is size of display controlling response? Smaller number items takes up less space
How did Pepperberg 1994 try to address perceptual matching problem
Alex the parrot about number of blocks that were green, or blue, or red
What is a sample trial of Pepperberg 1194 and Alex the Parrot
1 orange chalk, 2 orange wood, 4 purple wood and 5 purple chalk
How many purple wood?
Used seeing smaller number items and can perceive directly. Larger numbers physically count
What is the alternative explanation of Subitising
Perception at a glance of number items present without counting them successively
Maximum number items be counted this way is 5
If you are counting then RT increase with every time
How does effect size criticise the Subitising approach
Effect of display size with displays less than 5 items
Takes longer perceive twoness than oneness etc
Even with small displays we are using a counting process
Outline Meck and Church 1983 study on serially presented items
Rats trained 2 signals - 2 or 8 pulses
After 2 - press left lever
After 8 - press right lever
Criticism of Meck and Church 1983 original study
We’re animals responding on basis of total time rather than number pulses?
Meck and Church 1983 experiment 2 on serially presented items
Both stimuli lasted 4 seconds 2 bursts or 8 bursts light If rats were responding based on stimulus durations this task be impossible Continue to respond correctly Evidence against perceptual matching
Outline Davis and Bradford 1986 study on rats
Rats access to plank with food pellets on
Eat rat designated number pellets to eat
Ate right amount rewarded. Ate more shouted at.
Continued to get it correct even when no longer rewarded. Transferred to sunflower seeds
Train and generalise
Outline Capaldi and Miller 1988 study on rats
Rats trained runway sometimes with food at end.
Rats expect food they run fast
Trained following sequences RRRN and NRRRN
Learn to anticipate final N trial and run slow
Generalised to other rewards e.g. coco pops
Helmand and Gallistel 1978 study on the ability to count
Counting involved mapping numerosity (property display) onto label represented numerosity
Animals use nonverbal labels = numerons
Outline concept of Absolute Number
Understand 4 bananas and 4 elephants have something in common i.e. number is not intrinsically related to what you are counting
Outline Koehler study on Absolute Number
Jakob the raven could choose pot with 5 spots from array, even when size spots varied 50-fold
Outline Matsuzawa 1985 study on the concept of Absolute Number
Chimp Ai had select 1 of 6 response keys when shown arrays red pencils, with 1-6 pencils per array. Achieved > 90% accuracy
Outline criticism of Matsuzawa 1985 study
Not necessarily counting, could be learning specific perceptual pattern - perceptual matching (look similar nothing to do with number)
What is Matsuzawa counter-argument
Ai could transfer her ability to array different types of item. Not just perceptual matching
Outline Perceptual Matching Problem
Number confounded with other factors such as time (serial items) and space (simultaneous).
E.g. smaller number items takes up less space. Size display control response?
Act as cues?
How did Pepperberg 1994 try to rule out use of visual arrays?
Alex the Parrot about number blocks green, blue or red in mixture blocks.
Are animals subitising?
Perception at a glance of number items present, without counting them successively, max number items counted 5.
If counting RT increase every item.
Subitising little increase RT per item for low numbers items.
Number bigger 6, have count each one.
Criticism of animals Subitising?
Effect of display size with displays less than 5 items or less. Takes longer perceive “twoness” than “oneness”. Suggests even with small displays we are using counting process
Outline Meck and Church 1983 study on serially presented items
Rats trained 2 and 8 pulses white noise. After 2 pulses rewarded left lever. After 8 rewarded right lever.
But were animals responding on basis total time (8 pulses longer present), rather number pulses?
Outline Meck and Church 1983 study number 2 on serially presented items
Devised test both stimuli lasted 4 seconds. Presented 2 bursts or 8 bursts light both lasting 4 seconds causing them pay attention. If responding based stimulus durations task be impossible. Continue to respond correctly.
Evidence against perceptual matching.
Outline Davis and Bradford 1986 study on rats
Access plank with food pellets. Each rat designated number pellets eat. Ate more = experimenter shouted NO. Eat right amount = rewarded. Continued get correct even when no longer rewarded. Transferred sunflower seeds. Train and generalise
Outline Capaldi and Miller 1988
Rats trained runway, sometimes food end. Rts expected food run fast. Trained following sequences reinforced trials and non-reinforced trials. Learn anticipate final N trial and run slow.
Not result of time.
Same findings for coco pops.
Outline Gelman and Gallistel 1978 study on the Ability to Count
Mapping numerosity- property display onto label represented numerosity.
Animals nonverbal labels call numerons.
What are the 3 principles involved in counting
- One-to-One counting
- Stable-Order principle
- Cardinal-Principle
Outline principle involved in counting
- One-to-One counting - each item assigned only 1 numeron
- Stable-Order principle - numerons always assigned same order
- Cardinal-Principle - final numeron assigned applies whole display
Implies knowledge order labels. Relative quantity (ordinal scale) and size difference between each item same (interval scale)
Outline Biro and Matzuzawa 2000 study of the representation of number in chimps
Ai trained touch Arabic numerals ascending order
Some argued rote learning particular stimulus-response sequence - no knowing quantitative relation between numbers
Outline Brannon and Terrace 2000 study on the representation of number in chimps
Chimps trained order arrays 1-4. Learn ascending and descending orders but not arbitrary order.
Generalise from ascending order immediately to higher numbers. Descending order only generalise after further training. Implies limited understanding ordering quantities.
Outline Pepperberg 2000 study
Alex the Parrot. Knew naming quantities and identifying numbers - not about applying numbers to quantities
Perform better than chance from start - relate written numbers with quantities
Outline the ability to do arithmetic
Perform addition, subtraction, some extent by rote learning
But mathematical competence allow operations be generalised new situations in way implies concept number
Outline Boysen and Berntson 1989 study on maths in chimps
Chimp Sheba trained label arrays counters, then Arabic numerals. e.g. when presented item, press number 1. Generalised to everyday objects. Final test: number oranges hidden lab. Sheba find them. Pick Arabic number represented sum all oranges. After 12 training sessions 85% correct.
Outline the issues with Boysen and Bernston 1989 study with Sheba
Argue she memorised all ways of adding to total of 4
Effects of contextual variables. Animals can be more competent than they appear
Counter-argument of criticisms of Boysen and Bernston 1989 study with Sheba
Sheba also perform accurately when experimenters hid cards with numbers written on, rather than oranges. Performed above chance straight away. Implies understanding interval scale. If she only understood that 1 number bigger than another she would have chosen 4 as often as 3.
Outline Boysen and Bertson 1995 study
Chimp A choice between 2 amount candy. Whichever chimp A chose was then given to chimp B, Chimp A got the unchosen one.
It was in Chimps A interest choose smaller quantity so it could eat larger.
Completely unable solve this task. Unless candy substituted by numerals.
Evidence cant count? Or cant resist a treat?
