Midterm 3 Flashcards
Nativist perspective of number representation
our ability to have number representation goes beyond sensory information; not based on our environment; some parts are innate; core knowledge of numbers in infants and adults
Empiricist perspective of number representation
number representations are sensory representations; capacity to form associations; all parts of number representation are learned; knowledge of numbers are constructed from sensory representations
three of the four systems underlying number representation
shared with other animals
experiment found different parts of the brain activate when you are calculating exact numbers or approximate numbers
left inferior frontal –> exact
bilateral parietal –> approximate
four systems underlying number representation
ratio, representations are abstract, can add/subtract representations, positive integers
number sense
the sense that there are numbers and there are different numbers/different quantities of things
the number sense is…
evolutionarily ancient; available to rats, pigeons, and monkeys; available to human infants and adults; continuous throughout the lifespan
experiment judging numerosity
quickly flash two images of varying numbers of dots; participants had to judge which image had more dots
OR
quickly flashing an image of dots; participants had to estimate how many dots there were
BOTH WERE SUCCESSFUL
large number representations in adults
1) the ratio signature –> representations are approximate
2) representations are abstract –> cross-modal comparisons are about as easy as visual comparisons
3) representations enter into arithmetic computations –> addition and subtraction
the ratio signature
the discriminability between two numerosities; depends on the ratio
ratio signature and judging numerosity experiment (signature 1)
two images are flashed quickly with different numbers of dots; participants will be more accurate the greater the disparity between the amount of dots in the images
representations are abstract experiment (signature 2)
participants flashed an image of dots and then presented auditorily with a certain number of tones; told to determine which had more; participants still performed well
representations enter into arithmetic computations experiment (signature 3)
participants shown two images and a separate third image; asked if the addition of the first two images is less or more than the third image; participants performed estimations well
large number representations in infants
habituate the infant to several different images that each contain 8 dots; then, present the infant an image of 16 dots; infant will stare longer at the image of 16 dots because it is a new number of dots
critical ratio for infants vs. for adults
infants = 2.0
adults = 1.15
suggests ratios are learned to a certain extent
two possibilities as to why the ratio may decline with age
1) experience with symbolic numbers –> counting and mathematics education
2) maturation and non-specific experience –> development of visual acuity
study by Xu and Arriaga (2003)
suggests maturation and non-specific experience decreases the ratio because generally do not really teach an infant anything about numbers between 6 and 9 months
signature 2 (abstraction) in infants
habituation of head orientation toward a sound source (Lipton’s task); two speakers on either side; present 8 tones until the infant gets bored; during the test, the infant is presented with 8 tones again or 16 tones; infant will orient their head toward the 16 tones because it is new
signature 3 (arithmetic operations) experiment
infants presented with a screen displaying five objects that drop down from the top of the screen to the bottom; then, an occluder rises to cover the objects; five additional objects emerge from the side and go behind the occluder; the occluder drops to reveal either five objects or ten objects; results found that the infants looked longer when the occluder dropped to reveal five objects because they were surprised; similar results for same experiment but with subtraction
infant number representation
display all three signatures of number representation that adults do; before they learn counting or symbolic arithmetic, infants represent and discriminate large numerical magnitudes; number representations are approximate and show a signature ratio limit; precision of numerical discrimination increases over infancy, similar to other perceptual functions
testing number representation in non-human animals
Skinner rat experiment: trained rats to press a lever to receive food pellets; rat learns how many lever presses it takes to receive the food; deviation slightly from the desired amount of presses on average; deviation grew as the number of presses increased; shows a ratio limit
Tamarin monkeys and number representation
habituate monkeys to a certain number of tones; at the test phase, either present the monkey with the same number of tones or a different number; if the monkey is surprised they’ll go to the side of the cage where the tone came from and make a fuss; ratio limited; similar to what a 9-month-old human infant can do with number representations and tones (similar ratio signatures)
Capuchin monkeys and number representations
put two capuchin monkeys side-by-side and have them both complete the same task then give them both cucumbers; repeat the same procedure but one monkey gets grapes and the other gets cucumber; monkey that got the cucumber becomes upset; shows the monkeys understand unequal pay; understanding ratios on a social level
abstract number representations in non-human animals
place a rat in a box with two levers; trained to know that if the light flashes twice, they should hit the left level but if the light flashes eight times, they should hit the right lever –> receive food; if the light flashes twice, 10% of the time the rat will press the correct lever; if the light flashes four times, 50% of the time the rat will press the correct lever; if the light flashes eight times, 90% of the time the rat will press the correct lever; same procedure but with tones found the same findings; evidence for cross-modal transfer/abstraction
Island of Cayo Santiago experiment with 800 wild monkeys
show the monkeys a box, drop two lemons into the box, then drop a third into the box, then show that there are three total in the box –> monkey is bored; show the monkeys a box, drop two lemons into the box, then drop two more lemons into the box, then show that there are three lemons total in the box –> monkey is surprised; shows that wild monkeys can innately do addition and subtraction
large number representations in non-human animals
represent large, approximate numerosities; the same ratio and cross-modal signatures as those of human infants and adults
the Parahã
semi-nomadic hunter-gatherers in lowland Amazon; no external representations (writings, art, toys, etc.); only have words that mean “one”/”a few”, “two”/”some”, and “many”; experimenter gave participants a piece of paper with 1 tally, 2 tallies, 3 tallies, 4 tallies, and 5 tallies; told to recreate each set of tallies; difficulty recreating the tallies past 3 and impossible past 6; found they are not capable of representing large exact numbers; one of the only cultures known that does not have exact number representation (because their culture does not need it)
24 months
start counting
30 months
understand the meaning of “one,” but think all other number words mean “plural” or “some”
36 months
understand the meaning of “two” but think all other number words mean “more than two”
40 months
understand the meaning of “three,” but think all other number words mean “more than three”
45 months
children figure out that +1 in the count list means one more object in a set
understanding of positive integers
does not come until 45 months of life
origins of natural number
primate heritage, human evolution
primate heritage
representations of objects; approximate number representations; singular/plural; serial order
human evolution
explicit symbol system (words); conceptual change capabilities; analogy, inference to best explanation