PSY210 ch7

What are the three broad divisions that children make?

• forming broad divisions for inanimate objects, people, and other animals is crucial because different types of concepts apply to different types of objects

  • forming these general categories of objects allows children to draw accurate inferences about unfamiliar objects

• category hierarchies = a

What are category hierarchies?

• category hierarchies = a category that is organized by sub-set relations, such as animal/dog/poodle

  • greatly simplifies the world for children by allowing them to draw accurate inferences

What did Quinn and Eimas find when showing 3-4-month olds photos of cats?

• Quinn and Eimas (1996) -> when 3- and 4-month olds were shown a series of photographs of cats, they habituated to the general category of cats

  • when infants were subsequently shown a picture of a dog, lion, or other animal, they dishabituated

  • their habituation to the cat photographs suggests that the infants saw all the cats, despite their differences in colour, size, etc.

  • their subsequent dishabituation to the photo of the other animal suggests that they saw those creatures as members of categories other than cats

What did Bel-Chadha find when showing 6-month-olds pictures of mammals?

• Behl-Chadha (1996) -> 6-month-olds habituated after being shown pictures of different types of mammals and dishabituated when they were shown a picture of a bird/fish

What is perceptual categorization?

• perceptual categorization = the grouping together of objects that have somewhat similar appearances

At age 2, how do children increasingly categorize objects?

• during age 2, children increasingly categorize objects on the basis of overall shape

  • e.g. when toddlers are shown an unfamiliar object and told it is a “dax,” they assume that other objects of the same shape are also “daxes,” even though the objects differ from each other in size, texture, and colour

  • we rarely do the same if we know only the object’s colour, size, or texture

  • reliance on shape for categorization emerges early in development

    • e.g. when 15-month-old Canadian infants were shown an unfamiliar object with a specific property, they assumed that objects of the same shape also share that property even when the objects differ from one another in size and colour

Define superordinate level, subordinate level, and basic level.

• superordinate level = the general level within a category hierarchy (e.g. animal in animal/dog/poodle)

• subordinate level = the most specific level within a category hierarchy (e.g. poodle in the animal/dog/poodle example)

• basic level = the middle level, and often the first level learned, within a category hierarchy (e.g. dog in animal/dog/poodle example)

What category hierarchy do children form first?

• children tend to form basic-level categories first

  • subordinate-level categories have the same consistent characteristics as the basic-level category and some additional ones

  • it’s relatively difficult to discriminate amongst different subordinate categories within the same basic-level category (e.g. maples vs oaks)

How do parents and others use children’s basic-level categories to teach them more general categories?

• parents and others use children’s basic-level categories as a foundation for explaining more specific and more general categories

  • when parents teach children superordinate categories (e.g. furniture), they typically illustrate properties of the relevant terms with basic-level examples that the child already knows

  • parents also refer to basic-level categories to teach children subordinate-level terms (e.g. a parent might say “belugas a kind of whale”)

  • sensitivity to the differences between these kinds of statements emerges early in development

Do children have a rudimentary understanding of causal interactions?

• even in the first few months, infants have a rudimentary understanding of causal interactions amongst objects (e.g. interactions involving gravity, inertia, and support)

  • this understanding gradually increases during their first year

  • at 3 months, infants look longer if a box that is released in midair remains suspended rather than falling

When do infants appreciate the relevance of the type of contact involved in support?

• by ~5 months, infants appreciate the relevance of the type of contact involved in support

  • they now know that the box will stay aloft only if it is released on top of the support

  • ~6 months they recognize the importance of the amount of contact, looking longer when a box stays put with only a small portion of its bottom surface on the support

  • shortly after 1st birthday, infants also take into account the shape of the object and are surprised if an asymmetrical object remains stable

Does causal understanding extend to moving and stationary objects?

• causal understanding extends to moving and stationary objects

  • 5-month-olds look longer at an object that travels more slowly as it rolls down a slope than at one that picks up speed as its descends

  • also seem to know that an object cannot pass through a grid with openings smaller than the object but liquids can

What did Kracsum and Andrews find when they told 4-5 year olds about wugs and gillies?

• Krascum and Andrews (1998) -> told 4- and 5-year olds about two categories of imaginary animals: wugs and gillies

  • some preschoolers were provided only physical descriptions

  • other children were provided with physical descriptions and a simple causal story that explained why wugs and willies are the way they are

  • children who were told why wugs and gillies have the physical features they do were better at classifying the pictures into the appropriate categories

  • when tested the next day, those children also remembered the categories better than did the children who were given physical descriptions without explanations

What are headcams and eyecams and how did they help research?

• headcams and eyecams are a technological breakthrough that has helped solve the problem of how to assess infant’s visual understanding in natural settings

  • headcams -> small, lightweight cameras that are attached to the middle of an infant’s forehead to show the environment in front of the infant

  • eyecams -> cameras that point towards an infant’s eye to record the part of the environment towards which the infant is looking

  • studies using headcams and eyecams have shown what infants watch, the locations where their looking occurs, the parts of their own bodies at which they look, the objects they examine, etc.

  • infants look most at other people

What is naïve psychology and what are the three concepts and three properties?

• naïve psychology = a commonsense level of understanding of other people and oneself

  • 3 concepts -> desires, beliefs, and actions

  • 3 properties -> many refer to invisible states; psychological concepts are linked to one another in cause-effect relations; they develop surprisingly early in life

Describe naïve psychology in infancy.

• nativists believe that early understanding is possible only because children are born with a basic understanding of human psychology but empiricists argue that experiences with other people and general information-processing capacities are the key sources of the early understanding of other people

Do infants have an implicit-self-consciousness?

 

• infants seem to be born with a kind of implicit self-consciousness, a rudimentary understanding that they are separate from other people and can act in ways that accomplish their goals

  • 4 months -> infants show basic understanding of what they can and cannot do

  • 18-34 months -> infants try to wipe smudges off their faces when they see them in mirrors and make efforts to look good to other people, reflecting a more explicit kind of self-consciousness

Do infants prefer looking at people’s faces or the same parts arranged haphazardly?

• infants prefer to look at other people’s faces and movements of cartoons of human bodies over cartoons showing the same parts arranged haphazardly but with equal amounts of movement

  • by imitating other people and forming emotional bonds with them, infants encourage more interaction, creating additional opportunities for the infants to acquire psychological understanding

  • these interactions help infants learn both about people in general and about differences between individuals

What did Woodward find when showing 6-month-olds goal-direct behaviour?

• Woodward (1988) -> 6-month-olds saw a hand repeatedly towards one of two objects sitting side by side in a display

  • then the position was reversed and the hand reached again

  • infants looked longer when hand went to the object they had not reached for previously

  • infants even move their eyes to the goal object before the hand gets there

  • this is only true when a human hand does it, doesn’t work if it’s a mechanical claw

Are 10-month-olds more likely to choose a food offered by a speaker of their language or another language?

• e.g. 10-month-olds are more likely to choose a food offered or by a speaker of their language than by a speaker of another language and more likely to select a toy that was previously held by someone who speaks their language

What aspects of psychological understanding emerge in second year?

• several important aspects of psychological understanding emerge in second year -> a sense of self, joint attention, intersubjectivity

  • includes some insight into other people’s emotions

  • experiences with own emotions and what soothes them when they are upset is the basis for such insights

What is theory of mind?

• theory of mind = an organized understanding of how mental processes such as intentions, desires, beliefs, perceptions, and emotions influence behaviour

  • understanding the connection between other people’s desires and their actions emerges by the end of the first year

  • understanding that desires lead to actions is firmly established by 2 years

  • by 3 years, children show some understanding of the relation between beliefs and actions

How are 3-year-olds’ understanding of the relation between people’s beliefs and actions limited?

• 3-year-olds’ understanding of the relation between people’s beliefs and their actions is limited in important ways

  • false-belief problems = tasks that test a child’s understanding that other people will act in accord with their own beliefs even when the child knows that those beliefs are incorrect

What is the theory of mind module?

• theory of mind module (TOMM) = a hypothesized brain mechanism devoted to understanding other human beings

  • amongst typical children exposed to a typical environment, TOMM matures over the first five years, producing an increasingly sophisticated understanding of people’s minds

  • studies with children with ASD are often cited to support the idea of TOMM

    • some children with ASD have difficulty with false-belief problems and understanding people more generally

    • consistent with the idea of a TOMM< one reason for these differences in understanding the social world appears to be atypical sizes and activity of certain brain areas that are crucial for understanding people

What do empiricist theorists suggest for the emergence of theory of mind?

• theorists who take an empiricist stance suggest different explanations for the emergence of theory of mind

  • some emphasize learning from experiences with physical situations and with other people

  • other empiricist research emphasizes interactions with other people

  • others emphasize growth of general information-processing skills as essential to understanding other people’s minds

    • they cite evidence that children’s understanding of false-belief problems is substantially correlated with their ability to reason about complex counterfactual statements and with their ability to inhibit their own behavioural propensities when necessary

    • ability to reason about counterfactual statements is important because false-belief problems require children to predict what a person would do on the basis of a counterfactual belief

    • ability to inhibit behavioural propensities is important because false-belief problems also require children to suppress the assumption that the person would act on the truth of the situation as the child understands it

What is pretend play?

• pretend play = make-believe activities in which children create new symbolic relations, acting as if they were in a situation different from their actual one; between 12-18 months

  • object substitution = a form of pretense in which an object is used as something other than itself, for example, using a broom to represent a horse

  • often emerges in interactions between infants and their parents in those societies that emphasize such interaction

What is sociodramatic play?

• sociodramatic play = activities in which children enact miniature dramas with other children/adults, such as “parent comforting baby”

  • young children’s sociodramatic play is typically more sophisticated when they engage with a parent/older sibling who can scaffold the play sequence than when they are pretending with a peer

How does play evolve in elementary school?

• by elementary school, play becomes more complex and social

  • begins to include activities (e.g. sports and board games) which have conventional rules that participants must follow

  • pretend play can extend into weekly at ages 10-11 and monthly at 12-13 years old

How does pretend play expand children’s understanding of the social world?

• pretend play may expand children’s understanding of the social world

  • children who engage in greater amounts of pretend play tend to show greater understanding of other people’s thinking and emotions

  • social pretend play is more strongly related to understanding other people’s thinking than is nonsocial play

  • preschoolers also learn from watching others’ pretend play

Describe 4-5 year olds’ understanding of living things.

• by the time children are 4-5 years old, their fascination with living things translates to biological knowledge

  • however, there are a variety of immature beliefs and types of reasoning

    • e.g. children often fail to understand the difference between artifacts, such as chairs and cars, and living things, such as monkeys

  • they also have incorrect beliefs about which things are living and which are not

    • e.g. most 5-year-olds believe that plants are not alive, and some believe that moon and mountains are alive

  • some investigators conclude that children have only a shallow and fragmented understanding of living things until they are 7-10 years old

  • other investigators believe that by age 5 years, children understand essential characteristics of living things and what separates from nonliving things but are just confused on a few point

  • others believe that young children simultaneously possess both mature and immature biological understanding

Do infants act differently towards other animals than they do people?

• infants act differently towards other animals than they do towards people

  • e.g. 9-month-olds pay more attention to rabbits than they do to inanimate objects, but they smile less at rabbits than they do at people

How do 1-year-olds distinguish between people, other animals, and inanimate objects?

• infants in their first year distinguish people from other animals and that they distinguish both from inanimate objects

  • reactions don't indicate when children construct a general category of living things that includes plants and animals or when they recognize humans as a type of animal

  • it's difficult to assess knowledge of these and many other properties of living and nonliving things until age 3-4 years old, when children can comprehend and answer questions about these categories

    • by this age, they clearly know quite a bit about similarities amongst all living creatures and about the differences between living creatures and inanimate objects

  • their knowledge of living things includes visible properties (e.g. having legs, moving) and biological processes (e.g. digestion and heredity)

    • through 5-6 years old, many children deny that people are animals

What do infants and children understand about plants? 

• understanding the life status of plants is a challenge to young children

  • most preschoolers know that plants, like animals but unlike inanimate objects, grow, heal themselves, and die

  • however, most preschoolers believe that plants are not alive

  • it's not until age 7-9 years that a clear majority of children realize that plants are living things

  • letting 5-year-olds know that plants bend towards sunlight and that their roots grow toward water leads the children to conclude that plants, like animals, are living things

• culture and direct experience influence at which children understand that plants are, in fact, alive

  • e.g. children growing up in rural areas realize that plants are living things at younger ages than do children growing up in cities/suburbs

What do preschoolers understand about biological processes?

• preschoolers understand that biological processes (e.g. growth, digestion) differ from psychological ones

• preschoolers also recognize that properties of living things often serve important functions for the organism, whereas properties of inanimate objects don't

  • 5-year-olds recognize that the green colour of plants is crucial for them to make food, whereas the green colour of emeralds has no function for the emerald

What do children understand about heredity?

• 3-4 year olds know nothing about DNA/mechanisms of heredity but do know that physical characteristics tend to be passed on from parent to offspring

  • e.g. they predict that a baby mouse will eventually have hair of the same colour as its parents

• most older preschoolers also know that certain aspects of development are determined by heredity rather than by environment

  • e.g. most 5-year-olds realize that an animal of one species raised by parents of another species will become an adult of its own species

• there are numerous misguided beliefs about inheritance

  • many preschoolers believe that mothers' desires can play a role in their children's inheritance of physical qualities

  • preschoolers also believe that adopted children are at least as likely to look like their adoptive parents as like their birth parents

• essentialism = the view that living things have an essence inside them that makes them what they are

  • e.g. most preschoolers believe that puppies have a certain "dogness" inside them

  • this essence is viewed as being inherited from one's parents and being maintained throughout the organisms' life

What do preschoolers understand about growth, illness, and healing?

• preschoolers realize that growth is a product of internal processes

  • e.g. they recognize that plants and animals become bigger and more complex over time because of something going on inside them

• preschoolers show a basic understanding of illness

  • 3-year-olds have heard of germs and have a general sense of how they operate

  • e.g. they know that eating food that is contaminated with germs can make a person sick, even if the person is unaware of the germs' presence

• preschoolers know that plants and animals, unlike inanimate objects, have internal processes that often allow them to regain prior states/attributes

  • e.g. 4-year-olds realize that a tomato plant that is scratched can heal itself and that an animal's hair can grow back after being cut, but that a scratched chair cannot heal itself and that a doll's hair cannot grow back

  • preschoolers also understand that both illness and old age can cause death, from which no recuperation is possible

How do nativists explain how children acquire biological knowledge?

• nativists propose that humans are born with a "biological module" much like the TOMM

  • this brain structure/mechanism helps children learn quickly about living things

  • nativists use 3 main arguments to support the idea that people have a biology module

    • during earlier periods of our evolution, it was crucial for human survival that children learn quickly about animals and plants

    • children throughout the world are fascinated by plants and animals and learn about them quickly and easily

    • children throughout the world organize information about plants and animals in very similar (in terms of growth, reproduction, inheritance, illness, and healing)

How do empiricists explain how children acquire biological knowledge?

• empiricism maintains that children's biological understanding comes from their personal observations and from information they receive from their parents, teachers, and the general culture

  • e.g. when mothers read to 1-2 year olds about naimals, many of their comments suggest that animals have intentions and goals, that different members of the same species have a lot in common, and that animals differ greatly from inanimate objects

  • such teaching is often elicited by children's questions

  • children's biological understanding reflects the views of their culture

    • e.g. 5-year-olds in Japan are more likely than their peers in the US and Israel to believe that nonliving things and plants are able to feel physical sensations, which echoes Buddhist tradition, which views all objects as having certain psychological properties

How do nativists and empiricists disagree about the origins of understanding of physics?

• nativists and empiricists disagree about the origins of understanding of physical cause

  • nativists propose that infants possess an innate causal module/core theory that allows them to extract causal relations from the events they observe

  • empiricists propose that infants’ causal understanding arises from their observations of innumerable events in the environment and the causal effects of their own actions

  • both sides agree that children show impressive causal reasoning from infancy onwards

When can children infer causal impact?

• by end of age 2, children can infer the causal impact of one variable based on indirectly relevant information about another

What is the “blicket detector” experiment?

 

• Sobel and Kirkham (2006) -> presented 19- and 24-month olds with a box called a “blicket detector” that played music when a type of object called a blicket was placed on it

  • experimenter simultaneously placed objects A and B on the blicket detector and the music played

  • experimenter placed object A alone on blicket detector and the music dind’t play

  • children were asked to turn on blicket detector

  • 24-month-olds consistently chose object B, suggesting that seeing the ineffectiveness of object A led them to infer that object B must be the blicket

  • 19-month-olds chose object A as often as object B, suggesting they didn’t draw this inference

How is causal reasoning in preschool?

• preschoolers seem to expect that if a variable causes an effect, it should do so consistently

  • when 4-year-olds see a potential cause produce an effect inconsistently, they infer that some variable that they cannot see must cause the effect

    • when the same effect occurs consistently, they don’t infer that a hidden variable was important

What is the nativist/empiricist debate about spatial thinking?

• nativist/empiricist debate about spatial thinking

  • nativists argue that children possess an innate module that is specialized for representing and learning about space and that processes spatial information separately from other types of information

  • empiricists argue that children acquire spatial representations through the same types of learning mechanisms and experiences as those that produce cognitive growth in general, that children adaptively combine numerous types of spatial and non-spatial information to reach their goals, and that experience with locomotion, language, and cultural tools (e.g. jigsaw puzzles) shapes spatial development

What do nativists and empiricists agree on about spatial thinking?

• issues that nativists and empiricists agree on

  • early in infancy, children show impressive understanding of some spatial concepts (e.g. above, left)

  • self-produced movement around the environment stimulates processing of spatial information

  • certain parts of the brain are specialized for coding particular types of spatial information (e.g. hippocampus appears to produce improvements in place learning) 

  • geometric information (information about lengths, angles, and directions) is important in spatial processing 

How do infants and children represent space relative to themselves?

• from early in infancy, children code the locations of objects in relation to their own bodies

• over the ensuing months, infants’ representations of spatial locations become increasingly durable, enabling them to find objects they observed being hidden just moments earlier

  • e.g. 7-month-olds reach to the correct location for objects that were hidden 2 seconds earlier under one of two identical opaque covers but not for objects hidden 4 seconds earlier; most 12-month-olds accurately reach for objects hidden 10 seconds earlier

  • increasingly enduring object representations partially reflect brain maturation, particularly of dorsolateral prefrontal cortex (area in frontal lobe that is involved in formation and maintenance of plans and in the integration of new and previously learned information)

  • improved object representations reflect learning as well

What is egocentric spatial representations?

• egocentric spatial representations = coding of spatial locations relative to one’s own body, without regard to the surroundings

  • only kind of spatial coding that infants can do according to Piaget

  • however if toys are hidden adjacent to a distinctive landmark, infants usually find the toy despite changes in their own position

How does self-locomotion enhance older children’s spatial coding?

• a major factor in helping infants acquire a sense of space independent of their location is self-locomotion

  • infants who crawl/have had experience propelling themselves in walkers more often remember the locations of objects on object-permanence task

  • similar to how being a driver enhances their representation of space better than being in the passenger seat

How does self-locomotion enhance older children’s spatial coding?

• self-locomotion also enhances older children’s spatial coding

  • e.g. kindergarteners were asked to stand in place and imagine themselves walking from their seat in the classroom to the teacher’s chair and then turning around to face the class

    • next they were asked to point from this imagined position in the classroom to the locations of various objects within it

    • other kindergarteners were instructed to actually walk through their kitchen and turn around as they imagined themselves to the teacher’s chair and then turning to face the class, and they were much more accurate

How do puzzles contribute to spatial development beyond infancy?

• assembling puzzles also contributes to spatial development beyond infancy

  • children who played with puzzles more often than their peers between their 1st-4th birthdays were more successful than 4.5 year olds on a spatial transformation task

Do blind children have spatial awareness?

• blind children can represent space impressively well despite their vision loss but the lack of visual experience also imposes some limitations on their sense of space

How does development influence infants choosing alternative potential landmarks?

• with development, infants become increasingly able to choose amongst alternative potential landmarks

  • e.g. when 12-month-olds are presented a single yellow cushion, a single green cushion, and a large number of blue cushions, they have little trouble finding an object hidden under either the yellow/green cushion

  • e.g. by 5 years old, children can represent an object’s position in relation to multiple landmarks (e.g. midway between a tree and a streetlamp

How do toddlers and infants struggle with spatial representation without landmarks?

• children, like adults, have more difficulty forming a spatial representation when they move around in an environment without distinctive landmarks/when the only landmarks are far from the target location

• toddlers show some degree of navigational ability

• precisely coding locations in the absence of straightfowards landmarks continues to be difficult for people well beyond 2 years of age

  • 12-year-olds are better but even some adults vary a lot in their abilities to form this type of spatial representation

• the degree to which people develop spatial skills is strongly influenced by the importance of such skills in their culture

  • e.g. spatial ability is essential within Aboriginal culture in Australia because much of life consists of long treks between distant water holes

Do infants have a sense of order and duration of events?

• infants know the order in which events occur from as early as the capability can be effectively measured

  • 3-month-olds were presented a series of interesting photos, alternating from left to right, and within 20 seconds, they began to look at the side where each new photo was to appear even before the photo was presented

• infants also have approximate sense of duration of events

  • 4-month-olds saw periods of light and darkness alternate every 5 seconds for 8 cycles and then the pattern was broken by the light failing to appear

    • within half a second of the break, infants’ heart rates decelerated, a change that is characteristic of increased attention, suggesting that infants had a rough sense of the 5-second interval, expected the light to go on at the end of the interval, and increasing their attention when it didn’t appear

Can infants discriminate between longer and shorter durations?

• infants can discriminate between longer and shorter durations

  • 6-month-olds discriminate between 2 durations when their ratio is 2:1 (e.g. 1 second versus 0.5 second) but not when the ratio is 1.5:1 (e.g. 1.5 seconds versus 1 second)

  • 10-month olds discriminate when ratio of durations is 1.5:1

Do preschoolers possess knowledge about longer periods?

• preschoolers possess some knowledge about longer periods

  • e.g. when asked which of 2 past events occurred more recently, most 4-year-olds knew that Valentines (which had happened a week before the experiment) happened more recently than Christmas (which had happened 7 weeks earlier)

    • only answered questions accurately when the more recent event was quite close in time and much closer than the less recent one

How does the ability to distinguish more precisely past events and future events develop?

• ability to distinguish more precisely amongst the timing of past events develops slowly during middle childhood

  • e.g. when children who had been presented a distinctive classroom experience were asked 3 months later to recall the month in which the experience occurred, correct recall increased from 20% in 5-year-olds to 46% among 7-year-olds to 64% in 9-year-olds 

• understanding of timing of future events also increases during middle childhood

  • e.g. 5-year-olds predict a week after Valentine’s Day that the next Valentine’s Day will come sooner than the next Halloween but 6-year-olds generally predict correctly

  • improvement in children’s sense of future time between ages of 5-6 years is probably influenced by their experience in kindergarten classrooms, where the cycle of seasons, holidays, and daily routines is often emphasized, and increases in language abilities

Are children subject to illusions about time?

• children are subject to certain illusions about time in part because of the role attention plays in time perception

  • e.g. when 8-year-olds’ attention is focused on the passage of time, they perceive the duration as longer than the same interval when they aren’t anticipating a prize

How does reasoning about time improve?

• during middle childhood, children become increasingly proficient at reasoning about time

  • they become able to infer that if 2 events started at the same time, but one event ended later than the other, then the event that ended later lasted longer

• children as young as 5 years can sometimes much logical inferences about time but only in simple, straightfowards situations

  • e.g. 5-year-olds who see two toy trains travel in the same direction on parallel tracks and one train stops farther than the track, they usually say that the train that stopped farther down the track travelled for a longer time, even if the trains started moving from corresponding positions on the tracks and started and stopped at the same time

What is the nativist/empiricist debate about numbers?

• nativist/empiricist debate about numbers

  • nativists argue that children are born with a core concept of number that includes special mechanisms for representing and learning about the relative numbers of objects in sets, counting, and approximate addition and subtraction

  • empiricists argue that children learn about numbers through the same types of experiences and learning mechanisms that help them acquire other concepts and that infants’ numerical competence is not as great as nativists claim

    • also claim existence of large differences in numerical understanding amongst children from different cultures

What is numerical equality?

• numerical equality = the realization that all sets of N objects have something in common

  • newborns already have some sense of numerical equality in a nonlinguistic sense

    • e.g. after repeatedly hearing sets of four identical syllables, with adjacent sets separated by pauses (e.g. “tu, tu, tu, tu,” pause, “tu, tu, tu, tu”), newborns look more at four objects than at 12

What do infants’ discriminations about numerical sets depend on?

• infants’ discriminations between numerical sets depend in large part on the ratio of the number of entities in them

  • Izard et al. (2009) -> newborns showed the same tendency to discriminate 6 and 18 syllables and objects, but not with 4 versus 8, suggesting that they could discriminate the 3:1 ratio but not the 2:1 ratio

• discrimination amongst numbers becomes increasingly more precise during first year and beyond

  • by 6 months, infants discriminate between sets of 2:1 ratios but not 3:2 ratios

  • by 9 months, infants discriminate between 3:2 ratios but not 4:3 ratios

  • by adulthood, many people are able to reliably discriminate 8:7 ratios

• discrimination between very small sets (1-4 objects/events) is more accurate, faster, and less variable than would be expected from the ratios alone

  • e.g. infants discriminate 2 objects from 1 object and 3 objects from 2 objects before they can discriminate larger sets with the same ratio

Can infants perform arithmetic?

• infants can perform approximate arithmetic on these nonsymbolic representations

  • 4-5-month-olds dishabituate when it appears that adding 1 or 2 objects to an initial set of 1 or 2 objects has produced more/fewer objects than the correct number

• Wynn (1992) -> a 5-month-old sees a doll on stage, then the doll is hidden behind a screen

  • infant sees a hand place a hand place a second doll behind the screen and then sees the hand emerge from behind the screen without the doll

  • screen drops down and reveals either one or two dolls

  • most 5-month-olds look longer when there is only 1 doll, suggesting that they expected that 1+1=2 and that they were surprised when they saw only a single object

Can infants count?

• many children begin to count verbally at 2 years old but their initial understanding of what they are doing is severely limited

  • after counting from 1-10, many 2-year-olds don’t know if 3 is bigger than 5 or if 5 is bigger than 3

• learning number of counting words at first occurs number by number

  • after this slow early acquisition period, toddlers seem to realize that these counting words indicate differing quantities, and they subsequently learn the link between number words and the quantities they represent more quickly

• preschoolers also acquire understanding of 5 principles underlying counting

  • one-one correspondence -> each object must be labelled by a single number word

  • stable order -> numbers should always be recited in the same order

  • cardinality -> the number of objects in the set corresponds to the last number stated

  • order irrelevance -> objects can be counted left to right, right to left, or in any other order

  • abstraction -> any set of discrete objects/events can be counted

• the rate at which children learn number words is affected by the language for expressing numbers in their culture

  • Miller et al. (1995) -> most 5-year-olds in China can count to 100+ but most 5-year-olds in the US can’t; this is partly because counting proficiency seems to be the greater regularity in the Chinese number system

What did Piaget hypothesize about the understanding of space, time, and number, and is this still true?

• Piaget hypothesized that infants possess only a general, undifferentiated concept of magnitude, and lack specific concepts of space, time, and number

  • subsequent research has shown that infants can distinguish amongst size, duration, and number

    • e.g. after habituating to different displays with the same numbers of objects, infants dishabituate when the number of objects changes, even though the space occupied by the new objects and the time for which they are displayed is the same as previously

What did Lourenco and Longo find about 9-month-olds’ understanding of space, number, and time?

• Lourenco and Longo (2010) -> found that 9-month-olds have a general sense of magnitude that extends to space, number, and time alike

  • infants were initially habituated to display in which a particular decoration consistently accompanied the larger of 2 stimuli on one of the three dimensions (size of objects, number of objects, or duration of displays of the objects)

  • then infants were presented displays in which the link between decoration and relative magnitude on a different dimension either was maintained/changed

  • e.g. infants who had habituated to a link between black with white stripes and larger size might now see that direction accompanying either the more numerous set/less numerous set 

  • infants dishabituated when decoration that had accompanied the larger size stimulus now accompanied the stimulus that was smaller on another dimension, but not when that decoration accompanied the stimulus that was larger on that other dimension

  • similar results were obtained regardless of whether the habituated dimension was size, number, or time and regardless of whether the dimension that subsequently varied was size, number, or time