Conceptual DevelopmentWhen, Where, Why, and How Many?

Concepts are general ideas or understandings that can be used to group together similar

– Objects– Events– Properties etc.

Concepts help us simplify the world and think more efficiently.

e.g Boy Scout rule for being lost in the woods without foode.g. possible origin of stereotypes?

Perceptual CategorizationGrouping according to similar appearances (size, color, movement..)

• children first categorize according to overall shape, then later by function

• 9-10 month olds expect similar looking objects to perform the same function (e.g. castanets study)• By age 2, children can categorize to determine which actions go with which objects (e.g. knowing if a cup is used to “feed” an animal it can be used to feed a another animal but not a vehicle.)

Using Concepts to make Inferences

Language Concepts

• Language could not be learned without concepts (how would we know how to generalize word meanings?)

• Language can serve to point out NEW concepts (e.g. Xu and Carey--individuation)

• Pragmatics of language can emphasize importance or add weight to concepts (e.g. “carrot-eaters” versus people who eat carrots)

Time: Order of eventsKnowing what happened first, next, and so on…

• 3-month-olds can detect the order of events in a repetitive sequence.

– Pictures are shown alternately at A and B.

– Over time, infants start to anticipate the new picture.

• By 12 months, they can detect the order after only a single exposure to the sequence.

(Baby)Mom

A B

Haith, Wentworth, & Canfield, 1993; Bauer, 1995

Time• 4-year-olds can report that an event (e.g. birthday) that

occurred a week ago was more recent than an event that happened 7 weeks ago (e.g. Christmas)

• If event happened more than 2 mths ago, they aren’t very accurate until age 9

• By age 5, children can accurately estimate durations up to about 30 seconds

• Even young infants possess mechanisms for measuring the duration of arbitrary intervals (e.g., the duration of a tone)

Duration discrimination

6-month-old infants discriminate between tones of differing lengths at a 1:2 ratio, but not a 2:3 ratio.

• Expt. 1 -- 2 vs. 4 sec– Success

• Expt. 2 -- 3 vs. 4.5 sec – Failure

• Expt. 3 -- .5 vs. 1 sec– Success

• Expt. 4 -- .67 vs. 1 sec – Failure

Wynn & vanMarle, 2003

Space

• Infants tend to use egocentric representations

• Can use allocentric system but early in development landmarks must be obvious and right next to object (~9mths)

• Concepts like “next to” or “in between” emerge ~11 mths

Spatial RepresentationSelf-locomotion is important for understanding spatial

relationsExamples: • Visual cliff studies (understanding of depth)• Gap studies• crawlers or infants using walkers remember objects’

locations better than non crawlers of same age. • toy hidden in 1 of 2 wells babies who crawled to the other

side did better than those carried. Driver vs. Passenger in a car analogy!

Hermer & Spelke, 1994, 1996

2-year-olds encoded geometric landmarks but not featural ones even though featural information is more informative. Even rats and adults seem to have a preference for geometric cues over featural cues.

A = ~ 41% B = ~ 7%

D = ~ 45%C = ~ 7%

Spatial Representation

Dead Reckoning and ‘Mental Maps’• The ability to keep track of one’s location relative to the starting point and return directly back to it.• Rats, ants, and geese (and humans to some degree) can do it• 2-year-olds show some dead reckoning abilities--if led on circuitous routes they can return to the starting point more often than chance (this typically increases over development somewhat)

Same/Mirror Image Tasks

Dead Reckoning and Other Spatial Skills

• Sociocultural factors influence these abilities(e.g. aboriginal desert dwellers over city-dweller, video gamers)

• Gender differences favoring males (e.g. waterline on cup task)

Causality

Kotovsky & Baillargeon, 1994

• By 11 months, infants expect the size of an object to be related to the amount of force it can exert on another object.

OR

Habituation

Test

Causality (con’t)Causal Relations

• 2 1/2 year-olds select the appropriate tool for retrieving the toy more frequently than 1 1/2 year-olds.

Tool Use– structural properties are causally related to tool’s

function(Chen & Seigler, 2000)

Figure 7.8, from text

Cause–effect relations

Hearing that wugs are well prepared to fight and gillies to flee helped preschoolers categorize novel pictures like these as wugs or gillies (Krascum & Andrews, 1998). In general, understanding cause–effect relations helps people of all ages learn and remember.

It’s easier to remember concepts and order of events if they are causally connected

Causality (con’t)Causal Relations

Magic tricks - searching for causes

– Most 3- and 4-year-olds do not understand the point of magic tricks. By age 5 fascinated by magic tricks because causal mechanism is hidden. (Rosengren & Hickling, 1994)

– 4- and 5-year-olds, but not 3-year-olds, will actively search for the cause of an apparent magic trick.

• The “Why” stage begins…

Number is...• not a directly perceivable property of any

individual object.• an abstract concept that applies to sets of

items.• Numerical equality: realization that all

sets of a certain number of objects have something in common is the most basic numerical understanding.

Numerical Discrimination• 5-month-old infants can discriminate between

pictures containing 1, 2, or 3 items.– They fail to discriminate larger sets in this way unless the difference

between the sets is large enough.

Habituation

… and so on

Test

Starkey, Spelke, & Gelman, 1990; Van Loosbroek & Smitsman, 1990)

or

or

or

… and so on

or

Two core systems of number

• Core System 1– Object tracking: up to 3 or 4 objects

• Core System 2– Approximate representations of large

numerosities

Infants’ Arithmetic• infants of 5 months seems to have a basic

understanding of arithmetic.

Large number discrimination

• 6-month-old infants discriminate:– 4 vs. 8, 8 vs. 16, 16 vs. 32– BUT NOT: 8 vs. 12, 16 vs. 24

• For larger sets (more than 4 items):– Infants can discriminate values

that differ by a 1:2 ratio, but not a 2:3 ratio.

(Xu, in press; Xu & Spelke, 2000; Xu, Spelke, & Goddard, 2000)

Habituation Habituation

Test Test

Habituation Habituation

Test Test

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+ = or

Number vs. Continuous Extent

• Pitting number against continuous extent by manipulating the size of the objects in the outcomes.

wrong # right #

right amount wrong amount

(Feigenson, Carey, & Spelke, 2002)

Counting• Some facts…

– Most children can count to 10 by age 3– Most 5-year-olds can count to 100– Most children do not understand relative magnitudes (i.e., ordinality) of the different

numbers between 1 and 10 until age 5.e.g. that 6 apples is more than 4 apples.

– Most children do not understand cardinality until age 5.e.g. Give-a-number task• 2-year-olds:1 (and more than 1)• 2 and a half-year-olds: 1, 2, (and more than 2)• 3-year-olds: 1, 2, 3, (and more than 3)• 3.5- to 4-year-olds: all numbers

Gelman and Gallistel’s (1978) 5 Counting Principles

• One-to-one correspondence- each object receives a single number label

• Stable order- number list is always said in same order

• Cardinality- total number corresponds to last number word said

• Order irrelevance- objects can be counted in any order

• Abstraction- any set of individuals can be counted