Number Development Across Infancy and Childhood Flashcards
(15 cards)
Types of Number Knowledge
Number systems are cultural tools that represent and allow us to talk about quantities
* Quantity: A property of magnitude
- Cardinality: Being represented by a cardinal number
- Using a number to represent magnitude
- Ordinality: Numbers come in a serial order of magnitude
- Transitive inferences are possible
Infants’ Knowledge of Numbers
Starkey & Cooper (1980)
Perceiving Numbers
Can 4 month olds perceive number?
* Habituation and Looking time measure
* Infants discriminate differences between small quantities
Infants are born with ability to understand number
Infants’ Knowledge of Numbers
Wynn (1992)
Adding and Subtracting
Tested 5 month olds’ knowledge of mathematical operations
* Violation of Expectation
* Infants were surprised by impossible outcomes
* Infants understand mathematical operations
Infants have innate number structures
Infants’ Knowledge of Numbers
Is Number Knowledge Innate?
Alternative Explanation of Wynn (1992)
Impossible outcome is the same as starting point: Infants surprisal could be related to expecting a change
* Mixed success in replications
* Limited to small numbers <3
Infants results could be based on perceptual features
* Numbers need to be separated from continuous dimensions of sets
* Infants may perceive differences between continuous quantity not precise number relations
Infants’ Knowledge of Numbers
Xu & Spelke (2000)
Tested 6 month old infants’ discrimination of large numbers
* Habituation procedure
* Infants discriminated large differences (8 vs 16, but not 8 vs 12)
Infants’s perception is based on approximate representations not exact numbers
Counting Behaviour
Abstract Counting: Reciting number sequence
* Not using number knowledge
Object Counting: Determining a quantity
* Uses number knowledge
Counting Behaviour
Gelman’s Counting Principles
Nativist Perspective
How to count principles
* One-to-one → Count each item in a set once and only once
* Stable order → Produce the number word in the same set order
* Last number → The last number counted represents the value of the set
Counting Behaviour
Gelman and Gallistel (1978)
Children were accurate with small sets
* Understand counting principles
Children made errors with larger sets
* Attributed to performance errors
Counting Behaviour
Carey’s Individuation Hypothesis (2004)
Children gradually develop number understanding through combination of innate knowledge and experience
* Parallel Individuation: Infants recognise and represent small numbers exactly
- Children recognise one, then one vs two, then vs three
- Can do without knowledge of the number system
* Enriched parallel individuation: Children learn larger numbers, bootstrapping from counting
- Learning the count list reached them that quantities extend beyond three and helps children discriminate larger numbers
- Cardinal principle knower: Know that numbers continue on a scale / learned to count (Acquired ~ 2-5 years)
Counting Behaviour
Criticisms of Carey (2004)
Requires analogical process to understand/form link to understand how they map onto each other
* Not really showing an understanding of cardinality
- Understand quantity is the same as another set of quantity
Counting Behaviour
Comparing Sets
Number words imply relationship between sets
* Cardinality: Any set of items with a particular number is equal in quantity to any other set with the same number
- According to Piaget, understanding cardinality is key to understanding numbers
Counting Behaviour
Greco (1962)
Comparing Sets
Test 4-8 year olds on three tasks
* Classic conservation
* Classic conservation + counting 1 set
* Classic conservation + counting both sets
Suggests children do not understand cardinality
Counting Systems
Counting Systems
Number systems are cultural tools that represent quantities
* Decimal system: Base of 10
Number words used reflect muliplicative ad additive nature of number
* Multiplicative: Two hundred
* Additive: Twenty-One
Counting Systems
Miller & Stigler (1987)
Cross-Linguistic Differences
Some languages have more transparent number words
* Tested 4-6 year old English and Chinese speaking children
- Abstract and object counting
* Chinese speaking children count better than English-speaking children
Counting Systems
Alternative Possible Explanations of Miller & Stigler (1987)
- Education systems differ
- Parental expectations differ
- Language characteristics influence the representation of number due to the greater transparency of number names
