Week 8 Flashcards
Describe an analog magnitude system
A number system which allows you to judge the numerosity of large sets of data, with large differences (e.g. 10 > 20)
Describe an object individuation system
A number system which tracks small numbers of individuals and supports very precise representations of the numerosity of small sets
- does have signature limit
Is language necessary for numerosity? Explain your reasons
No
1. Available to non-human animals = suggesting that human intelligence isn’t necessary to represent numerosity
2. Without counting = allows us to track numerosity without thinking or knowing number words
Name the methods to study whether and how infants represent numerical information
Violation of expectation
Preferential looking
Manual search
Choice
What methods are preferred when studying infants? Why?
Manual search and choice -> as you record where the baby actually goes = means you have more of an accurate take on the babies thoughts
Describe the results from Spelke and Xu (2000) analog magnitude study
6 months
Infants dishabituated when presented with a different number of dots; so they responded with number change = suggests they came up with sufficiently robust numerical model
What is a limitation of Spelke and Xu (2000) study?
Only used visual display = couldn’t control density of things on screen -> are infants truly sensitive to number or to visual pattens formed by the stimuli?
What were the results of the more developed and valid version of Spelke and Xu (2000) study?
Infants can match numerical arrays across modalities at birth
Newborns display sensitivity to abstract aspects of numerosity = suggests, humans have access to the analog magnitude system at birth and can represent abstract numerical properties of the world
What is the difference in infants object individuation system 5 months, 10-12 month and 12-14 month olds?
5 months: infants can interpret addition and subtraction
10-12 months: Infants track precise numbers and use this information to guide their choice
12-14 months: Infants can set up precise representations of small numerocities that then guide their behaviour
Do infants have intermodal preferential looking?
Yes
6-8 months
Infants can extract and match the numerosity across two different modalities and formats > infants seem to have cross modal number representation
What is an Object Individuation System?
- Operational during 1st year of life
- Supports precise representation of a small number of sets by tracking individual objects
- Allows infants to interpret events involving addition and subtraction
- Limited to maximum of 3 objects
- Part of core number knowledge
Describe the Symbolic number system
- A number system which allows us to very precisely represent and record numerical information
- Only humans
How do 2-4 year olds count?
Stable order = counting involves using the same labels in the same order
One to One = counting involves using one label per object
What has the N task demonstrated to us about children’s counting?
Children learn number words in stages (each stage may span up to several months):
1. Children learn gradually the exact meanings of individual number words without knowing how counting encodes number
2. Make an inductive leap and figure out how the counting algorithm works > grasp the Cardinality principle and the successor function
Define cardinality
The number of elements in a set
Define the cardinality principle
The number word applied to the final item in a set represents the number of elements in the set
Define successor function
Tells us what the relations between the numerals
Are these stages universal?
Yes
Why is counting so hard?
Counting relies on algorithms that children need to discover
Is there a relationship between early numerical skills and later maths learning?
Evidence suggests = yes
Both infant non-symbolic number representation skills and later developing symbolic number representations
