Numerical cognition Flashcards
What is the Two Non symbolic number representation?
- These systems operate without counting, enabling us to track numerosity without knowing number words
- Analog Magnitude system
- Object individuation system
What is the Analog Magnitude system
Also known as “approximate number system” or “number sense”
Yields noisy representations of approximate number that capture the inter relations between numerosities that are distant enough
What is the Object individuation system
Also known as “parallel individuation system or “distinct individuals’”
Tracks small numbers of individuals (up to 4) and supports very precise representation of the numerosity of small sets
What are the Methods to test infants knowledge about number
Looking time methods
- Violation of expectation
- Preferential looking
Manual search
Choice
Describe the analog magnitude system in infants
- available since birth
- Supports approximate representation of large sets
- subject to ratio limits
- Is a part of core number knowledge
Describe the object individuation system in infants
- operational during the first year of life
- allows infants to interpret events involving addition and subtraction
- is limited to tracking at maximum 3 objects at a time
- Is a part of core number knowledge
When do infants have a sense of exact number
when they are presented with up to 3 objects at a time
What is Symbolic number representation?
We developed number words and counting represent numerical information.
- Infants begin to learn language in utero
- By 6 months infants have learned the meanings for common words
Describe early “counting”
Toddlers know stable order = counting involves using the same labels in the same order
They know one to one counting involves using one label per object
When can toddlers count list?
At 2 years old they can count list
However
They do not figure out what number words mean and how counting works until 4
Children learn number words in stages. Each stage may span up to several months. what are these stages?
“One-knower” stage
“Two-knowers” stage
“Three-knowers” stage
For some “Four-knowers” stage
“Cardinal principle knowers” stage
What is Cardinality
The number of elements in a set
What is the cardinality principle
the number word applied to the final item in a set represents the number of elements in the set
What is the Successor function
Tells us what are the relations between the numerals
Does infants’ innate ability to represent number via analog magnitude system matter for their later mathematical reasoning and maths learning?
Starr et al:
Used a longitudinal design to test whether infants abilities to represent approximate numerosity matter for their later maths learning
Infants showed more robust numerical discriminations when presented with arrays of dots at 6 months were better at maths at 3.5 years
does early ability effect later ability of symbolic number representation?
Children showed greater symbolic mathematical abilities at 3 years of age go on to show greater learning of symbolic numbers in school.
Do children lose access to the non symbolic number systems?
no they retain them
Do non symbolic and symbolic number systems represent the same information?
No they represent different kinds of numerical information symbolic representations allows for precise unlimited representation of any number
