Numerical cognition notes needed

Question 1

What is the Two Non symbolic number representation?

Answer 1

• These systems operate without counting, enabling us to track numerosity without knowing number words

1. Analog Magnitude system
2. Object individuation system

Question 2

What is the Analog Magnitude system

Answer 2

used to represent large, approximate quantities.

Question 3

What is the Object individuation system

Answer 3

supports very precise representation of the numerosity of small sets (up to 4)

Question 4

what methods are used to test how infants represent numerical information?

Answer 4

Looking time methods
- Violation of expectation
- Preferential looking
Manual search
Choice

Question 5

Describe the analog magnitude system in infants

Answer 5

• available since birth
• subject to ratio limits
• Is a part of core number knowledge

Question 6

Describe the object individuation system in infants

Answer 6

• operational during the first year of life
• allows infants to interpret events involving addition and subtraction
• Is a part of core number knowledge

Question 7

analog magnitude system study

Answer 7

at 6 months Infants dishabituated when presented with a different number of dots, they responded to the number change.

Question 8

object individuation system study

Answer 8

Infants can track 1 to 3 objects in parallel, but their number representation in this context collapses when there is more than 3 objects involved.

Question 9

What is Symbolic number representation?

Answer 9

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

Question 10

Describe early “counting”

Answer 10

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

Question 11

When can toddlers count list?

Answer 11

At 2 years old they can count list
However
They do not figure out what number words mean and how counting works until 4

Question 12

What is the cardinality principle

Answer 12

the number word applied to the final item in a set represents the number of elements in the set

Question 13

Children learn number words in stages. Each stage may span up to several months. what are these stages?

Answer 13

“One-knower” stage
“Two-knowers” stage
“Three-knowers” stage
For some “Four-knowers” stage
“Cardinal principle knowers” stage

Question 14

Does infants’ innate ability to represent number via analog magnitude system matter for their later mathematical reasoning and maths learning?

Answer 14

Starr et al:
Used a longitudinal design to test whether infants abilities to represent approximate numerosity matter for their later maths learning

Infants who showed more robust numerical discriminations when presented with arrays of dots at 6 months were better at maths at 3.5 years

Question 15

does early ability effect later ability of symbolic number representation?

Answer 15

Children who show greater symbolic mathematical abilities at 3 years of age go on to show greater learning of symbolic numbers in school.

Question 16

Give your own study

Answer 16

A study in 2021 found Kindergarten mathematics predicts 5th grade mathematics and reading achievement.