Numerical Cognition

Question 1

what are the non-symbolic number representations?

Answer 1

analog magnitude system
object individuation system

Question 2

analog magnitude system

Answer 2

yields noisy representations of approximate numbers that capture the inter-relation between different enough numerosities, e.g., 10 and 20.

Question 3

object individuation system

Answer 3

tracks small numbers (up to 4) and precise representation of the numerosity of small sets, e.g., can quickly count 2 from 4.

Question 4

what do these non-symbolic number representations provide evidence of?

Answer 4

the human mind having access to distinct non-symbolic systems for representing numerosity, which is able to track numbers without even having to think of or know number words

Question 5

what did spelke and xu (2002) find after testing visual modality of 6m infants?

Answer 5

dishabituated when presented with a different number of dots.

evidence of representing numerosity via analog magnitude system

Question 6

what did izard (2009) find about newborns and the AMS?

Answer 6

newborns can match numerical arrays across visual and auditory modalities

they have access to the analog magnitude system at birth to represent abstract properties of the world

Question 7

where is there evidence of developmental progression in the precision of AMS?

Answer 7

this is subject to a ratio limit in newborns – can differentiate large numerosities only if they are sufficiently differenT

Question 8

development of AMS

Answer 8

the precision of the system improves over the first year of life and is a part of core number knowledge

Question 9

what did wynn (1992) find about 5m infants?

Answer 9

displayed surprise when the screen revealed the wrong number of puppets, revealing they were able to interpret events involving addition and subtraction

Question 10

feigenson (2002) tested 10-12m infants and found…

Answer 10

they could track precise numbers and use this information to guide their choices, due to the development of their working memory

Question 11

manual search task evidence to support OIS

Answer 11

when 12-14m infants still expected objects to be in the box and continued to look longer (feigenson and carey, 2003)

Question 12

when did infants learn to extract and match numerosity across different modalities?

Answer 12

at 6-8m (starkey, 1990) via preferential looking tasks

they had cross-modal number representations for audition and vision

Question 13

what is the OIS limited to tracking?

Answer 13

tracking at maximum 3 objects in parallel (feigenson, 2002) and is operational during the first year of life.

Question 14

what are symbolic number representations?

Answer 14

humans developed number words and counting which allowed for precise representations of numerical information, even when recording very large numbers

Question 15

when can infants recite the count list?

Answer 15

at 2y

Question 16

when do infants work out how counting works?

Answer 16

at 4y

they struggle to figure out what number words mean, despite rapidly learning the meaning of object labels

Question 17

give-n task

Answer 17

tests developing understandings of number, via asking for N number of objects

Question 18

what do toddlers seem to know counting involves?

Answer 18

stable order
one-to-one

Question 19

stable order

Answer 19

using the same labels in the same order, even if 2ys may consistently recite an incorrect count list (Gelman and Gallistel, 1978)

Question 20

one-to-one

Answer 20

using one label per object (Gelman and Meck, 1983)

Question 21

what did lee and samecka (2010) find about the development of precise number representations?

Answer 21

children learn number words in stages, which may span across several month

Question 22

stages of number representation

Answer 22

1. they learn the exact meaning of individual number words without knowing how counting encodes number (one-knowers – four-knowers
2. make an inductive leap to understand the counting algorithm is governed by the cardinal principle and the successor function to reach the ‘cardinal principle knowers stage’

Question 23

what does learning to count require?

Answer 23

understanding complex concepts and rules

Question 24

cardinality

Answer 24

the number of elements in a set

Question 25

cardinality principle

Answer 25

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

Question 26

successor function

Answer 26

tells us what the relations are between the numerals (e.g., if numeral N represents cardinality N, then the next numeral represents the cardinality N+1)

Question 27

what did jara-ettinger (2017) find?

Answer 27

the stage-like process of discovering how counting works is universal, and independent of culture and mother tongue, although timing may vary across cultures

Question 28

examples of qualitative differences in how children learn number words of different sizes

Answer 28

1, 2, 3 – slow, stage-like, one number word at a time
4, 5, 6, 7 – fast, subsequent number words understood straight away

Question 29

why is counting hard?

Answer 29

1. number words work differently to other words, as they refer to sets rather than individuals
2. counting relies on an algorithm that children need to discover

Question 30

what does evidence suggest a relationship between?

Answer 30

early numerical skills at 6m and later maths learning at 3.5y (Starr, 2013), and greater learning of symbolic numbers in school

Question 31

continuity in early number representation and learning

Answer 31

1. children retain access to non-symbolic number systems
2. there is a link between number skills and later maths learning

Question 32

discontinuity in early number representation and learning

Answer 32

3. discontinuity as non-symbolic and symbolic number systems represent different kinds of numerical information.