Numerical Cognition Flashcards
what are the non-symbolic number representations?
analog magnitude system
object individuation system
analog magnitude system
yields noisy representations of approximate numbers that capture the inter-relation between different enough numerosities, e.g., 10 and 20.
object individuation system
tracks small numbers (up to 4) and precise representation of the numerosity of small sets, e.g., can quickly count 2 from 4.
what do these non-symbolic number representations provide evidence of?
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
what did spelke and xu (2002) find after testing visual modality of 6m infants?
dishabituated when presented with a different number of dots.
evidence of representing numerosity via analog magnitude system
what did izard (2009) find about newborns and the AMS?
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
where is there evidence of developmental progression in the precision of AMS?
this is subject to a ratio limit in newborns – can differentiate large numerosities only if they are sufficiently differenT
development of AMS
the precision of the system improves over the first year of life and is a part of core number knowledge
what did wynn (1992) find about 5m infants?
displayed surprise when the screen revealed the wrong number of puppets, revealing they were able to interpret events involving addition and subtraction
feigenson (2002) tested 10-12m infants and found…
they could track precise numbers and use this information to guide their choices, due to the development of their working memory
manual search task evidence to support OIS
when 12-14m infants still expected objects to be in the box and continued to look longer (feigenson and carey, 2003)
when did infants learn to extract and match numerosity across different modalities?
at 6-8m (starkey, 1990) via preferential looking tasks
they had cross-modal number representations for audition and vision
what is the OIS limited to tracking?
tracking at maximum 3 objects in parallel (feigenson, 2002) and is operational during the first year of life.
what are symbolic number representations?
humans developed number words and counting which allowed for precise representations of numerical information, even when recording very large numbers
when can infants recite the count list?
at 2y
when do infants work out how counting works?
at 4y
they struggle to figure out what number words mean, despite rapidly learning the meaning of object labels
give-n task
tests developing understandings of number, via asking for N number of objects
what do toddlers seem to know counting involves?
stable order
one-to-one
stable order
using the same labels in the same order, even if 2ys may consistently recite an incorrect count list (Gelman and Gallistel, 1978)
one-to-one
using one label per object (Gelman and Meck, 1983)
what did lee and samecka (2010) find about the development of precise number representations?
children learn number words in stages, which may span across several month
stages of number representation
- they learn the exact meaning of individual number words without knowing how counting encodes number (one-knowers – four-knowers
- 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’
what does learning to count require?
understanding complex concepts and rules
cardinality
the number of elements in a set
cardinality principle
the number word applied to the final item in a set represents the number of elements in the set
successor function
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)
what did jara-ettinger (2017) find?
the stage-like process of discovering how counting works is universal, and independent of culture and mother tongue, although timing may vary across cultures
examples of qualitative differences in how children learn number words of different sizes
1, 2, 3 – slow, stage-like, one number word at a time
4, 5, 6, 7 – fast, subsequent number words understood straight away
why is counting hard?
- number words work differently to other words, as they refer to sets rather than individuals
- counting relies on an algorithm that children need to discover
what does evidence suggest a relationship between?
early numerical skills at 6m and later maths learning at 3.5y (Starr, 2013), and greater learning of symbolic numbers in school
continuity in early number representation and learning
- children retain access to non-symbolic number systems
- there is a link between number skills and later maths learning
discontinuity in early number representation and learning
- discontinuity as non-symbolic and symbolic number systems represent different kinds of numerical information.
