W8 (TRIAL) Flashcards
(26 cards)
What is non-symbolic number representation?
The ability to understand and estimate quantities without using symbols like numerals. You can perceive numerical magnitude through visual arrays e.g collection of dots.
What are non-symbolic number systems?
Distinct systems for representing numerosity, allowing us to operate without counting and track numerosity without knowing number words.
What are the two non-symbolic number systems?
Analog magnitude system is our brain’s approximate number sense. It represents quantities as noisy magnitudes, enabling us to distinguish between significantly different amounts (like 10 vs. 20) but struggling with close values (like 20 vs. 21) estimating system for approximating large numbers
Object individuation system precisely represents small numbers of individuals (up to ~3). It allows for rapid discrimination of small sets (e.g., 2 vs. 3) but fails with larger numbers (e.g., 8 vs. 9). Precisely processing discrete small numbers
What methods are used to study numerical cognition in infancy?
Looking time methods e.g violation of expectation, preferential looking
Manual search
Choice (e.g crawling to selected location/object)
What is modality?
Modality refers to the sensory channel through which information is received or conveyed, such as visual, auditory, or tactile.
What is Visual Numerosity?
The ability to perceive the quantity of items seen.
What is Cross-Modal Numerosity?
The ability to recognize matching quantities across different senses.
What numerical abilities are evident in infants, and what does this suggest about their cognitive development?
Infants demonstrate an early sensitivity to numerosity, or the quantity of items.
Visual Numerosity (6-month-olds): The ability to perceive the quantity of items seen.
Spelke & Xu (2000) showed that 6-month-old infants can distinguish between different quantities of visual items (e.g., 8 vs. 16 dots). This suggests they possess an ‘analog magnitude system’ for representing approximate quantities.
Cross-Modal Numerosity (Newborns): The ability to recognize matching quantities across different senses.
Izard et al. (2009) found that newborns can match auditory and visual numerical information/arrays (e.g., 4 sounds matched with 4 visual items). This indicates that the ability to represent abstract numerical properties exists at birth and is not limited to a single sensory modality.
What is hard for infants?
Infants find it harder to discriminate between smaller numerical differences
Izard et al. (2009)
newborns struggle with congruent/incogruent number
Newborns struggle with 1:2 ratios (e.g., 4 vs. 8 items).
6-month-olds struggle with 2:3 ratios (e.g., 8 vs. 12 items).
What is the non-symbolic analog magnitude system?
Your brain’s built-in ability to estimate and compare quantities without using exact numbers or symbols
What are the key features of the non-symbolic analog magnitude system?
This system is available since birth 🍼
A part of core number knowledge
Supports approximate representation of large sets/number
What is the object individuation system?
The object individuation system is the cognitive ability to track and distinguish individual objects within a set, allowing one to understand ‘how many distinct things’ are present
What are the main features of the object individuation system?
Operational during the first year of life.
Supports precise representation of small number sets.
Tracks up to 3 objects at a time.
Enables interpretation of addition and subtraction.
Part of core number knowledge.
Can infants understand addition and subtraction? (conduct object individuation)
Wynn (1992) (5-month-olds) Infants looked longer, and were ‘surprised’ when the number of puppets was wrong. 👀 They can keep track of objects behind a screen. Suggests early understanding of addition & subtraction.
Can infants use number knowledge to guide actions?
Feigenson & Carey (2003) → Manual search with hidden balls. Infants searched longer when an expected object was missing. 🔍 Shows they form precise mental representations of small numbers to guide behaviour.
How many objects can infants track at once? Ball study again!
At 12-14 months Infants can track 1 to 3 objects simultaneously (in parallel)
Thus they can expect the correct number of objects when presented with simple additions like 1+1 → expect 2 or 1+1+1 → expect 3.
BUT their ability to track numbers collapses when there are more than 3 objects involved. (Feigenson & Carey, 2003)
Can infants match numbers across senses (modalities)?
Starkey et al. (1990) (6-8 months) studied infants through intermodal preferential looking.
They had visual displays side by side e.g 2 vs 3 objects and played audio e.g 2 or 3 drumbeats.
Infants look longer at a visual display that MATCHES the drumbeats.
Infants can extract and match numerosity across auditory and visual modalities. 🎵🔢👀 They have cross-model representation.
Does an infant’s innate ability to discriminate approximate numbers (AMS) predict later math skills?
Starr et al.’s (2013) longitudinal study found that infants who showed more robust numerical discriminations when presented with arrays of dots at 6 months were better at maths in preschool (at 3.5 years).
What is the symbolic number system?
The symbolic number system is how we use words and symbols (like ‘one,’ ‘two,’ or ‘1,’ ‘2’) to precisely represent and work with numbers, including very large ones. It’s the system behind counting and written numerals.
When do infants begin learning language/number words?
Infants begin learning language in utero and can distinguish their native language from a foreign language at birth (Mehler et al., 1988).
By 6 months, they understand the meanings of many common words (Bergelson & Swingley, 2012).
By 2 years, most children can recite the count list and use number words when asked ‘how many?’
What do toddlers understand about counting?
Toddlers seem to know that counting involves:
Counting is in a Stable order – using the same labels in the same order (even if idiosyncratic) (e.g., ‘1, 2, 3, 5, 6, 11’) (Gelman & Gallistel, 1978).
One-to-one – assigning one label per object (Gelman & Meck, 1983).
What is cardinality?
Cardinality refers to the understanding that the final number in a counting sequence represents the total quantity of items in a set. (the number of elements in a set)
What does it mean if a child can count but doesn’t understand cardinality?
It means the child can recite number words in order, but doesn’t grasp that the last number they say tells them ‘how many’ items there are in total. They may count ‘1, 2, 3,’ but not realize that ‘3’ represents the entire group.
What is a count list, and does reciting it mean a child understands numbers?
A count list is the ordered sequence of number words (e.g., ‘one, two, three…’). BUT reciting it does not mean a child understands what the words mean; children can say the numbers before grasping how counting works, which usually happens around age 4 (Lee & Sarnecka, 2010).
