Week 8 - Numerical cognition

• Analog magnitude system is our ability to tell number apart roughly using approximations without symbolic understanding of number
• Object individuation system is our ability to track a small number (up to 4) of objects with precise representations of the few objects. Beyond this number this system is useless
• These 2 non symbolic systems operate without counting enabling us to track number without thinking or counting
• Methods to study how infants represent numerical information:

  • Looking time methods - VOE
  • Manual search
  • Choice (choosing to crawl towards a location)
• Spelke, 2000 used visual modality to show infants are able to distinguish between two sets of dots meaning they can respond to number change using their analog number system (6mo)
• Izard, 2009 infants shown to look longer at matching visual arrays and display sensitivity to abstract aspects of numerosity. Suggests we have access to analog magnitude system from birth
• Newborns can discriminate between 1/3 ration but not 1/2. At 6 months they can do 1/2 but not 2/3 suggesting there is progression through age (Izard, 2009)
• Wynn, 1992 showed infants stared at the stage longer when there was an incorrect number of puppets showing they can keep track of number behind a screen and interpret events with adding and subtracting (5m)
• Feigenson (2002/3) Found 10-12mo reliably crawled to the bucket with more crackers. Shows they have WM and numerosity through object individuation system
• Starkey, 1990) 6-8m - Found infants can extract and match numbers of objects across modalities and formats so have cross modal representation across visual and auditory stimuli
• Infants can track 1-3 objects in parallel but over that they are unable to represent them in this context in parallel
• Infants also develop symbolic number systems allowing counting and record of numerical info
• Toddlers seem to know that there is a stable order in counting even if they cant remember all numbers and that counting involves one label per object
• Give N Task used to test childrens understanding of number with three children over 3 trials- Lee and sarnecka (2010)
• Shown that children learn number in stages and that each stage spans several months. They first learn exact meaning of individual numbers but not the links between the numbers in sequence eg "one knower"
• Once individual numbers are learnt they leap to understanding the counting algorithm
• Cardinality is understanding the number of elements in a set with cardinality principle being the understanding that the last word of a set is the total number in the set
• Successor function gives understanding to the relation between numbers such as 6 being one more then 5
• This stage like process is universal across cultures and children
• Starr, 2013 showed that infants ability to represent numerosity at 6mo are better at maths at 3.5 years
• Children showing greater symbolic mathematical abilities at 3 years of age go on to show greater learning of symbolic number in school.
• looking time methods include VOE (Baillargeon, 1985), Preferential looking (Starkey, 1900 and starr et al, 2013)
• izard tested newborns cross modality sensitivity to number, showing them numbers of sounds compared to visual stimuli. infants could match number across modality showing an innate system of AMS
• feigenson (2003) 12-14mo placed two objects on the box then hid them inside. Hide 1 far inside unretrievable. Infants search for longer when they expect both balls inside as a pose to expect nothing in the box.
• Both feigenson studies show infants can set up precise representations of small numerosities that guide their behaviour
• starkeys study involved 2 visual displays side by side with differing numerosity and an auditory stimuli of drum beats where they looked longer to the visual stimuli matching the drum beats
• infants begin learning language in utero
• newborns are able to distinguish their native language from a foreign one (mehler, 1988)
• By 6 months, infants have learned the meanings for many common words (Bergelson and swingley, 2012)
• By 2 years most children learn to recite the count list up to 4 and use number words in response to "how many"
• Give N task tested childrens counting skills of numerosity and their symbolic representations. Tests their cardinality, cardinality principle and successor function. Just because theyre able to recite low numbers doesnt mean they know what they mean or the relationship between them
• asked to give "N" toys which isolated their individual understanding of each number instead of just reciting a list. Also did it over 3 trials taking away anomalies
• counting is harder then speaking for infants due to number words working differently to other words "cat". They refer to sets not individuals. Relies on an algorithm entailing cardinality that children need to discover
• babies that looked more at the numerically changing screen at newborn age then had higher math score at 3.5
• in spelke, 2000 - dot experiment infants dishabituated when they were presented with a different number of dots - responding to the number change