Lecture 4 - Space and Number

Question 1

Historical research on space, number and maths

Answer 1

• Piaget conservation tasks - failures of reasoning about physical properties or spatial transformations until concrete operational stage (6-7).
• under 4 unable to choose pics showing how mountains would look from other pov & instead choose egocentric view
• piagets tasks show explicit reasoning about formal properties take time to develop but basic precursors develop early and are shown in less demanding tasks

Question 2

development of spatial representations

Answer 2

• recent and current research using simple direct responses rather than explicit reasoning.
  > from birth: spatial orienting (egocentric)
  > in 1st year: from egocentrism to spatial updating
  > 18-24m: use of spatial updating and landmarks- room geometry
  > 5+y: flexible coding using indirect landmarks

Question 3

neonatal spatial orienting

Answer 3

• newborns can roughly localise visual auditory and tactile stimuli in space
• early spatial coding is egocentric relative to own body

Question 4

1st year: from egocentrism to spatial updating

Answer 4

• infants learn to orient to a window where an experimenter is playing peekaboo whenever a buzze sounds. ability to update position correctly when moved to opposite side develops at around 1 year. fail at 11m but pass at 16m.
• infants at 11m look egocentrically but by 16m stop

Question 5

how to go beyond egocentrism

Answer 5

1. spatial updating - keeping track of locations as you move relative to start position. e.g. animals use. path integration/dead reckoning
2. landmark use - code where a target is relative to landmarks

Question 6

18 months: spatial updating and landmark use

Answer 6

• sandbox task - observed children search for objects in sandbox. 1 group looked for objects with visual access while other where landmarks hidden from view. use spatial updating.
  > same side (egocentric) above chance 16m
  > opp side (updating an/or landmarks) 16m
  > landmark use from 22m

Question 7

18 months: landmark use - room geometry

Answer 7

• another way to dissociate updating from landmark use is to disorient p’s to use geometry of room. forces them to use landmarks.
• Hermer & Spelke (1994) - 18-24m use room geometry as a landmark but ignore other featural cues - like adult rats
• did not find the feature info relevant for orienting a space
• Spelke - there is a dedicated innate geometric module for processing room shape. part of core knowledge
• the task is solved at 4y - due to language abilities according to spelke in combo with core geometric understanding

Question 8

5 years: flexible landmark use

Answer 8

• Nardini et al. (2006) - 3-6y recall location of toy within array surrounded by landmarks
  > changed viewpoint by walking = can use spatial updating. solved 3+y
  > changed viewpoint by rotating board = have to use landmarks. solved 5+

Question 9

what develops

Answer 9

• Spelke nativist approach: core knowledge of basic spatial concepts supplemented by learning & language
• Newcomve epiricist/neoconstructivist approach: sophisticated spatial coding schemes are constructed from experience
• evidence from animals:
  > dissociable neural basis for place vs response learning in rats. place = hipp

Question 10

space - formal abilities: maps

Answer 10

• a map symbolises the real environment - related to development of symbolic thought
• can find a toy in real room based on location in a model room @ 3y = symbolic understanding
• put kermit in place on map show better than chance performance at 2.5y > early developing abilities use maps as symbols and relate spatial relations in maps to spatial relaitons in real layouts

Question 11

space - formal abilities: geometry

Answer 11

• abstract concepts
• relate to real objects but do not exist in real life.
• euclid deduced euclidian geometry from small set of axioms
• Kant - human mind has euclidean intuations
• assessed in US adults. US children and amazonian culture adults. asked what shape was odd one out. found mundurucu and US children find similar items easy. although education inc % correct, there is a perception of similar geometric features independent of education = innate

Question 12

number - basic abilities

Answer 12

• keeping track of how many of something there is a kep perceptual/cog ability
  > small numbers: keep track of nearby object of interest
  > large numbers: judge which of 2 sets is more numerous

Question 13

small number tracking in infants

Answer 13

• 5m look longer at impossible events more: keep track of how many there are and understand adding and subtracting. were expecting to see 2 objects when adding 1 + 1.
• exact number representations are limited to aboit 3-4 items.
• may be related to the ‘object file’ system that evolved to allow us to keep track of 3-4 moving objects

Question 14

approximate numerosity of large sets in infants

Answer 14

• in infancy also an ability to keep track of large sets of items
• Xu & Spelke (2000) -6m discrim but 8 vs 16 but not 8 vs 12. innate.
• discrim depends on the ratio not dif in numbers.
• infants can discrim a ratio of 2x but not 1.5x
• also shown in auditory domain with tones.

Question 15

two basic number systems

Answer 15

• infants can do:
  1. subitising: keep track of exact numbers up to about 3-4
  2. approximate number syste,: discrim larger numbers with >1.5 ratios
• later humans uniquely also learn to deal with exact large numbers

Question 16

exact large number numerosity

Answer 16

• a foundation for exact numerosity is learning to count.
• Gelman - counting builds on nonverbal knowledge and serves as basis for future numerical understanding
• depends on education
• young children and adults from indigenous groups without formal ed rep large numbers on non-linear scale
• education affects this

Question 17

approximate large number numerosity

Answer 17

• testing accuracy of childrens approx number systems:
• accurcay of approx number system at 14yrs cor with exact numbers on school test at 5-11y