Lifespan A: Children's understanding of number, WEEK 5 Flashcards
1
Q
Number cognition
A
- Number abstraction: very basic ability to count + quantify things (intuitive) > can make rough estimations w/o counting > non-symbolic reasoning
- Numerical reasoning: product of our education (as not all species use maths) > explicit reasoning skill to solve maths problems + manipulations > symbolic reasoning as we use symbols our culture created to solve things
2
Q
Number sense & ratio
A
- can guess when things are more or less w/o counting, but depends on ratios
- if the ratio is far apart, we can easily identify or estimate accurately > when the ratio is close together, it will take longer to form an accurate estimation > number sense is ratio bound
- e.g: can see difference between 2 and 8 marbles but it is harder to see difference between 7 and 8 at first glance (number sense)
3
Q
Judging number inequalities w/ number symbols
A
- Plot our understanding of quantity onto symbolic numbers > we reason w/ numbers learnt from culture
- Make quick judgements about whether there is more or less in terms of dots/objects but about numbers learnt in ed too > it is more obvious that 9 is bigger than 2 so we react quicker but less obvious that 6 is bigger than 5 so react slower
- Errors are more common when numerical distance between digits is smaller
4
Q
Subitizing
A
- Rapidly enumerating a set of objects + is quick judgement > when objects are between 1-3 we subitize (know number w/o counting)
- Research shows beyond 3 we start counting + slow down reactions
- Some argue subitizing is an innate ability
- Positive correlation between time + amount of dots > more dots = more time taken
5
Q
Piagetian perspective
A
- Basic logical development forms basis for numerical reasoning > domain general process
- Piaget argues even if children can count verbally, this doesn’t show understanding of number
- Kid’s do not understand meaning of number until they real concrete operations > no innate understanding of number
- To understand number, you must be able to conserve, have class inclusion + seriation (concrete ops)
- Conservation = change in appearance doesn’t = change in quantity > requires understanding of quantity, space + amount
6
Q
Challenges to Piagetian perspective
A
- Basic understanding of no. > more/less > Piaget’s study requires ability to understand language
- McGariggle + Donaldson naughty teddy task > W3 cue cards
- Mehler & Behver split ppts into 2 groups > one used clay pellets + other m&ms
- were asked which row has more, are they the same + take the row you want to eat
- Children were right more in m&m conditions > Mehler & Bever argue kids have implicit understanding of number > before they learnt to count, they understood more vs less in a motivated task (they wanted to eat m&ms > wanted to eat row with more m&m)
7
Q
Implication’s of Piagetian perspective
A
- Piaget’s work suggested kid’s were not ready to reason numerically until age 7 (concrete ops) > lead to education systems not emphasising numerical reasoning up until this point
- Could be detrimental to maths ed + impacts society
8
Q
Gelman & Gallistel (1986)
Principles of counting
A
- Most researchers focused on conservation + dismissed counting but Gelman studied counting itself + counting behaviour in children to see if it shows how they reason about numbers > kids between 3.5-4.5yrs
- Argue learning to count is guided by innate abstract principles (schemes) guiding acquisition of no. concept + counting > due to these principles, greater attention is given to words about numbers
- Domain-specific view of numerical cognition > focuses only on number itself + is nativist
9
Q
Principles of counting
A
- one to one principle > set of objects tagged w/ a number (1,2,3,4)
- stable order p > order sequence (1-5) > repeatable
- Abstraction principle > anything can be counted w/ no.
- Order irrelevance > can count even if numbers aren’t in order or start at a random point
- Cardinal principle > full understanding of no. is when you recognise the final number in a set is equal to the amount of objects in that set
- Principles 1-4 = procedure while 5 is the concept of no.
- Gelman argues children’s behaviour during counting shows they understand basic principles of counting no.
- Experience counting refines understanding of no. through different procedure (1-4)
10
Q
Measure’s of children’s access to number
A
- Verbal counting task > how high can you count > measure the sequence of no + labels of no. understood
- Enumeration task > could you help big bird count his toys by pointing to each one? > record child + can measure 1-1 principle, order irrelevance + cardinality
- Numerical recognition > set of no. + ask which one is 2 e.g > doesn’t measure principles of counting but measures access to number, symbols + words > younger children won’t always be able to do this as it is a product of education
- Give-a-number task > Kermit asks for x amount of toys he wants from you > instead of watching the counting behaviour of children we look at if the child recognises the final number is the total amount Kermit wants
- Point-to-x task > can you point to 3? > sees if child counts the objects then points or if they do it w/o counting > tests cardinality
11
Q
Challenges to principles of counting
A
- Cannot be sure children’s counting because it’s innate > may have learnt from parents (EV) > children may derive principles after experience
- Gelman said counting is innate as she saw it in early childhood > just because you see something in early childhood doesn’t make it innate
- Wynn made a task where toys were counted when they were visible then went into a box where there were sounds + jumping in sets of 2,3,5,6 + asked how many were in the box > older children 3.5yrs counted more accurately than younger 2.5 year olds > they had to keep the number in mind + understand final number
- 3.5 year olds were more likely to use cardinality principle + understanding of cardinality is more important to understanding number
12
Q
Types of numbers
A
- Symbolic number: Abstract and exact representations, Number Words and Digits
- Non-symbolic number: Perceiving Quantities of Objects/Events, Comparing Quantities + imprecise
- We are quick at counting small sets of numbers but not big no. beyond 5 > can count non-symbolic no. quicker but is more imprecise > is this innate?
13
Q
Infant’s numerical ability: Starkey & Cooper (1980)
A
- Infant’s are non-verbal so we rely on looking beh
- If an infant recognises a visual change in the amount of something they will look longer (dishabituation)
- Starkey & Cooper look at 5.5 month old infants to see if they can subitize + discriminate between no. sets
- Found dishabituation in small number conditions when there was an extra dot added (e.g: 2 dots > 3 dots) > but no dishabituation when there were larger numbers (4-6)
- Habituation is where the infant’s looking behaviour is not surprised + more bored
- Suggests infant’s have basic subitization ability which is more advanced in adults
14
Q
Infant’s numerical ability: Wynn (1992)
A
- If the infant understands that a concept or rule has been broken, they will look longer than if it is knowledge consistent.
- Tested 5mo infants > condition 1: 1 mickey mouse puppet, cover w/ board, another puppet enters + hand in puppet leave + left w/ 2 puppet when board goes down (KC) > condition 2: same as above ^ but only 1 puppet is left
- Infant’s looked reliably longer in unexpected outcome
- Supports that infant’s aren’t perceiving the amount of space covered but counting somehow
15
Q
Infant’s numerical ability: reliable?
A
- Christodoulou wanted to see if claims were robust in meta-analysis reviewing studies replicating Wynn
- 26 studies used (550 infants)
- Found results are reliable that infant’s can detect difference in amount but cannot when it’s more than 3
- Results hold even when task factors change like number of objects, infant age, type of stimulus
- Cohen’s d- 0.34 > moderate effect of condition
