Lecture 4 Flashcards
(18 cards)
1
Q
Number abstraction
A
- Exact/approx representation of the numerosity (amount/quantity) of an array
- e.g. counting/estimating
2
Q
Numerical reasoning
A
- Understanding the principles of how manipulating affect sets
- E.g. Adding/subtracting
3
Q
Ratio bound number sense
A
- As adults able to make judgement about more or less = ability to estimate increases with age
- Errors are more common when numerical distance between digits is smaller
- When we have a small number of objects adults count in an automatic process
4
Q
Piagetian perspecitve
A
- Children count verbally but may not understand the concept of numerical value e.g. can count to 100 because learnt it off by heart
- Said they grasp what numbers mean at around age 7
- No innate sense of number
- Number concept = domain general process
5
Q
Challenges to Piagetian perspective
A
- McGarrigle and Donaldson (1974):
- -> Naughty teddy experiment (see lecture 3)
- -> Extra linguistic features influence interpretation of the question
- Mehler and Bever (1967)
- -> 200 children ages 2.4-4.5
- -> Half used M&Ms = asked traditional question: which one has more?
- -> Answered in way that was expected
- -> Failed conservation task as chose line that was longest not had the most
- -> Followed up wit question: Which row do you want to eat? They then reached to the one with more M&Ms (criticism)
6
Q
Principles of counting (Gelman and Gallistel)
A
- Series of experiments with pre school children to study counting behaviour
- They found learning to count is crucial to understanding numbers
- Learning to count is guided by innate abstract principles that guides or contains acquisition of number concepts
- Domain specific view of numerical cognition
- Born with ability to count
7
Q
Principles of counting
A
- One to one principle = each item in an array is tagged once
- Stable order = tags must be arranged in a stable, repeatable order e.g. order increases
- Cardinal = final tag represents number of items in a set
- Abstraction = any events can be classified for counting
- Order irrelevance = order of tagging does not matter e.g. if lecturer wants to count students in hall, can start anywhere as long as sequence is followed
4 and 5 = develop when slightly older
8
Q
Challenges to principles of counting
A
- Children derive the principles after experience so its not innate
- Wynn = transfer of counting principles:
- -> Said if children only use the one to one and stable order but didn’t understand cardinal would suggest they don’t have a concept of number
- -> Tested this by asking children to count events
- -> Found older children (3.5) counted more trials correctly than younger children (2.5) and 3.5 were more likely to use cardinal principle
- -> Concluded children don’t understand kink between counting and numerosity until 2.5
9
Q
Infants numerical abilities
A
Starkey and Cooper
- 5.5 month infants
- See whether infants could discriminate small numbers of items
- Habituation paradigm = to see whether infants could make distinctions between sets
- Showed infants series of 2 dots until they become bored
- Then gave new array of 3 dots
- Found looking times increased
- Was significant dishabituation in the small number conditions (2 and 3) but not large numbers (4-6)
10
Q
Wynn = violation of expectations
A
- Argues may not just be subsidisation (rapid enumeration of sets without counting) but infants may have some sort of counting ability
- Violation of expectations paradigm = one object placed on stage, screen goes up, second object placed beside it, screen went down then up again, 3 objects present
- -> Infants look longer during unexpected outcome
11
Q
Infants numerical abilities challenges
A
-Clearfield and Mix (1999):
–> Continuous variables = area and contour length and correlated with number
–> Contour length = sum of total perimeter of objects
–> Tested 7 month year olds to see if they were sensitive to numbers
(see notes)
12
Q
Criticism of infants numerical abilities challenges
A
- Xu and Spelke
- Experiment 1:
- -> Looking at whether infants can discriminate between 8 vs 16
- -> Infants look longer at displays with larger number of dots
- Experiment 2
- -> Looking at whether infants can discriminate between 8 vs 12
- -> No evidence that they could discriminate when the arrays are reduced
13
Q
Do infants have numerical abilities?
A
- Infants can approximate number values
- Imprecise and subject to ratio limits but can handle larger numerosities
- -> 6 month infants = 1:2 but not 2:3
- -> 10 month infants = 2:3
- Infants fail with smaller numerosities (2 vs 3) when tasks control for perceptual features
14
Q
The number sense hypothesis
A
- Innate capacity to detect numbers and approximate amounts due to its survival value
- Number sense is rapid but approximate
15
Q
Triple code model = number sense hypothesis
A
- Dehaene 1992
- Analogue Magnitude Representation System = basic number sense allows us to estimate quantities within ratio limits and subsidisation:
- -> Auditory verbal word system (addition, subtraction, devision)
- -> Visual Arabic number system (comparing symbols)
- -> Systems developed through education and culture (environmental exposure)
- -> Can engage in these abilities due to innate ability = interactionist approach
- -> Through development what we learn from culture maps back onto number sense = feedback system
16
Q
Support for number sense hypothesis
A
- Part of brain activated
- Horizontal segment of the BIPS
- Not a causal factors = could be specialised due to experience
- Meta analysis of 17,000 = performance on non-symbolic number sense tests correlative with maths but found it was weak
- Longitudinal study = number sense did not predict maths when controlling for number knowledge
17
Q
Genetic influence on maths
A
- Highly heritable
- Overlap between genetic influences on IQ and maths, and maths and literacy
- General genes involved rather than specific
- Study:
- -> Twin pairs ages 16 performed number sense test
- -> Found more modest heritability and substantial role for non shared environment
- -> Found heritability decreases with age F
18
Q
Environmental factors on maths
A
- Numeracy at start of primary school was examined in relation to social background
- Frequent engagement in learning activities at home predicted maths ability
