Flashcards in Number cognition Deck (25)
What are the 3 facets of number understanding (aka number concepts)?
1. Cardinality (abstract property; share same number)
2. Ordinality (abstract property; relations between sets; one set of objects is bigger than another)
3. Arithmatic relations (can move between sets of different sizes by adding or subtracting)
How can a habituation paradigm be used to assess children's number cognition?
Children are shown arrays of dots of a certain number (e.g. 3) and habituate to this number (repeated trials); when a different number of dots is presented (e.g. 2) children look longer at the array and dishabituate suggesting they can compare numbers
Outline habituation evidence that infants have basic number cognition (Cooper, 1984).
Two arrays of squares, either representing bigger than (e.g. 4 squares vs. 2 squares) or smaller than (e.g. 2 squares vs. 4 squares); e.g. first shown bigger than arrays (4 squares vs. 2 squares) then shown smaller than arrays (2 squares vs. 4 squares), equal arrays (4 squares vs. 4 squares), or novel bigger than arrays (3 squares vs. 1 squares)
- 10mo infants dishabituated to the equal arrays (could distinguish equal and unequal relations)
- 14mo infants dishabituated to equal arrays and less than arrays (could distinguish equal and unequal relations and reversed relations)
Outline violation-of-expectation evidence that infants have basic number cognition (Wynn, 1992).
1. 1 object is placed in a display, screen then covers/occludes the object and 1 object is placed in the display; the screen lowers to reveal either 2 objects (possible outcome) or 1 object (impossible outcome)
2. 2 objects are placed in a display, screen then covers/occludes the objects, 1 object is removed from the display; the screen lowers to reveal either 1 object (possible outcome) or 2 objects (impossible outcome)
- 5mo looked longer at the impossible outcome as this was unexpected
Is the finding of Wynn (1992) due to violation of physical principles rather than violation of mathematical principles?
When the objects were changed but the number of objects was the same, infants looked longer at the impossible outcome (Simon et al., 1995) so surprise is due to violation of mathematical principles not violation of physical principles
Children have number concepts but their numerical understanding is limited to small numbers. What does this mean?
Children get stuck with 4/5 objects and can't dishabituate
Outline evidence that infants need large ratios between large numbers in order to compare them (Xu and Spelke, 2000).
Infants were shown arrays of 8 or 16 objects, and were then tested on arrays of 8 and 16 objects
- 6mo infants need a larger difference between sets to distinguish between them - need 1:2 ratio (i.e. 8 vs. 16)
- 9mo infants need 2:3 ratio (i.e. 8 vs. 12)
Outline evidence that young infants can only distinguish betwen small numbers (Antell and Keating, 1983; Feigenson, Carey and Hauser, 2002).
Antell and Keating (1983) - 1-3 day old infants dishabituated to change from 2 to 3 objects but not changes from 4 to 6 objects
Feigenson, Carey and Hauser (2002) - 10mo and 12mo chose larger quantity of crackers when comparing smaller numbers (1 vs. 2, 2 vs. 3) but failed to discriminate when comparing larger numbers (3 vs. 4, 2 vs. 4, 3 vs. 6)
Infants rely on what type of representations instead of what type of representations?
Infants rely on object-file representations (each item in a set is represented by a distinct symbol/file, discriminate between numbers through one-to-one correspondence between files) instead of mental magnitude representations (number of items in a set is represented as a magnitude proportional to number, discriminate between numbers through ratio between numbers)
Infants ability to understand large numbers is limited to ________ and _______ ______.
Approximations and large ratios
Numbers that infants understand are limited to what they can subitize. What does this mean?
subitize = hold rapid sensory impressions
When do children start moving away from limitations to their numerical understanding?
when they start learning to count (3-4yo)
What is nature explanation of children's counting (Fuson)?
Counting starts as parroting adults and repeating sequences of numbers as uninterrupted chain without having numerical understanding
Uninterrupted chains of numbers only get segmented when children understand numbers
What is nurture explanation of children's counting (Gallistel and Gelman, 1978)?
Children have innate, implicit understanding of counting so errors are due to problems in performing a given task rather than incompetence
What are the 5 principles of counting (Gelman and Gallistel, 1978)?
1. One-on-one principle = each item should be counted/tagged with unique number
2. Stable-order principle = numbers should be ordered in same sequence across trials
3. Cardinal principle = last number represents cardinal/size of whole set
4. Abstraction = any objects can be counted
5. Order irrelevance = order in which items are counted/tagged doesn't matter
At what age to children show sensitivity to all 5 principles of counting?
4-5yo could detect variations in all 5 principles of counting (Gelman and Meck, 1983)
Outline evidence that infants are sensitive to contour length rather than number (Clearfield and Mix, 1999).
What does this suggest?
7mo habituated to 2 objects of the same contour length; then either number or contour length was changed
- Infants looked longer when contour length changed even though number stayed the same
- No change in looking time when number changed but contour length stayed the same
Suggests that infants discriminate based on basic perceptual features, such as contour length, and don't have numerical understanding
Feigenson and Spelke (1998) found that infants are sensitive to _____ rather than number.
Mass (i.e. smaller or larger)
Infants have similar numerical abilities to non-verbal animals such as mosquito fish. Why?
Mosquito fish can discriminate between numbers if the numbers are small (i.e. 2 vs. 3); can only discriminate between large numbers if the ratio is large (i.e. 8 vs. 16) (Agrillo et al., 2007)
What is the numerical hypothesis (Gallistel and Gelman, 1992)?
Humans and animals have an innate numerical sense, which is an imprecise/approximate mental system for processing numbers that doesn't rely on verbal ability
Is number sense still present in adults?
Yes - when adults are shown arrays of numbers that they're unable to count, show same fuzzy representation as infants and can discriminate between sets at certain ratios only (Feigenson et al., 2004)
Does counting replace number sense?
No - number sense underpins counting performance
Number sense is related to...
Can this be explained by other variables including IQ?
mathematical ability - mathematical performance at school in 14yo (Halberda et al., 2008)
relationship between number sense and mathematical ability can't be explained by other variables (inc. IQ) (Mundy and Gilmore, 2007)
Outline Siegler's (2009) intervention for improving children's maths skills.
Children played board game for 1hr; in experimental condition, each step had a number, creating direct association between the symbolic number and the position on analogue number line; in control condition, no numbers on number line
Children in the experimental group showed improvement in a range of maths skills (numerical magnitude comparison, number line estimation, counting, numeral identification) sustained over 9 week follow-up