NC 1 Flashcards
Mathematical cognition describes how our
Cog. system processes numerical information
Mathematical cognition considers three fields -
Psychology
Neuroscience
Education
Childhood low numeracy can impact future…
QOL (e.g. career path and health)
SYMBOLIC number processing is divided into
Verbal
Visual
NON-SYMBOLIC number processing, i.e.
Three dots representing the number 3
Two systems for language-independent number processing
- Small Exact Numerosity
2. Large approximate numerosity
Two examples of SMALL EXACT NUMEROSITY
Object tracking system
Parallel individuation
One example of LARGE APPROXIMATE NUMEROSITY
ANS (approximate number system)
Task to test the Small Exact Numerosity system
Enumeration tasks
How might enumeration tasks be solved (2)
- Counting
2. Subitizing
Subitizing is
Fast/accurate enumeration of small numerical quantities
Fast/accurate enumeration of small numerical quantities
Subitizing
Subitizing ______ with age
Develops
Svenson + Sjoberg (1983)
Subitizing
Between 2 and 5 years old
Children can subitize 1-3 items
Svenson + Sjoberg (1983)
Subitizing
Between 7 years old and adulthood
Children can subitize 3-4 items
Svenson + Sjoberg (1983)
Subitizing
At what age can we subitize 3-4 items?
Between 7 and adulthood
Piazza et al., (2011)
Theory for limited subitizing capacity in early age?
Visuo-spatial working memory
Piazza et al., (2011)
As VS WM capacity increases
So does subitizing capacity
(Schleifer + Landerl, 2011)
How might dyscalculia (math disability) affect subitizing?
Children with D have STEEPER subitizing slopes
(Schleifer + Landerl, 2011)
“Children with dyscalculia have steeper subitizing slopes”
What does this mean?
As number of dots increases, so does RT (time spent subitizing)
“The system dedicated to the perception of small numerosities (3-4 items)”
Subitizing
Preschool children can subitize 1-3, older children can subitize 3 to 4. However, there is
Variability
The subitizing system is most likely related to the
Visuospatial working memory
The ANS (Approximate Number System) is based on
Estimation
The ANS is used for large/small numerosities
Large
ANS involves an ________ representation of large numerical quantities
Approximate
Example of an ANS task
“Which has more dots?”
Ratio effect in ANS
Ability to discriminate between large quantities relates to the RATIO of numerical sets
12 dots vs 16 dots
How would you work out the ratio?
16/12
20 dots vs 16 dots
What is the distance?
4
If the ratio is close to 1,
It is hard to discriminate
If the ratio is far from 1,
It is easy to discriminate
This ratio is easy to discriminate
Far from 1
As the ratio increases, the percent ________ also increases
Correct
What is a Gaussian curve?
Internal continuum of numbers - each number is 1 Gaussian curve
Gaussian Curve
Each numerosity is represented
As a Gaussian curve
Gaussian curves follow a _____ model
Linear
Gaussian Curve
No overlap indicates
High accuracy
Gaussian Curve
Overlapping indicates
Low accuracy
Gaussian Curve
With 9 and 8, there is _____ overlap
Huge
Gaussian Curve
overlapping is negatively correlated with
Accuracy
Weber Fraction
The lower,
The better
Xue + Spelke (2000)
What ratio can 6 month old infants correctly detect?
Ratio 2 (i..e 8 vs 16)
Xu + Arriaga (2007)
10 month old infants can correctly detect a ratio of
1.5
1.5
This is the ratio a _____ old infant can detect
10
(Halberda et al., 2012)
Proposed that there is ___________ of the ANS from childhood to adulthood
Rapid amelioration
(Halberda et al., 2012)
Proposed there is rapid amelioration of the ANS from childhood to adulthood, then
A slow decline
Starr et al., (2013)
ANS acuity predicts
Later math achievement
Weber Fraction is a way of measuring
ANS acuity
Libertus et al., (2011)
ANS acuity in preschool correlates with
Math achievement
ANS acuity is correlated with math achievement in both __________ and __________
Preschoolers
Adolescents
ANS acuity is reduced in children with
Dsycalculia
What difficulties are faced when studying the ANS? (4)
- Reliability
- Perceptual confounds
- Influence of executive skills
- Does the ANS exist?
ANS studies
Reliability is _____
Low
How do we know reliability is low in ANS studies?
- Diff. ANS tasks have weak correlations
- Low test-retest reliability
(DeWind + Brannon, 2016)
Found different ANS tasks have weak
Correlations
(DeWind + Brannon, 2016)
Found different ANS tasks have _____ correlations
Weak
Limitations of ANS studies
What does ‘Perceptual Confounds’ refer to?
Idea that spatial dimensions covary with numerosity
Perceptual Confounds
Spatial dimensions covary with numerosity, e.g. (4)
Density
Area
Perimeter
Item size
GIlmore et al.., (2013)
_______ may explain the relation between ANS and math achievement
Inhibition
Is there a real ANS?
Which theory challenges the idea of an ANS?
Sensory-intergration theory
Sensory-intergration theory
Proposes numerosity estimation is ACTUALLY the product of (2)
- Non-numerical sensory cues
2. Non symbolic stimuli
Part of the motivation to study mathematical cognition comes from
Increasing awareness that many struggle with mathematics
There is ______ in RT for each additional item in the subitizing range
Small/NO RT INCREASE
There is a larger increase in RT per item outside the ….
Subitizing range
___________ in subitizing may be related to the development of counting skills
Individual differences
When using the ANS, irrelevant visual information (e.g. surface area) has to be ignored. This is known as…
Inhibitory control
When using the ANS, irrelevant visual information (e.g. _____) has to be ignored. This is known as inhibitory control
Surface area
Inhibitory control
The ability to suppress irrelevant information
A smaller Weber fraction denotes
More accurate number representations
