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NUMERICAL COGNITION
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Lecture notes of 8 pages for the course NEUROPSYCHOLOGY at UNN (LECTURE 10/15)
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Lecture 9 – numerical cognitionTheories of number processing:
- Transcoding Model (McCloskey 1992)
- Dual-Code Model (Cohen-Kadosh & Walsh 2009)
- Triple-Code model (Dehaene & Cohen 1995)
Introduction;
- Numerical cognition studies cognitive, evolutionary, developmental, and
neuroanatomical bases of number and magnitude processing as well as mental
arithmetic.
- Interdisciplinary: Mathematics, Psychology, Neuroscience, Linguistics, Education, etc.
Vocabulary;
- Numerosity = Approximate sense of numbers and quantities. Ability to approximate
numbers automatically, without the use of language and/or explicit counting.
- Subitizing = An individual’s capacity to quickly make judgments about numerosity’s
without counting.
- Magnitude = The relative size of a number, object, or any other scalar object.
- Parity test: Judging whether the number is even or odd. Parity test involves
differential response (e.g. right/left key press) to indicate odd vs. even numbers.
- Weber’s Law = Psychological law quantifying dependency between change in a given
stimulus and the corresponding response change: Just-noticeable difference
between two stimuli is proportional to the relative difference between the stimuli.
Symbolic approach (number code components);
- An abstract/symbolic view assumes number representations are independent of
sensorimotor processes.
- According to abstract views, understanding numbers involves transcoding inputs into
a symbolic code.
- Transcoding leads to storing of abstract representations used for mental calculations
- McCloskey 1992;
- Classical modular theory shows that all these systems
(inputs and outputs) are based on semantic
representation. So, based on action.
Dual-Code Model;
- Cohen-Cadosh & Walsh 2009
- Two types of codes involved in number processing.
- Abstract Code: Modality-independent and symbolic
- Non-Abstract Code: Concrete and non-symbolic
- Automatic code dominates over intentional one: Mental calculations can be
performed without access to abstract codes.
- Non-abstract and abstract codes are activated simultaneously.
- Therefore, it predicts interactions between them. So not useful to have a radical
theory (just symbolic or nonsymbolic) more useful to see it as a continuum to find an
optimum level.
, Triple code model;
- Dehaene & Cohen 1995
- Shows three types of areas in the brain.
- One area stores verbal codes for numbers
- One area stores visual Arabic codes for numbers
- One area stores sensory motor (magnitude) code for
number
- Can predict interactions within the three networks. Not
all three are necessary to preform number tasks.
- The verbal code is stored in the language-related areas.
- The visual code is stored in the inferior temporal cortex. It supports the
understanding of written numbers and mathematical symbols.
- The magnitude code is stored in the parietal lobe (HIPS). It supports automatic and
notation-independent operations like numerosity and set judgments.
- The three codes are interfaced, so they can exchange information.
- Not all three are necessary to perform most mental calculations.
Other models;
- Campbell and Clark (1988):
- Encoding Complex Hypothesis.
- 1) Both modality-specific and abstract codes
- 2) Different surface forms can influence strategies
- 3) A single numerical function can involve several codes
- Noël and Seron (1993):
- Preferred Entry Code Model.
- 1) Certain representations may be more suitable to certain tasks
- 2) Individuals may prefer certain representations for idiosyncratic reasons
- Fischer (2012):
- A radically embodied account
Approximate number sense (ANS);
- E.g. how many red dots did you see on the screen? The screen passed very quickly so
how does the brain know roughly how many dots where shown.
- Capacity for ANS is a feature of the perceptual system to automatically and
intuitively estimate numerosities.
- Burr & Ross 2008;
- Participants would look at the cross (shown to the right) for 30 seconds.
The screen is then replaced by another screen with dots on (second
picture).
- When the second picture is shown participants should say there are
more dots on the left-hand side. However, they are identical.
- So this visual adaptation is based of quantity not the perception
differences.
- This is known as the numerosity adaptation effect.
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