This document discusses cognitive psychology concepts related to numerical processing and executive brain functions. It highlights the universal nature of numerical understanding, the implications of dyscalculia, and the neural substrates associated with numerical cognition. Additionally, it covers executive functions, their relation to problem-solving, and their neural correlates in the prefrontal cortex.

1. Cognitive Psychology
Lesson 09 - Spring 2019
The numerate brain
The executive brain
Professor Valentina Bazzarin
USAC Reggio Emilia

2. The numerate brain
This part is not concerned with
algebra but with a core set of
numerical abilities that seem to be
common to almost all humans from
infants to elderly, from the
unschooled to the mathematical
prodigy. Also many other animals have
a basic understanding of numbers.
Dyscalculia (acalculia): difficulties
in understanding numbers; calculation
difficulties.
https://youtu.be/u-Ak83B_G6E

3. The percentage of the population
with developmental dyscalculia is
estimated to be between 3­6
percent, or one in twenty
individuals,” says Line Rothmann,
and she is one of them. As a
dyscalculic, she has difficulty
understanding anything and
everything math related.
https://www.youtube.com/watch?v=rlPFv_E
DnvY

4. Knowledge of numbers has a dedicated neural substrate
Knowledge of numbers is a basic and near universal aspect of
cognition. It is aided by language and cultural knowledge but it is
not dependent on these.
Number meanings can be selectively impaired by damage (dyscalculia)
and may have a dedicated neural substrate (including the
intraparietal sulcus).
Whereas the right hemisphere enables the approximate representation
of number (e.g. about 10), the left hemisphere may enable exact, or
countable, quantification (e.g. exactly 10). This is likely because
the left hemisphere number meaning system can interface with
symbolic/linguistic representations.

5. Teaching math
without words
https://youtu.be/7odhYT8yzUM

6. The meaning of numbers and counting
The meaning of numbers has been variously referred to as magnitude,
quantity (Dehaene 1997) or numerosity (Butterworth 1999). Number
meaning is abstract and independent from of the format used to
denote (e.g. 3, III, three, tre). Integer numbers or whole numbers
are properties of a collection.
Counting is the process of putting each item in a collection in a
one-to-one correspondence with a number or some other
internal/external tally.
Different types of calculation procedure (addition, division, etc.)
may be selectively impaired by brain damage.

7. Examples of
algebraic
visualizations
https://www.youtube.com/watch?v=bbKjX
KV9QNA

8. Counting with fingers, bodies and bases
We need a method to keep track of how many
items have been counted so far.
- External items (marks on bones)
- Internal aids (linguistic symbols).
There is a restricted number of ways of
counting
- Use body parts
- Use base systems.
In Papua New Guinea Yupno have no
specialised words but they use the name of
body parts.
https://www.youtube.com/watch
?v=Jfmzm_qKzd0

9. Finger agnosia - Gerstmann's syndrome
Finger agnosia, first defined in 1924 by
Josef Gerstmann, is the loss in the ability
"to distinguish, name, or recognize the
fingers",[1]
not only the patient's own
fingers, but also the fingers of others, and
drawings and other representations of
fingers. It is one of a tetrad of symptoms
in Gerstmann syndrome, although it is also
possible for finger agnosia to exist on its
own without any other disorders. Usually,
lesions to the left angular gyrus and
posterior parietal areas can lead to finger
agnosia.
Source: wikipedia “finger agnosia”
https://www.youtube.com/watch
?v=vGr8Nbh0Qyw

10. Key-words
Finger agnosia is an inability to identify
individual fingers by touch.
Gerstmann's syndrome is a set of four deficits
(acalculia, finger agnosia, agraphia and
left-right disorientation) believed to be
associated with a damage to the left parietal
lobe.

11. Transcoding
Transcoding means that one symbol is translated into another
of a different type (it encompasses processes such as
reading, i.e passing from written symbols to verbal ones,
writing, i.e verbal labels to written symbols and others).
A number of studies have provided empirical evidence for a
direct route between arabic numeral recognition and verbal
output that bypasses number semantics (Cipollotti 1995).

12. Are numbers represented in a visuospatial code?
Numbers have a visuospatial component
that may relate to the fact that they
form an ordered set.
SNARC effect: if people are asked to
make judgements about numbers (e.g.
odd/even judgments) they are faster
with their left hand for small
numbers but faster with the right
hand for large numbers
https://technabob.com/blog/2011/1
1/11/virtual-icub-robot-counts-li
ke-a-human/

13. The executive brain
The executive functions of the brain can be defined as the
complex processes by which an individual optimizes his or
her performance in a situation that requires the operation
of a number of cognitive processes (Baddeley 1986).
Metaphor → brain’s conductor which instructs other regions
to perform or to be silenced, and generally coordinates
their synchronized activity (Goldberg 2001)
Metacognitive role: supervisory or controlling

14. Anatomical and functional divisions of the prefrontal cortex
Wikipedia : executive functions

15. Optimize executive functions
Executive functions are needed to performance when:
- Several cognitive processes need to be coordinated;
- A situation is novel or difficult;
- A situation does not require an automatic response;
Functional imaging studies and studies on brain-damaged patients
point to a key role of the prefrontal cortex in executive functions.
Patients with lesions here may have difficulties in problem solving,
overcoming habitual responses, multi-tasking and so on.
Working memory is involved too and may consist of several
subsystems, including maintenance and manipulation.

16. Executive functions in practice
https://www.youtube.com/watch?v=Vo-iygv
8s7M
https://www.youtube.com/watch?v=tXZa
u5VIIvU

17. Key words
Ecological validity: the extent to which a task
relates to everyday situations outside the laboratory
Wisconsin Card Sorting Test: A test of executive
functions involving rule induction and rule use
Stroop test: Response interference from naming the ink
color of a written color name (e.g. the word RED is
printed in blue and participants are asked to say the
ink color, that is blue)

18. Neuroeconomics
The use of brain
based
methods/theories in
order to account for
economic decision
making.
https://www.youtube.com/watch?v=2uca-L
oSqwE