Q1. Does learning symbolic arithmetic inhibit the innate non- symbolic approximate abilities? (Sarah) No! Quite on the contrary! 10 20 30 40 50 0 0.2 0.4 0.6 0.8 1 2 Infants (Izard et al., 2009; Xu & Spelke, 2000; Xu & Arriaga, 2007) Piazza et al., Cognition 2010; Chinello et al., submitted. Halberda et al., 2008 Pica et al., 2004 Piazza et al., 2004 Power function fit The precision of numerical discrimination (JND or Weber fraction) increases with age. Round numbers accurately discriminated 0 1 2 3 4 5 6 7 10 5:6 4:5 3:4 2:3 1:2 Age in years
Transcript
Q1. Does learning symbolic arithmetic inhibit the innate non-symbolic approximate abilities? (Sarah)
No! Quite on the contrary!
10 20 30 40 500
0.2
0.4
0.6
0.8
1
2
Infants (Izard et al., 2009; Xu & Spelke, 2000; Xu & Arriaga, 2007)Piazza et al., Cognition 2010; Chinello et al., submitted.
Halberda et al., 2008Pica et al., 2004Piazza et al., 2004Power function fit
The precision of numerical discrimination (JND or Weber fraction) increases with age. Round numbers accurately
discriminated
0 1 2 3 4 5 6 7 10
5:6
4:5
3:4
2:3
1:2
Age in years
Does math education affect the
ANS ?(disentangling maturation from
education factors)
The Munduruku is an indigenouspopulation of the Amazon (Brasil)
- They have number words only up to 5.- They fail in tasks of exact calculation
- They have a spontaneous capacity for approximate estimation, comparison, addition
- As a group, they have a normal non-verbal magnitude system, even for very large quantities
[Piazza, Pica, Dehaene, in preparation]
0
0.1
0.2
0.3
0.4
0.5
0 10 20 30 40 50 60 70
Munduruku, uneducated
Munduruku, some education
Italian participants (group means)
Age
Weber fraction Weber fraction
0.0
0.1
0.2
0.3
0.4
0.5
0 1 2 3 4 5 6 7 8Years of Education
r²=26.8%, p=0.001
36 Munduruku subjects [aged from 4 to 67]
12 Completely uneducated24 Received some education
0.7 1 1.40
20
40
60
80
100
0.7 1 1.40
20
40
60
80
100
Uneducated (n=7) Some education (n=13)
Performance of Munduruku adults
w = 0.288 w = 0.177
% larger responses
Ratio of n1 and n2 (log scale)
*“choose the larger”
Math education starts
• Symbolic and non-symbolic competences go hand in hand during development and enhance one another in a form of circular or spiral causality
Symbolic number code
Non-symbolic number code
Intra Parietal Sulcusneuronal populations
• More exact• More linear
• More approximate• More compressed
Q2. Can non-symbolic numerical abilities be trained ? Which kindsof games/manipulations can be used to enhance them? (Timothée)
• We just completed a training study on kindergarteners of 4 to 6 years of age!
• The games was a “matching card game”, whereby children were given a card and had to match it with the card containing the same number of items among several distracting cards. It was a small group training – suited for real classroom!
• Results: after a ½ hour group training every week for 4 weeks the acuity of the approx number system is significantly higher then in a group trained on the same stimuli but on items’ shapes recognition memory.
• Future project: investigate the impact on learning symbolic numbers (could not be done because research in Italy and was only funded for one year…thus cannot do a longitudinal follow-up).
• Starting project ion training Mundurukus involving 4 groups:1. training with approximate quantities (no symbols)2. training with exact quantities (no symbols/one-to-one correspondence)3. training with exact verbal symbols (verbal sequence/verbal counting)4. training with exact visuo-spatial symbols (abacus-like/visual shape recognition)
Q3. Does making kids aware of their existing abilities help themfeeling learning of symbolic arithmetic less complicated? Role ofmeta-cognition and self-esteem in learning (Muriel)
• Having the pupils experiencing that they can COUNT ON THEIR INTUITIONS should be extremely useful and important to boost their motivation and self-confidence.
• In domains classically treated as being “hard” such that of mathematics, there seems to be a strong (and largely unconscious) effect of STEREOTYPE THREAT. (Italian study of north vs. south stereotype in math abilities)
• Math performance heavily influenced by gender stereotypes (i.e., you do not even need to know it, your teacher “shows it” … )
Q4. Questioning the current educational system: are we introducingsymbolization and symbolic calculation rules too early? When shouldwe start teaching symbolic maths? Shall we train the pre-existingapproximate abilities first, or shall we train approximate abilities andexact calculation at the same time? (Muriel, Marie, Théophile, Asma)
According to the results of the present research, we should propose to:
1. Make children aware that by relying on their intuition of magnitude they can get very accurate, even though sometimes only approximate, answers to symbolic number problems that may seem very complex (and, in passing, that there are NO gender difference in these basic abilities!).
2. Train children in performing approximate calculation
3. Train them to make calculation in the more intuitive way (e.g, subtractions starting from the large number and not from the units, using decomposition), and only MUCH LATER introducing calculation procedures such that of carrying.
This WILL AVOID the presence of major but frequent calculation ERRORS (e.g., the result of a subtraction is larger than the subtraend) due to bad understanding of the calculation procedures, and withdrawing from math BECAUSE of no or little understanding of calculation procedures.
“Number neurons” in macaque
[Nie
der,
Sci
ence
200
2]
Raster-plot
Each line corresponds to a trialEach train is an ACTION POTENTIAL (spike)
The you calculate the mean across trials (spike rate), and compare spike rates of a given (set of) neuron(s) in different conditions .So you derive responce functions (“tuning curves”).A “tunig curve” for a given stimulus parameter (here movement direction) is a curve describing how the neuron(s) responds to different values of that parameter:
Recording neuronal firing example:
Neurons in motor cortex coding the direction of the arm movement
0 4 3 2 1 8 7 6 5 4directions
Spi
kes/
sec
“Tuning curves” for numerosity
Single neurons recording.in monkeys performing the numerosity comparison task
Weber law for numerosity coding at the level of single neuron tuning curves
Number is initially extracted from parietal neurons and then the information is transmitted to prefrontal cortex neurons.
Responce latency (ms)
Multiple regions contain neurons coding for number. Which does what?
Key function of PARIETAL CORTEX = DYNAMIC REMAPPING OF SPACE
Pairetal cortex CONTAINS MULTIPLE REPRESENTATIONS OF SPACE in different egocentric frames of reference FOR ACTION PREPARATION
Spatial location of stimuli are remapped from the coordinate of the RECEPTOR SURFACE (retina, coclea, ...) To the coordinates of the EFFECTOR (eyes, head, hands, ...)
• Highly plastic (tool use changes the receptive field of MIP arm-centred neurons)
• Perform operations equivalent to vector addition
Putative homologies in parietal cortex maps of man and monkeys
-NUCLEAR MAGNETIC RESONANCE consists in the absorbtion by protons of Idrogen of electromagnetic waves of given frequency (MegaHz ), in the presence of a magnetic field. Protons’s spins are usually randomly distributed, while in the absence of a strong magnetic field align to the directions generated by the electromagnetic field.
- If we give an electromagnetic impulse at an adequate frequency (dipendent upon the magnetic field) spin change their rotatio axes. Then they go back to their initial state. The retourn to the initial equilibrium generates the emission of electromagnetic waves measurable at distance, which constants of relaxations (T1, T2) are dependent upon the tissue in which the atom is embedded into.
How to make the RMN signal sensitive to the CEREBRAL ACTIVITY?
- Deoxi-emoglobin is paramagnetic thus perturbs the RMN signal (effect on T2 apparent, o T2*)
- Brain activity generates:- Increased oxigen consumption and increased blood supply.- Oxi/deoxi emoglobine ratio increase- Magnetic susceptibility decreases- T2* parameter increases- RM signal increases
Since BOLD (blood oxygen level dependent) signal is linked to changes in blood flow BOLD response is:
1. SLOW compared to the neural response2. DELAYED compared to the neural response
secondsstimulus
BOLD
Still quite *&^%$#@ clueless here!
This link is studied by neurophysiology and is
approximately understood
This link is studied by MR physics and approximately
understood
BUT….. LUCKILY …Simultaneous measures of electric NEURAL and fMRI BOLD signals demonstrate
that the two ARE HIHGLY CORRELATED!!!!!!!
STRONG CORRELATION NETWEEN BOLD and elettrophysiological measures(1. average on action potentials over multiple neurons (MUA), and 2. Local field potential (LFP) on under threashold activity).
Example: BOLD variation with stimolus intesity
tuning curves
stimulus space
stimulus S1 stimulus S2
total I(S1) total I(S2)=
CLASSIC SUBTRACTION METHOD
total I(S2, S2) total I(S1,S2)<
S2 preceded by S2
ADAPTATION METHOD
Using “adaptation” we can increase spatial resolution
sampled volume (voxel, typically 2X2X2 mm)
Different populations code for S1 and S2, but the total activation is = for S1 and S2
Measurable difference in activation, indicating that S1 and S2 are coded by different neural populations
S2 preceded by S1
Adattamento dell’attività neurale
0
Firing rate 1 2 3 5 84 6 7 9…
Using “adaptation” we can decipher neural coding schemes (“tuning curves”)
0
Firing rate 1 2 3 5 84 6 7 9…
Adattamento dell’attività neurale
Using “adaptation” we can decipher neural coding schemes (“tuning curves”)
0
Firing rate 1 2 3 5 84 6 7 9…
Adattamento dell’attività neurale
Using “adaptation” we can decipher neural coding schemes (“tuning curves”)
0
Firing rate 1 2 3 5 84 6 7 9…
1 2 3 5 84 6 7 9… Test numbers
Adattamento dell’attività neurale
Using “adaptation” we can decipher neural coding schemes (“tuning curves”)
0
Firing rate 1 2 3 5 84 6 7 9…
1 2 3 5 84 6 7 9… Test numbers
Adattamento dell’attività neurale
Using “adaptation” we can decipher neural coding schemes (“tuning curves”)
Piazza, M. Izard, V., Pinel, P., Le Bihan, D. & Dehaene, S. (2004) Neuron
fMRI “adaptation” experiment to investigate numerosity coding scheme
Regions where activity increases with a CHANGE
in NUMBER
L R
Risponse to deviant numerosities in the IPS bilaterally
Left intraparietal cortex Right intraparietal cortex
8 16 32 64-0.4
-0.2
0
0.2
0.4
Deviant numerosity (linear scale)
Nadapt 16Nadaptt 32
Deviant numerosity (linear scale)8 16 32 64
-0.4
-0.2
0
0.2
0.4
Nadapt 16Nadapt 32
8 16 32 64-0.4
-0.2
0
0.2
0.4
8 16 32 64-0.4
-0.2
0
0.2
0.4
Deviant numerosity (log scale)
Nadapt 16Nadapt 32
Nadapt 16Nadapt 32
Deviant numerosity (log scale)
0.5 1 2-0.4
-0.2
0
0.2
0.4
0.5 1 2-0.4
-0.2
0
0.2
0.4
Deviation ratio (log scale)Deviation ratio (log scale)
z = 42
Weber law in intraparietalsulcus
Multiple replications using the same paradigm (e.g., Cantlon et al., 2005)
4 YEARS OLD KIDS
ADULTS
Especially in the RIGHT HIPS!
Possible test stimuli:
…
…
A. Experimental design
Risposta alla numerosità nel cervello di bebè già a 3 mesi !!! Tecnica dell’EEG
Response to number change in 3 months old babies!! EEG (ERPs)
Stesso numeroDiversa forma
Stesso numeroDiversa forma
Diverso numero Stessa forma
Stesso numeroStessa forma
RIGHT HEMISPHE
• WHY IS THIS INTERESTING ? ? ? ? ? ???????????????????????????????
• Hp: the non-verbal intuitions of NUMEROSITY GROUND our capacity to understand numbers and arithmetic (Butterworth, Dehaene, etc...)
If we better understand the cognitive and neural basis underlying such start-up-tool we can better understand the development of numerical abilities and maybe help developing tools which improve teaching efficacy and therapeutic tools in cases of dysfunctioning systems (sia dello sviluppo che acquisite)
• Criteria for a start-up function / brain region:
(1)-> its integrity should be a necessary condition for normal development of symbolic number skills.
(2)-> its computational constraints should predict the speed and ease of symbolic number acquisition.
(3)-> some traces of its computational signatures may be present when humans process symbolic numbers.
• If the ANS grounds the cultural acquisition of symbolic number skills it should guideand constrain it:
(1)-> its integrity should be a necessary condition for normal development of symbolic number skills.
(2)-> its computational constraints should predict the speed and ease of symbolic number acquisition.
(3)-> some traces of its computational signatures may be present when humans process symbolic numbers.
Numbers are treated as representing APPROXIMATE QUANTITIES since the initial
stages of learing
Gilmore et al., Nature 2007
(1) Traces of the ANS in symbolic number processing - behavioural
(1) Traces of the ANS in symbolic number processing - behavioural
Same Ratio-dependent responses in non-symbolic and symbolic number
processing
0,75
0,8
0,85
0,9
0,95
1
1 2 3
Acc
urac
y
*“choose the larger”
*“choose the larger”
12 16
Symbolic comparison
Non-symbolic comparison
1.1 1.3 1.6Ratio (bigger/smaller set)
[Chinello et al., under revision]
ADULTS
Numbers are treated as analogical APPROXIMATE
QUANTITIES throughout the life-span
AFFERMAZIONE:
EVIDENCES (behavioral):
1) “EFFETTO DISTANZA” CON NUMERISIMBOLICI
Tempi di risposta
Errori
Numeri presentati
Più piccolo Più grande
Ai soggetti viene presentato un numero e viene chiesto di rispondere se sia più grande o più piccolo di un numero di riferimento (ad es. 65).
3225
7663
I tempi di risposta e gli errori sono modulati dalla distanza (numerica) tra i numeri e questo è indice che vi sono tracce di una rappresentazione ANALOGICA dei numeri
(1) ANS correlates with symbolic number processing throughout life-span
• All numerical tasks activate this region(e.g. addition, subtraction, comparison, approximation, digit detection…)
• This region fulfils two criteria for a semantic-level representation:- Format invariance- Quantity-related
Crucial parameter coded: numerical quantity
Parietal cortex in symbolic number cognition
• Subjects are asked to respondto a given infrequent stimulus (number « 5 », letter « B», color« red »)• Numbers, letter, and coloursare presented visually and auditory•Only non-target stimuli are analysed
Example of parietal activation “specific” to numbers (Eger et al, Neuron 2003)
Numbers-(letters&colors)
Deviant number
17, 18, o 19
47, 48, o 49
20 50
close far
far close
Adaptation number
NUMBER
Deviant format
Dots
Arabic digits
dots digits
same different
different same
Adaptation format
FORMAT
2 CRITERA DEFINITIONAL For a SEMANTIC representation:•INVARIANCE TO ENTRY FORMAT
=
=
•SEMANTIC METRIC
<
>
(1) Convergence towards a quantity code in the IPS in adults
(1) Convergence towards a quantity code in the IPS in adults
50
18 1919
HABITUATION 20
DEVIANTS
or
Number adaptation protocol(brain response to a change in number)
[Piazza et al., Neuron 2007]
-8
-6
-4
-2
0
2
4
6
8
10
Act
ivat
ion
(bet
as)
closefar
Right Parietal Peak
DOTS(among
dots)
DOTS(among arabic)
ARABIC(among arabic)
ARABIC(among
dots)
samedifferent-8
-6
-4
-2
0
2
4
6
8
10
Act
ivat
ion
(bet
as)
closefar
DOTS(among
dots)
DOTS(among arabic)
ARABIC(among arabic)
ARABIC(among
dots)
Left Parietal Peak
Symbolic number code
Non-symbolic number code
• If the ANS grounds the cultural acquisition of symbolic number skills it should guideand constrain it:
(1)-> its integrity should be a necessary condition for normal development of symbolic number skills.
(2)-> its computational constraints should predict the speed and ease of symbolic number acquisition.
(3)-> some traces of its computational signatures may be present when humans process symbolic numbers.
10 20 30 40 500
0.2
0.4
0.6
0.8
1
2
(2) ANS maturation may account for lexical acquisition pattern
Infants (Izard et al., 2009; Xu & Spelke, 2000; Xu & Arriaga, 2007)Piazza et al., Cognition 2010; Chinello et al., submitted.
Halberda et al., 2008Pica et al., 2004Piazza et al., 2004Power function fit
The precision of numerical discrimination (JND or Weber fraction) increases with age.
Age in years
Estim
ated
web
erfra
ctio
n
Round numbers accurately discriminated
0 1 2 3 4 5 6 7 10
5:6
4:5
3:4
2:3
1:2
Age in years
(2) ANS maturation may account for lexical acquisition pattern
In the NUMBER domain, lexical acquisition is a slow and serial process.
2 years of age
3 years of age
4 years of age
Number words refer to quantities
Understand “one” Understand
“two” Understand “three”
Counting principles “discovered”
Understand “four”
Round numbers accurately discriminated
Age in years0 1 2 3 4 5 6 7 10
5:6
4:5
3:4
2:3
1:2
0.5 1 adults
1
2
3
4
OTS capacity (number of objects attended at a time)
Age in years
The OTS reaches the adult capacity by 12 months: 4 “attentional pointers” already available. This does not account for the lexical acquisition pattern!
2 years of age
3 years of age
4 years of age
Number words refer to
quantities Understand “one” Understand
“two” Understand “three”
Counting principles “discovered”
Understand “four”
Symbolic number acquisition
• If the ANS grounds the cultural acquisition of symbolic number skills it should guideand constrain it:
(1)-> its integrity should be a necessary condition for normal development of symbolic number skills.
(2)-> its computational constraints should predict the speed and ease of symbolic number acquisition.
(3)-> some traces of its computational signatures may be present when humans process symbolic numbers.
0.7 1 1.40
20
40
60
80
100
4-6 years 8-11 years Adultsw=0.15
0.7 1 1.40
20
40
60
80
100
n1/n2 (log scale)
w=0.34
0.7 1 1.40
20
40
60
80
100 w=0.25
n1/n2 (log scale) n1/n2 (log scale)
% re
sp «
n2 is
larg
er»
4 groups of subjects(1) 8-11 years old dyscalculic (diagnosis: Italian standardized test), no neurological problems(2) 8-11 years old matched for IQ and cronological age(3) 4-6 years old(4) Adults
RESULTS (non dyscalculic subjects)
*
“choose the larger”
n1 n2
(3)The necessity of ANS for numeracy development: dyscalculia
[Piazza et al., Cognition 2010]
0,10
0,15
0,20
0,25
0,30
0,35
0,40
0,45
0,50
0 5 10 15 20 25 30
non-dyscalculics
power function (R2 = 0.97)
Age (years)
Est
imat
ed w
eber
fract
ion
[Piazza et al., Cognition 2010]
Estimated w
Dis
tribu
tion
Est
imat
es
-0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90
1
2
3
4
5
6
7
adults10 yo5 yo10 yo dyscalculics
R2 = 0,17P=0.04
0
0,5
1
1,5
2
2,5
3
3,5
4
0,1 0,3 0,5 0,7
Estimated wN
erro
rs in
num
ber c
ompa
rison
ta
sks
Impairment in the ANS predicts symbolic number impairement but not performance in other domains (word
reading)
(3)The necessity of ANS for numeracy development: dyscalculia
In dyscalculic children the ANS is substantially impaired:
*
“choose the larger”
n1 n2
dyscalculics
Correlations does not imply causation The “circular causality” issue
• During development, attaching “meaning” to numerical symbols may entail:1. Mapping numerical symbols onto pre-existing approximate quantity representations.2. Refining the quantity representations
• It is thus possible that the core quantity system is:–Not only fundational for the acquisition of numerical symbols and principles –But also deeply modified by the acquisition of numerical symbols and numerical principles.
10 20 30 40 500
0.2
0.4
0.6
0.8
1
2
Development of ANS
[Piazza & Izard, The Neuroscientist , 2009]
Estim
ated
web
erfra
ctio
n
Power function:Exponent = -0.43R2=0.74p=0.001
Infants (Izard et al., 2009; Xu & Spelke, 2000; Xu & Arriaga, 2007)Piazza et al., Cognition 2010; Chinello et al., submitted.
Halberda et al., 2008Pica et al., 2004Piazza et al., 2004Power function fit
Age in years
The precision of numerical discrimination increases with age.
What is the role of maturation?What is the role of education?
Does math education affect the
ANS ?(disentangling maturation from
education factors)
The Munduruku is an indigenouspopulation of the Amazon (Brasil)
- They have number words only up to 5.- They fail in tasks of exact calculation
- They have a spontaneous capacity for approximate estimation, comparison, addition
- As a group, they have a normal non-verbal magnitude system, even for very large quantities
[Piazza, Pica, Dehaene, in preparation]
0
0.1
0.2
0.3
0.4
0.5
0 10 20 30 40 50 60 70
Munduruku, uneducated
Munduruku, some education
Italian participants (group means)
Age
Weber fraction Weber fraction
0.0
0.1
0.2
0.3
0.4
0.5
0 1 2 3 4 5 6 7 8Years of Education
r²=26.8%, p=0.001
36 Munduruku subjects [aged from 4 to 67]
12 Completely uneducated24 Received some education
0.7 1 1.40
20
40
60
80
100
0.7 1 1.40
20
40
60
80
100
Uneducated (n=7) Some education (n=13)
Performance of Munduruku adults
w = 0.288 w = 0.177
% larger responses
Ratio of n1 and n2 (log scale)
*“choose the larger”
Conclusions
-There is some good evidence for a fundational role of the parietal system for approximate numerosity in symbolic numerical representations.
But there is a lot to be discovered:
1) A true causal role of the ANS in dyscalculia awaits confirmation (longitudinal studies)
2) What are the neural mechanisms that drive the refinement of the quantity code for symbolic stimuli? Are they necessarily mediated by language?
3) Which aspects of maths education enhance approximate number prepresentation acuity?
THREE PARIETAL CIRCUITS FOR NUMBER PROCESSING
z = 44 x = 39x = - 48
x = 54x = - 49 z = 30
x = 12
A.
B.
C.
Left hemisphere Right hemisphereAxial slice50 %
22 %
z = 49
z = 61x = - 26
HORIZONTAL SEGMENT OF THE INTRAPARIETAL SULCUS (hips)
LEFT ANGUALR GYRUS
POSTERIOR SUPERIOR PARIETAL LOBE (more right)
Left hemisphere Right hemisphere
Seen from top
LEFT ANGUALR GYRUS (l AG)-Retrieval of arithmetical facts (multiplications, additions)-Simple exact calculation
POSTERIOR SUPERIOR PARIETAL LOBE (more right)(PSPL) vLIP?-Subtractions-Complex additions-Approximate calculation
HORIZONTAL SEGMENT OF THE INTRAPARIETAL SULCUS (HIPS) hVIP?-Number comparison-Ratio effect-Numerical priming-Approximate calculation
CS
IPS
Three parietal circuits for number processing (Dehaene, Piazza et al.,2003)
Evidence for a verbal code in arithmetical facts retrieval
• Interference on TRs in calculation
Task1 (arithmetic): Multiplicazions or subtractionsTask 2 (short term memory): Phonological (whisper a non-word) o visuo-spatial (remember the position of an object)
Single taskPhonological dual taskVisuo-spatial dual task
1. Training experiment: Trained to memorize complex two digits number arithmetical facts and measure the effects on brain activity
Left angular gyrus in arithmetical facts retrieval
TRAINED >
UNTRAINED
UNTRAINED>
TRAINED
Ischebeck et al., 2009
2. Arithmetical tasks performed in the scanner and activation correlated with subsequent subjects’ report on the strategy used (fact retreival or computation)
[Grabner et al., 2009 ]
Left angular gyrus in arithmetical facts retrieval
Evidence for a spatial code in arithmetical computations
• Interference on TRs in calculation
Task1 (arithmetic): Multiplicazions or subtractionsTask 2 (short term memory): Phonological (whisper a non-word) o visuo-spatial (remember the position of an object)
Single taskPhonological dual taskVisuo-spatial dual task
Do spatial/motor processes interfere with calculation ?
« Answer the arithmetical problems whileperforming a sequence of finger movements in the same time ! »
Evidence for a spatial code in arithmetical computations
MULTIPLICATION ADDITION SOUSTRACTION600
700
800
900
1000
1100
1200
NO MVTS MVTS
RT
(mse
c)
**
In the dual task, sequential finger movements were found to slow down responsesto additions and subtractions, whereas multiplications (matched for difficulty) were unaffected
Regioni corticali tipicamente dannegggiate nel neglect
Tipico disegno (copia da modello) di un paziente con negelct
Modello Copia del paziente
Test dello sbarramento di lineeTest della bisezione di linee
Evidence for a spatial code in arithmetical computations: neglect
Numerical bisection test :“What is the number between 2 and 6?”“Answer: 5” RIGHT BIAS!
Zorzi et al., Nature 2002
Evidence for a spatial code in arithmetical computations: neglect
Posterior parietal saccade regions in
calculation
Shaki et al., 2009 (Psych Bull Rev)
Spatial code in number representations: the mental number
