Does math education affect approximate number sense

Q1. Does learning symbolic arithmetic inhibit the innate non-
symbolic approximate abilities? (Sarah)

No! Quite on the contrary!

The precision of numerical discrimination
(JND or Weber fraction) increases with
age. Round numbers accurately
discriminated
2 1:2

1

0.8
2:3
0.6

0.4
3:4
0.2
4:5
0
10 20 30 40 50
5:6

Infants (Izard et al., 2009; Xu & Spelke, 2000; Xu & Arriaga, 2007) 0 1 2 3 4 5 6 7 10
Piazza et al., Cognition 2010; Chinello et al., submitted. Age in years
Piazza et al., 2004 Pica et al., 2004 Halberda et al., 2008
Power function fit

Does math
education affect the
ANS ?
(disentangling maturation from
education factors)

The Munduruku is an indigenous
population 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]

36 Munduruku subjects Performance of Munduruku adults

[aged from 4 to 67] Uneducated (n=7) Some education (n=13)
12 Completely uneducated % larger responses
100 100
24 Received some education
80 80
w = 0.288 w = 0.177
60 60
“choose the larger”
40 40
*
20 20

0 0
0.7 1 1.4 0.7 1 1.4
Ratio of n1 and n2 (log scale)

Weber fraction Munduruku, uneducated Weber fraction
0.5 Munduruku, some education 0.5
Italian participants (group means) r²=26.8%, p=0.001

0.4 0.4
Math education starts
0.3 0.3

0.2 0.2

0.1 0.1

0 0.0
0 10 20 30 40 50 60 70 0 1 2 3 4 5 6 7 8
Age Years of Education

• Symbolic and non-symbolic competences go hand in hand during
development and enhance one another in a form of circular or spiral
causality

• More exact
Symbolic
number • More linear
Intra Parietal Sulcus code
neuronal populations
Non-
symbolic
number • More approximate
code • More compressed

Q2. Can non-symbolic numerical abilities be trained ? Which kinds
of 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 them
feeling learning of symbolic arithmetic less complicated? Role of
meta-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 introducing
symbolization and symbolic calculation rules too early? When should
we start teaching symbolic maths? Shall we train the pre-existing
approximate abilities first, or shall we train approximate abilities and
exact 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

[Nieder, Science 2002]

Recording
neuronal firing example:
Neurons in motor cortex coding the
direction of the arm movement

Raster-plot
Each line corresponds to a trial
Each 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:

Spikes/sec 0 4 3 2 1 8 7 6 5 4
directions

Single neurons
recording.in
monkeys
performing the
numerosity
comparison task

“Tuning curves” for
numerosity

Weber law for
numerosity
coding at the level
of single neuron
tuning curves

Multiple regions contain neurons coding for number. Which does what?

Responce latency (ms)

Number is initially extracted from parietal neurons and then the information is
transmitted to prefrontal cortex neurons.

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

Macaque monkey VIP (visual-tactile-vestibular-mutlisensory
head centered - NUMEROSITY)
LIP (visual - saccades – eye centered)

AIP (motor-tactile- grasping- hand centered)

Human VIP (multisensory – face – NUMEROSITY?)

LIP (saccades - eyes)

AIP (grasping, hand)

How to study the “neural code” in humans?
Principles of fMRI Control condition
(funtional magnetic resonance)
-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? Activity condition

- 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

↑Neural activity  ↑ blood flux  ↑ oxi-hemoglobin  ↑ T2*  ↑ BOLD signal

Since BOLD (blood oxygen level dependent) signal is linked to changes in blood
flow BOLD response is:

1. SLOW compared to the neural response
2. DELAYED compared to the neural response

BOLD

seconds
stimulus

This link is studied by Still quite *&^%$#@ clueless This link is studied by MR
neurophysiology and is here! physics and approximately
approximately understood understood

BUT….. LUCKILY …
Simultaneous measures of electric NEURAL and fMRI BOLD signals demonstrate
that the two ARE HIHGLY CORRELATED!!!!!!!

Example: BOLD variation with
stimolus intesity

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).

Using “adaptation” we can increase spatial
resolution
sampled volume (voxel, typically 2X2X2 mm)
tuning curves

stimulus space

CLASSIC SUBTRACTION METHOD ADAPTATION METHOD

stimulus S 1 stimulus S 2 S2 preceded by S 2 S2 preceded by S 1

total I(S1 ) = total I(S2 )

Different populations code for
total I(S2, S2 ) < total I(S1,S 2)
Measurable difference in activation,
S1 and S2, but the total
indicating that S1 and S2 are coded by
activation is = for S1 and S2
different neural populations

Using “adaptation” we can decipher neural coding
schemes (“tuning curves”)

Adattamento dell’attività neurale

Firing rate 1 2 3 4 5 6 7 8 9…

0

Using “adaptation” we can decipher neural coding
schemes (“tuning curves”)


Firing rate 1 2 3 4 5 6 7 8 9…

0
1 2 3 4 5 6 7 8 9… Test numbers

Corse weberian coding
Firing rate 1 2 3 4 5 6 7 8 9…

0
1 2 3 4 5 6 7 8 9… Log (test numbers)
Precise weberian coding
Firing rate 1 2 3 4 5 6 7 8 9…

0
1 2 3 4 5 6 7 8 9… Log (test numbers)

fMRI “adaptation” experiment to investigate
numerosity coding scheme

Adaptation stimuli (16 dots)
[150 ms]

[1050 ms]

Deviant stimuli (10% trials)

8 (far) 10 (medium) 13 (close) 16 (same) 20 (close) 24 (medium) 32 (far)

Piazza, M. Izard, V., Pinel, P., Le Bihan, D. & Dehaene, S. (2004)
Neuron

Risponse to deviant numerosities in the IPS
bilaterally

Regions where
activity increases
with a CHANGE
in NUMBER

L R

Weber law in Left intraparietal cortex Right intraparietal cortex

intraparietal 0.4 0.4

sulcus
0.2 0.2

0 0

-0.2 Nadapt 16 -0.2 Nadapt 16
Nadaptt 32 Nadapt 32
z = 42
-0.4 -0.4
8 16 32 64 8 16 32 64
Deviant numerosity (linear scale) Deviant numerosity (linear scale)

0.4 0.4

0.2 0.2

0 0

-0.2 Nadapt 16 -0.2 Nadapt 16
Nadapt 32 Nadapt 32
-0.4 -0.4
8 16 32 64 8 16 32 64
Deviant numerosity (log scale) Deviant numerosity (log scale)

0.4 0.4

0.2 0.2

0 0

-0.2 -0.2

-0.4 -0.4
0.5 1 2 0.5 1 2
Deviation ratio (log scale) Deviation ratio (log scale)

Multiple replications using the same paradigm (e.g., Cantlon et al., 2005)

ADULTS

4 YEARS OLD KIDS

Especially in the RIGHT HIPS!

Risposta alla numerosità nel cervello di
bebè già a 3 mesi !!! Tecnica dell’EEG

A. Experimental design

…

…

Possible test stimuli:

Response to number change in 3 months old babies!! EEG (ERPs)

RIGHT
Stesso numero
Diversa forma
Diverso numero
Stessa forma
Stesso numero Stesso numero
Diversa forma Stessa forma
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 guide
and constrain it:




(1) Traces of the ANS in symbolic
number processing - behavioural

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
Same Ratio-dependent responses
in non-symbolic and symbolic number
processing

ADULTS
“choose the larger” “choose the larger”

* 12 * 16
Numbers are treated as
1 Symbolic comparison analogical APPROXIMATE
QUANTITIES throughout the life-
0,95
span
Accuracy

0,9
Non-symbolic comparison
0,85

0,8

0,75
11.1 2 1.3 3 1.6
Ratio (bigger/smaller set)

[Chinello et al., under revision]

AFFERMAZIONE:

EVIDENCES (behavioral):

1) “EFFETTO DISTANZA” CON NUMERI
SIMBOLICI

Tempi di risposta
63
76
25
32

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).

Più piccolo Più grande

Errori
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 Numeri presentati

(1) ANS correlates with symbolic
number processing throughout life-span

Number kindergarteners (3 to 6 yoa, N=
Finger gnosis Comparison Visuo-spatial memory
94) and of adults (N = 36)
Grasping
23 5 “dorsal” tasks:
• visuo-spatial memory (Corsi)
• numerosity comparison
• symbolic number comparison
• finger gnosis
• grasping

2 “ventral” tasks (Golara et al., 2007):
• face recognition memory
• object recognition memory
Objects

[Simon et al., Neuron 2002] Faces

[Chinello et al., under revision]

Numerosity comparison Finger gnosis Face recognition
4
2 100
3
80
1,5 R² = 0,26 p<.00 2
60 R² = 0,42 p<.00 1

d'
Error (%)
1
W

40 0

0,5 -1 3 4 5 6
20
-2 R² = 0,07 p<.01
0 0 -3
3 4 5
Age (years) 6 3 4 5 6 Age (years)
Age (years)

(1) ANS correlates with symbolic
number processing throughout life-span
…Correlates with math scores up
to 10 years earlier ...

at 8 yoa
at 14 yoa

w measured at 14 years of age … … …

Symbolic number cognition is associated to
parietal cortex
Missing gray matter
in premature children with dyscalculia
PARIETAL [Isaacs et al., Brain, 2001]

DYSFUNCTIONS
CAUSE ACALCULIA
developmental
acquired

Classical lesion site for
acalculia Abnormal gyrification and activation
[Dehaene et al., TICS, 1997] in Turner’s syndrome with dyscalculia
[Molko et al., Neuron, 2003]

Parietal cortex in symbolic number cognition
PARIETAL ACTIVATION IS SYSTEMATICALLY
OBSERVED IN SYMBOLIC NUMBER
PROCESSING
x = - 48 L z = 44 z = 49 x = 39 R 50 %

HIPS

22 %

• 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
[Dehaene, Piazza, Pinel, & Cohen,
Cognitive Neuropsychology 2003]

Example of parietal activation “specific” to numbers
(Eger et al, Neuron 2003)
Numbers-(letters&colors)
• Subjects are asked to respond
to a given infrequent stimulus
(number « 5 », letter « B», color
« red »)
• Numbers, letter, and colours
are presented visually and
auditory
•Only non-target stimuli are
analysed

(1) Convergence towards a
quantity code in the IPS in adults
FORMAT NUMBER

Deviant format Deviant number
Adaptation number
Adaptation format dots digits 20 50

Dots same = different 17, 18, o 19 close < far

Arabic digits different = same 47, 48, o 49 far > close

2 CRITERA DEFINITIONAL
For a SEMANTIC representation:
•INVARIANCE TO ENTRY FORMAT
•SEMANTIC METRIC

(1) Convergence towards a
quantity code in the IPS in adults
1010
close
close
Left Parietal Peak
Right Parietal Peak
Number adaptation protocol far
8 8 far
(brain response to a change in number) DEVIANTS
66

HABITUATION 20

Activation (betas)
Activation (betas)
4
4
2
18 19 2
19
0

or -2
0

50 -2
-4

-6 -4
DOTS DOTS ARABICARABIC
-8 -6 (among(among (among (among
dots) arabic) arabic) dots)
DOTS DOTS ARABIC ARABIC
Symbolic -8 (among (among (among (among
number
code samedifferent
dots) arabic) arabic) dots)

Non-
symbolic
number
code

[Piazza et al., Neuron 2007]

(2) ANS maturation may account
for lexical acquisition pattern
The precision of numerical discrimination
(JND or Weber fraction) increases with
age. Round numbers accurately
discriminated
2 1:2
Estimated weber fraction

1

0.8
2:3
0.6

0.4
3:4
0.2
4:5
0
10 20 30 40 50
5:6
Age in years

Infants (Izard et al., 2009; Xu & Spelke, 2000; Xu & Arriaga, 2007) 0 1 2 3 4 5 6 7 10
Piazza et al., Cognition 2010; Chinello et al., submitted. Age in years
Power function fit

(2) ANS maturation may account
for lexical acquisition pattern
In the NUMBER domain, lexical acquisition is a slow and serial process.

Number words
refer to quantities
Understand
“one” Understand
“two” Understand
“three” Understand
2 years of age “four” Counting principles
“discovered”
3 years of age

4 years of age

Round numbers accurately
1:2 discriminated

Symbolic number
Number words
refer to
acquisition
quantities Understand
“one” Understand
“two” Understand
“three” Understand
2 years of age “four”
2:3 Counting principles
“discovered”
3 years of age
3:4
4 years of age
4:5
5:6

0 1 2 3 4 5 6 7 10
Age in years

OTS capacity (number of objects attended at a time)
4
The OTS reaches the adult
3 capacity by 12 months: 4
“attentional pointers”
2 already available. This
does not account for the
1
lexical acquisition pattern!

0.5 1 adults
Age in years

• If the ANS grounds the cultural acquisition
of symbolic number skills it should guide
and constrain it:



(3)The necessity of ANS for numeracy
development: dyscalculia
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
n1 n2 (3) 4-6 years old
(4) Adults

RESULTS (non dyscalculic subjects)

4-6 years 8-11 years Adults
100 100 100
w=0.34 w=0.25 w=0.15
80 80 80
% resp « n2 is larger »

60 60 60

40 40 40

20 20 20

0 0 0
0.7 1 1.4 0.7 1 1.4 0.7 1 1.4
n1/n2 (log scale) n1/n2 (log scale) n1/n2 (log scale)

[Piazza et al., Cognition 2010]

(3)The necessity of ANS for numeracy
development: dyscalculia
“choose the larger” Impairment in the ANS predicts
7
symbolic number impairement but not
* performance in other domains (word
adults
10 yo
6
4
reading) yo
5

Distribution Estimates
N errors in number comparison
10 yo dyscalculics
n1 n2 5
3,5
4 3
In dyscalculic children the ANS is
2,5
substantially impaired: 3

tasks
0,50 2
2
non-dyscalculics
0,45 1,5
dyscalculics
1
1

0,40 R2 = 0,17
00,5 P=0.04
-0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0,35
0
Estimated w
0,30 0,1 0,3 0,5 0,7

0,25 Estimated w
power function
(R2 = 0.97)
0,20

0,15

0,10
0 5 10 15 20 25 30

Age (years) [Piazza et al., Cognition 2010]

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.

Development of ANS

2
The precision of numerical
discrimination increases with age.

Power function: What is the role of maturation?
Exponent = -0.43
R2=0.74
What is the role of education?
1
p=0.001
0.8

0.6

0.4

0.2

0
10 20 30 40 50
Age in years

Infants (Izard et al., 2009; Xu & Spelke, 2000; Xu & Arriaga, 2007)
Piazza et al., Cognition 2010; Chinello et al., submitted.
Power function fit

[Piazza & Izard, The Neuroscientist , 2009]

36 Munduruku subjects Performance of Munduruku adults

[aged from 4 to 67] Uneducated (n=7) Some education (n=13)
12 Completely uneducated % larger responses
100 100
24 Received some education
80 80
w = 0.288 w = 0.177
60 60
40 40
*
20 20

0 0
0.7 1 1.4 0.7 1 1.4
Ratio of n1 and n2 (log scale)

Weber fraction Munduruku, uneducated Weber fraction
0.5 Munduruku, some education 0.5
Italian participants (group means) r²=26.8%, p=0.001

0.4 0.4

0.3 0.3

0.2 0.2

0.1 0.1

0 0.0
0 10 20 30 40 50 60 70 0 1 2 3 4 5 6 7 8
Age Years of Education

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
Left hemisphere Axial slice Right hemisphere
A. x = - 48 z = 44 z = 49 x = 39 50 %

HORIZONTAL SEGMENT OF THE
INTRAPARIETAL SULCUS (hips)

22 %

B. x = - 49 z = 30 x = 54

LEFT ANGUALR GYRUS

C. x = - 26 z = 61 x = 12

POSTERIOR SUPERIOR
PARIETAL LOBE (more right)

Three parietal circuits for number processing
(Dehaene, Piazza et al.,2003)
CS

Left hemisphere Right hemisphere
IPS

HORIZONTAL SEGMENT OF THE
INTRAPARIETAL SULCUS (HIPS) hVIP?
-Number comparison
-Ratio effect Seen from top
-Numerical priming
-Approximate calculation

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

Evidence for a verbal code in
arithmetical facts retrieval
• Interference on TRs in calculation
Task1 (arithmetic):
Multiplicazions or subtractions
Task 2 (short term memory):
Phonological (whisper a non-
word) o visuo-spatial (remember
the position of an object)

Single task
Phonological dual task
Visuo-spatial dual task

Left angular gyrus in arithmetical
facts retrieval
1. Training experiment: Trained to memorize complex two digits number arithmetical
facts and measure the effects on brain activity

UNTRAINED
>
TRAINED

TRAINED
>
UNTRAINED

Ischebeck et al., 2009

Left angular gyrus in arithmetical
facts retrieval
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 ]

Evidence for a spatial code in
arithmetical computations
• Interference on TRs in calculation
Task1 (arithmetic):
Multiplicazions or subtractions
Task 2 (short term memory):
Phonological (whisper a non-
word) o visuo-spatial (remember
the position of an object)

Single task
Phonological dual task
Visuo-spatial dual task

arithmetical computations
Do spatial/motor processes interfere with calculation ?

« Answer the arithmetical problems while
performing a sequence of finger movements in
the same time ! »

NO MVTS MVTS
*
1200
*

1100

1000
RT (msec)

900

800

700

600
MULTIPLICATION ADDITION SOUSTRACTION

In the dual task, sequential finger movements were found to slow down responses
to additions and subtractions, whereas multiplications (matched for difficulty)
were unaffected

arithmetical computations: neglect
Modello Copia del paziente

Regioni corticali tipicamente
dannegggiate nel neglect

Tipico disegno (copia da modello) di un paziente
con negelct

Test della bisezione di linee
Test dello sbarramento di linee

arithmetical computations: neglect
Numerical bisection test :
“What is the number between 2 and 6?”
“Answer: 5”  RIGHT BIAS!

Zorzi et al., Nature 2002

Posterior parietal
saccade regions in
calculation

Spatial code in number
representations: the mental number
line (SNARC effect) is culture
dependent

Shaki et al., 2009 (Psych Bull Rev)

Does math education affect approximate number sense

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