Dyscalculia –
the neglected learning disorder
Karin Landerl
University of Graz
Dyscalculia – the neglected learning disorder
(Pubmed Database)
Celebrities with dyslexia
Hans Christian Andersen
John Irving
Agatha Christie
Cher
Winston Churchill
Leonardo DaVinci
Charles Darwin
Walt Disney
Whoopi Goldberg
Tom Cruise
Thomas Edison
Swedish Royal Family
Greg Louganis
Jackie Stewart
Michelangelo
Pablo Picasso
August Rodin
Nelson Rockefeller
Franklin Roosevelt
Vincent VanGogh
Woodrow Wilson
Celebrities with dyscalculia??
Prevalence rates:
Studies in GB, Germany, Greece, India, Israel
(Badian, 1983; Gross-Tsur, Manor, & Shalev, 1996; Hein, Bzufka &
Neumärker, 2000; Klauer, 1992; Kosc, 1974; Koumoula, Tsironi,
Starmouli, Bardani & Siapati, 2004; Lewis, Hitch & Walker, 1994; Ramaa
& Gowaramma, 2002; von Aster, Schweiter & Weinhold Zulauf, 2007)
Comparable prevalence rates ranging from 3 to 8.3 %
No clear gender differences
Overview
 What
is dyscalculia?
 Neuro-cognitive
theories of learning
disorders
 Core
deficits in processing numerosities
 Implications
for diagnosis and intervention
DYSCALCULIA
Definition: (ICD-10)
"...a condition that affects the ability to acquire arithmetical skills.
Dyscalculic learners may have difficulty understanding simple number
concepts, lack an intuitive grasp of numbers, and have problems learning
number facts and procedures. Even if they produce a correct answer or
use a correct method, they may do so mechanically and without
confidence" (UK Department for Education and Science, 2001).
Case description .
in elementary school, I didn´t understand for a long time
why 1 + 1 = 2 – I thought it should be 11
I always had problems when new concepts or procedures
were introduced, I was insecure and didn´t get it. Only
when we were almost through and everzbody else
understood, I sometimes got a basic idea, understood
maybe half of it. Still, I mostly learned procedures by
heart, without really understanding. If there was only a
small change in the problems given, I was again
completely lost.
Case description
.
I never understood word problems – still
don´t. I just don´t get what I´m supposed
to do
I cannot visualise amounts or magnitudes.
How much are 100 g? I just don´t have it
in my head.
I cannot convert – for example grams in
kilograms. So I have problems to bake a
cake when the recipe has other measures
than what I need
Case description .
I am poor in mental calculations… most often I keep
counting in my head. For example, when I´m asked
to add up 16 + 18, I can do 10 + 10 alright –
that´s 20. But the 6 and the 8 are difficult then,
that takes longer. I need to add them to the 20 and
at the same time remember… and when it gets
more diffcult with divisions or so, I give up
completely.
I still count on my fingers – if anybody is watching me,
I try to do it in my head.
Case description .
I have problems with percentages – they just
don´t mean anything to me.
Decimals I find especially hard – adding or
subtracting them – oh my god – there´s
only chaos in my brain
I don´t realise it when I come up with a
completely incorrect result, because the
numbers don´t mean anything to me, I
cannot estimate if my result might be right
or wrong
Case description .
or to remember things like: "were
there 600 or 6000 people at the
festival?". I cannot estimate the
number of inhabitants of some place, it
just doen´t mean anything to me. Are
there 10.000 people living in Germany
or was it 100.000 or more or less? I
don´t have a clue.
10000 - 204 =

First, I needed to think how to calculate
10000 - 204. At some point I decided to
do 10000 - 100 = 9000 and then again
subtract 100 = 8000. and then there´s
only 4 left of the 204, which I needed to
subtract. It was easy to write down 79,
same with the following 9 (799), though a
bit slower, and then the 6. So the result is
7996. I have no idea if this could be
correct as I don´t have my calculator with
me.
Neurocognitive Theories of
Inborn Core Mechanisms
 Babies are born with a number
of simple core mechanisms that
critical for further development
are
 These inborn core mechanisms
enable fast-track learning (with normal environmental
stimulation)
 What happens if the core mechanism doesn´t
function properly?
 Developmental disorder
What is the critical core
mechanism of dyslexia?
Phonological processing
Enables fast-track learning of language
and literacy
Phonological deficits – delay in language
development and serious problems in
reading acquisition
Learning is slow and compensatory
Is there a core
mechanism for
arithmetic skills?
Same as for dyslexia?
Population
based
sample
% of
N
2586
Arithmetic disorder
158
Percent of N
+ AD
6.1
+ RD
+ SD
25.9
37.3
Reading disorder
181
7.0
22.7
8.8
25.9
Spelling disorder
228
Landerl & Moll (2010), Journal of Child Psychology and Psychiatry
Phonological awareness?
„Say /ti:k/ without /k/“
100
% correct
80
60
40
20
0
control
dyslexia
dyscalculia
dyslexia/dyscalculia
Landerl, Fussenegger, Moll & Willburger (2009),
Journal of Experimental Child Psychology
Naming Speed for Digits
140
digits / min
120
100
80
60
40
control
dyslexia
dyscalculia
combined
Landerl, Fussenegger, Moll & Willburger (2009),
Journal of Experimental Child Psychology
Babies process numerosties
Starr, Libertus, & Brannon (2013) PNAS
Babies process numerosities
Xu, Spelke & Goddard (2006)
Babies can do simple
arithmetic

Wynn (1992)
Babies are attentive towards numerosities
= core system
number sense – Dehaene (1997)
number module – Butterworth (1999)
Dysfunctional core system
atypical development of the cognitive
representation of numbers
DYSCALCULIA
Deficits in numerical processing
in dyscalculia:
Magnitude comparison
Magnitude comparison
Lese-Kontrast:
Gruppe: F < 1, n.s.
Arabic numbers = symbols for
numerosities
2
32
8
58
Number comparison –
Requires access to the magnitudes represented by the symbols
Number comparison
Landerl, Fussenegger, Moll & Willburger (2009),
Journal of Experimental Child Psychology
Basic numerical processing
as a core deficit of
dyscalculia N – Numerical comparison
5 7
P – Physical comparison
(neutral condition): 5
5
Comparison of two-digit
numbers
Compatible: 52 76
incompatible: 47 62
Landerl (2013) Frontiers in Psychology
Dot counting
(Schleifer & Landerl, 2011, Developmental Science)
4500
4000
3500
RT
3000
2500
2000
1500
1000
500
0
1
2
3
4
5
6
7
Num ber of dots
Grade 2 dyscalculic
Grade 2 control
Grade 3 dyscalculic
Grade 3 control
Grade 4 dyscalculic
Grade 4 control
8
Butterworth (1999)
Everybody counts…
Biology
Cognition
Visual-spatial skills
Problem solving skills
Executive functions
Working memory
Long term memory
Verbal skills
reading
teaching
intervention
basic numerical
skills
Arithmetic
skills
attention
Behaviour
Basic numerical skills
Biology
IPS
Analog magnitude representatio

Visual-arabic
representation

stimulation
teaching
intervention

Cognition
Auditory-verbal
representation
Mental number line
Read/write/compa
re Arabic
numbers
Subitizing
estimation
Fingerrepresentation
Process number
words
magnitude
comparison

counting
Written
calculations
Fingercalculation
Number facts
Behaviour
Schematische Darstellung der in der Literatur postulierten (und zum Teil noch
Brain
areas that have been identified to be active
kontrovers diskutierten) neuronalen Netzwerkkomponenten der
during Zahlenverarbeitung
numerical und
processing
/arithmetic
des Rechnens
Präfrontale Areale
Monitoring,
Arbeitsgedächtnis,
Strategien etc
:
SMA (Supplementär-motorisches
Areal): antwortbezogene Konfliktresolution, ev. Fingerrechnen
PSPL (Posteriorer superiorer
parietaler Lappen):
räumliche
Aufmerksamkeit auf der
mentalen Zahlenlinie
SMA (Supplementär-motorisches
Areal): antwortbezogene Konfliktresolution, ev. Fingerrechnen
Präfrontale Areale
Monitoring,
Arbeitsgedächtnis,
Strategien etc
Posteriorer IPS und (H)IPS:
R epräsentation des Basis-10(Platz x Wert) Systems
HIPS (horizontales Segment d.
intraparietalen Sulcus):
mentale
Mengen-repräsentation per se
Perisylvische
Areale:
Zählsequenzen,
Benennen von
Zahlen, verbales
Rechnen
Gyrus fusiformis:
visuelle
Verarbeitung von Wörtern / ev.
Arabischen Zahlen
Gyrus angularis:
Faktenabruf (v.a.
Multiplikationsfakten)
Cerebellum: Aufgaben mit hoher
Komplexität und/oder Neuheitswert
(domänen-unspezifisch), eventuell auch
Zählsequenzen
Kaufmann & Nuerk (2007; Abb. 1)
:
Dyscalculia and Dyslexia :
different neuro-functional abnormalities
Dyscalculia: under-activation in
intraparietal sulcus (bilaterally)
Molko et al. (2003)
Dyslexia: under-activation in
left temporo-parietal areas
Paulesu et al. (2001)
Specialization of the neurocognitive network for
numbers/arithmetic happens during
development
Areas whose
activation increases
with age
Areas whose
activation decreases
with age
Rivera et al. (2005)
Summary

Doing arithmetic requires a highly
specified neuro-cognitive network

The starting point for the development of
this network is an early core mechanism

The development and specification of the
neuro-cognitve network for arithmetic
takes many years and is strongly
dependent on environmental factors
(stimulation, teaching, intervention)
Dyscalculia

Inborn core mechanism is not functioning properly
„Everybody counts, but not everybody understands
numbers“ (Butterworth, 2005)

Development of the neuro-cognitive network underlying
arithmetic is atypical, right from start. Learning is slow
and compensatory

Early identification and intervention is important in order
to support learning and avoid secondary symptoms
(maths anxiety, behavioural problems)
Implications for diagnosis and
intervention

Establish a profile of strengths and weaknesses in
arithmetic and numerical processing as well as
other ressources (and comorbidities)

Tailored intervention based on fine-grained
diagnosis

Learning will often be compensatory and take
more time