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Dyscalculia: From Brain to Education


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Recent research in cognitive and developmental neuroscience is providing a new approach to the understanding of dyscalculia that emphasizes a core deficit in understanding sets and their numerosities, which is fundamental to all aspects of elementary school mathematics. The neural bases of numerosity processing have been investigated in structural and functional neuroimaging studies of adults and children, and neural markers of its impairment in dyscalculia have been identified. New interventions to strengthen numerosity processing, including adaptive software, promise effective evidence-based education for dyscalculic learners.
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DOI: 10.1126/science.1201536
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Dyscalculia: From Brain to Education
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Dyscalculia: From Brain to Education
Brian Butterworth,
*Sashank Varma,
Diana Laurillard
Recent research in cognitive and developmental neuroscience is providing a new approach to
the understanding of dyscalculia that emphasizes a core deficit in understanding sets and their
numerosities, which is fundamental to all aspects of elementary school mathematics. The neural
bases of numerosity processing have been investigated in structural and functional neuroimaging
studies of adults and children, and neural markers of its impairment in dyscalculia have been
identified. New interventions to strengthen numerosity processing, including adaptive software,
promise effective evidence-based education for dyscalculic learners.
Developmental dyscalculia is a mathemat-
ical disorder, with an estimated prevalence
ofabout5to7%(1), which is roughly the
same prevalence as developmental dyslexia (2).
A major report by the UK government con-
cludes, Developmental dyscalculia is currently
the poor relation of dyslexia, with a much lower
public profile. But the consequences of dyscalculia
are at least as severe as those for dyslexia[(3),
p. 1060]. The relative poverty of dyscalculia fund-
ing is clear from the figures: Since 2000, NIH has
spent $107.2 million funding dyslexia research but
only $2.3 million on dyscalculia (4).
The classical understanding of dyscalculia as
a clinical syndrome uses low achievement on
mathematical achievement tests as the criterion
without identifying the underlying cognitive
phenotype (57). It has therefore been unable to
inform pathways to remediation, whether in
focused interventions or in the larger, more
complex context of the math classroom.
Why Is Mathematical Disability Important?
Low numeracy is a substantial cost to nations, and
improving standards could dramatically improve
economic performance. In a recent analysis, the
Organisation for Economic Co-operation and De-
velopment (OECD) demonstrated that an improve-
ment of one-half standard deviation in mathematics
and science performance at the individual level im-
plies, by historical experience, an increase in an-
nual growth rates of GDP per capita of 0.87%[(8),
p. 17]. Time-lagged correlations show that improve-
ments in educational performance contribute to
increased GDP growth. A substantial long-term
improvement in GDP growth (an added 0.68% per
annum for all OECD countries) could be achieved
just by raising the standard of the lowest-attaining
students to the Programme for International Stu-
dent Assessment (PISA) minimum level (Box 1).
In the United States, for example, this would
mean bringing the lowest 19.4% up to the min-
imum level, with a corresponding 0.74% increase
in GDP growth.
Besides reduced GDP growth, low numeracy
is a substantial financial cost to governments and
personal cost to individuals. A large UK cohort
study found that low numeracy was more of a
handicap for an individuals life chances than
low literacy: They earn less, spend less, are more
likely to be sick, are more likely to be in trouble
with the law, and need more help in school (9). It
has been estimated that the annual cost to the UK
of low numeracy is £2.4 billion (10).
What Is Dyscalculia?
Recent neurobehavioral and genetic research
suggests that dyscalculia is a coherent syndrome
that reflects a single core deficit. Although the
literature is riddled with different terminologies,
all seem to refer to the existence of a severe dis-
ability in learning arithmetic. The disability can
be highly selective, affecting learners with normal
intelligence and normal working memory (11),
although it co-occurs with other developmental
disorders, including reading disorders (5)andat-
tention deficit hyperactivity disorder (ADHD) (12)
more often than would be expected by chance.
There are high-functioning adults who are severe-
ly dyscalculic but very good at geometry, using
statistics packages, and doing degree-level com-
puter programming (13).
There is evidence that mathematical abilities
have high specific heritability. A multivariate
genetic analysis of a sample of 1500 pairs of
monozygotic and 1375 pairs of dizygotic 7-year-
old twins found that about 30% of the genetic
variance was specific to mathematics (14). Al-
though there is a significant co-occurrence of
dyscalculia with dyslexia, a study of first-degree
relatives of dyslexic probands revealed that nu-
merical abilities constituted a separate factor,
with reading-related and naming-related abilities
being the two other principal components (15).
These findings imply that arithmetical learning is
at least partly based on a cognitive system that is
distinct from those underpinning scholastic at-
tainment more generally.
This genetic research is supported by neuro-
behavioral research that identifies the representa-
tion of numerositiesthe number of objects in a
Centre for Educational Neuroscience and Institute of Cognitive
Neuroscience, University College London, Psy chologica l Sc i-
ences, Melbourne University, Melbourne VIC 3010, Aus-
Department of Educational Psychology, University of
Minnesota, Minneapolis, MN 55455, USA.
Centre for Educa-
tional Neuroscience and London Knowledge Lab, Institute of
Education, University of London, London WC1N 3QS, UK.
*To whom correspondence should be addressed. E-mail: uk
Box 1: PISA question example
AtLevel1,studentscananswerquestions involving familiar contexts in which all relevant
information is present and the questions are clearly defined. They are able to identify information and
carry out routine procedures according to direct instructions in explicit situations. They can perform
actions that are obvious and follow immediately from the given stimuli. For example:
Mei-Ling found out that the exchange rate between Singapore dollars and South African rand was 1
SGD = 4.2 ZAR
Mei-Ling changed 3000 Singapore dollars into South African rand at this exchange rate.
How much money in South African rand did Mei-Ling get?
79% of 15-year-olds were able to answer this correctly.
Box 2: Dyscalculia observed
Examples of common indicators of dyscalculia are (i) carrying out simple number comparison and
addition tasks by counting, often using fingers, well beyond the age when it is normal, and (ii)finding
approximate estimation tasks difficult. Individuals identified as dyscalculic behave differently from
their mainstream peers. For example:
To say which is the larger of two playing cards showing 5 and 8, they count all the symbols on
each card.
To place a playing card of 8 in sequence between a 3 and a 9, they count up spaces between the two
to identify where the 8 should be placed.
To count down from 10, they count up from 1 to 10, then 1 to 9, etc.
To count up from 70 in tens, they say 70, 80, 90, 100, 200, 300…”
They estimate the height of a normal room as 200 feet? SCIENCE VOL 332 27 MAY 2011 1049
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setas a foundational capacity in the develop-
ment of arithmetic (16). This capacity is impaired
in dyscalculic learners even in tasks as simple as
enumerating small sets of objects (11)orcompar-
ing the numerosities of two arrays of dots (17).
The ability to compare dot arrays has been cor-
related with more general arithmetical abilities
bothinchildren(18) and across the age range
(17,19). This core deficit in processing numer-
osities is analogous to the core deficit in phono-
logical awareness in dyslexia (Box 2) (2).
Although there is little longitudinal evidence,
it seems that dyscalculia persists into adulthood
(20), even among individuals who are able in
other cognitive domains (13). The effects of ear-
ly and appropriate intervention with dyscalculia
have yet to be investigated. This also leaves open
the question as to whether there is a form of dys-
calculia that is a delay, rather than a deficit, that
will resolve, perhaps with appropriate educational
Converging evidence of dyscalculia as a dis-
tinct deficit comes from studies of impairments in
the mental and neural representation of fingers. It
has been known for many years that fingers are
used in acquiring arithmetical competence (21).
This involves understanding the mapping be-
tween the set of fingers and the set of objects to
be enumerated. If the mental representation of
fingers is weak, or if there is a deficit in under-
standing the numerosity of sets, then the childs
cognitive development may fail to establish the
link between fingers and numerosities. In fact,
developmental weakness in finger representation
(finger agnosia)isapredictorofarithmetical
ability (22). Gerstmanns Syndrome, whose symp-
toms include dyscalculia and finger agnosia, is
due to an abnormality in the parietal lobe and, in
its developmental form, is also associated with
poor arithmetical attainment (23).
Numbers do not seem to be meaningful for
dyscalculicsat least, not meaningful in the
way that they are for typically developing learn-
ers. They do not intuitively grasp the size of a
number and its value relative to other num-
bers. This basic understanding underpins all
work with numbers and their relationships to
one another.
What Do We Know About the Brain
and Mathematics?
The neural basis of arithmetical abilities in the
parietal lobes, which is separate from language
and domain-general cognitive capacities, has been
broadly understood for nearly 100 years from re-
search on neurological patients (24). One par-
ticularly interesting finding is that arithmetical
concepts and laws can be preserved even when
facts have been lost (25), and conversely, facts
can be preserved even when an understanding of
concepts and laws has been lost (26).
Neuroimaging experiments confirm this pic-
ture and show links from the parietal lobes to the
left frontal lobe for more complex tasks (27,28).
One important new finding is that the neural or-
ganization of arithmetic is dynamic, shifting from
one subnetwork to another during the process of
learning. Thus, learning new arithmetical facts
primarily involves the frontal lobes and the intra-
parietal sulci (IPS), but using previously learned
facts involves the left angular gyrus, which is also
implicated in retrieving facts from memory (29).
Some of the principal links are summarized in
Fig. 1. Even prodigious calculators use this net-
work, although supplementing it with additional
brain areas (30) that appear to extend the capacity
of working memory (31).
There is now extensive evidence that the IPS
supports the representation of the magnitude of
symbolic numbers (32,33), either as analog mag-
nitudes or as a discrete representation that codes
cardinality, as evidenced by IPS activation when
processing the numerosity of arrays of objects
(34). Moreover, when IPS functioning is dis-
turbed by magnetic stimulation, the ability to esti-
mate discrete magnitudes is affected (35,36). The
critical point is that almost all arithmetical and
numerical processes implicate the parietal lobes,
especially the IPS, suggesting that these are at the
core of mathematical capacities.
Patterns of brain activity in 4-year-olds and
adults show overlapping areas in the parietal
lobes bilaterally when responding to changes in
numerosity (37). Nevertheless, there is a devel-
opmental trajectory in the organization of more
complex arithmetical abilities. First, the organi-
zation of routine numerical activity changes with
age, shifting from frontal areas (which are as-
sociated with executive function and working
memory) and medial temporal areas (which are
associated with declarative memory) to parietal
areas (which are associated with magnitude
processing and arithmetic fact retrieval) and
occipito-temporal areas (which are associated
with processing symbolic form) (38). These
changes allow the brain to process numbers more
efficiently and automatically, which enables it to
carry out the more complex processing of arith-
metical calculations. As A. N. Whitehead ob-
served, an understanding of symbolic notation
relieves the brain of all unnecessary work
and sets it free to concentrate on more advanced
This suggests the possibility that the neural
specialization for arithmetical processing may
arise, at least in part, from a developmental inter-
action between the brain and experience (40,41).
Thus, one way of thinking about dyscalculia is
that the typical school environment does not
provide the right kind of experiences to enable
the dyscalculic brain to develop normally to learn
Of course, mathematics is more than just sim-
ple number processing and retrieval of previously
learned facts. In a numerate society, we have to
Educational context
Exercises on
of numbers
Exposure to
digits and facts
Experience of
reasoning about
Practice with
Parietal lobe
Frontal lobe
fact retrieval
number tasks
Fig. 1. Causal model of possible inter-relations between biological, cognitive, and simple behavioral
levels. Here, the only environmental factors we address are educational. If parietal areas, especially the
IPS, fail to develop normally, there will be an impairment at the cognitive level in numerosity rep-
resentation and consequential impairments for other relevant cognitive systems revealed in behavioral
abnormalities. The link between the occipitotemporal and parietal cortex is required for mapping number
symbols (digits and number words) to numerosity representations. Prefrontal cortex supports learning new
facts and procedures. The multiple levels of the theory suggest the instructional interventions on which
educational scientists should focus.
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learn more complex mathematical concepts, such
as place value, and more complex procedures,
such as longaddition, subtraction, multiplica-
tion, and division. Recent research has revealed
the neural correlates of learning to solve com-
plex, multidigit arithmetic problems (24). Again,
this research shows that solving new problems
requires more activation in the inferior frontal
gyrus for reasoning and working memory and the
IPS for representing the magnitudes of the num-
bers involved, as compared with retrieval of pre-
viously learned facts (42).
The striking result in all of these studies is the
crucial role of the parietal lobes. That the IPS is
implicated in both simple and complex calcu-
lations suggests that the basic representations of
magnitude are always activated, even in the re-
trieval of well-learned single-digit addition and
multiplication facts (43). This is consistent with
the well-established problem-size effect,in
which single-digit problems take longer to solve
the larger the operands, even when they are well
known (44). It seems that the typically devel-
oping individual, even when retrieving math
facts from memory, cannot help but activate the
meaning of the component numbers at the same
time. If that link has not been established, cal-
culation is necessarily impaired.
What Do We Know About the Brain
and Dyscalculia?
The clinical approach has identified behavioral
deficits in dyscalculic learners typically by per-
formance on standardized tests of arithmetic.
However, even in primary school (K1 to 5), arith-
metical competence involves a wide range of
cognitive skills, impairments in any
of which may affect performance,
including reasoning, working mem-
ory, language understanding, and
spatial cognition (45). Neural differ-
ences in structure or functioning may
reflect differences in any of these cog-
nitive skills. However, if dyscalculia
is a core deficit in processing nu-
merosities, then abnormalities should
be found in the parietal network that
supports the enumeration of small
sets of objects (11) and the compar-
ison of numerosities of arrays of
dots (17).
The existence of a core deficit in
processing numerosities is consist-
ent with recent discoveries about dys-
calculic brains: (i) Reduced activation
has been observed in children with dyscalculia
during comparison of numerosities (46,47),
comparison of number symbols (46), and arith-
metic (48)these children are not using the
IPS so much during these tasks. (ii) Reduced
gray matter in dyscalculic learners has been ob-
served in areas known to be involved in basic
numerical processing, including the left IPS (49),
the right IPS (50), and the IPS bilaterally (51)
these learners have not developed these brain
And (iii) differences in connectivity among the
relevant parietal regions, and between these
parietal regions and occipitotemporal regions
associated with processing symbolic number form
(Fig. 2), are revealed through diffusion tensor im-
aging tractography (51)dyscalculic learners
have not sufficiently developed the structures
needed to coordinate the components needed
for calculation.
Figure 1 suggests that the IPS is just one
component in a large-scale cortical network that
subserves mathematical cognition. This network
different dyscalculia patterns of presenting symp-
toms when the core deficit is combined with
other cognitive deficits, including working mem-
ory, reasoning, or language (52).
Moreover, the same presenting symptom could
reflect different impairments in the network. For
example, abnormal comparison of symbolic num-
bers (53,54) could arise from an impairment in
the fusiform gyrus associated with visual process-
ing of number symbols, an impairment in IPS
associated with the magnitude referents, analog or
numerosity, of the number symbols, or reduced
connectivity between fusiform gyrus and IPS.
How Is This Relevant to Maths Education?
There have been many attempts to raise the
performance of children with low-numeracy, al-
though not specifically dyscalculia. In the United
States, evidence-based approaches have focused
on children from deprived backgrounds, usually
low socioeconomic status (46,47). The current
National Strategy in the United Kingdom gives
special attention to children with low numeracy
by (i) diagnosing each childs conceptual gaps in
understanding and (ii) giving the child more
individual support in working through visual,
verbal, and physical activities designed to bridge
each gap. Unfortunately, there is still little quan-
titative evaluation of the effectiveness of the
strategy since it was first piloted in 2003: the
evaluations used very diverse measures; and
most did not include ratio gains or effect sizes
or data from which these could be obtained
[(55), p. 13].
It has not been possible to tell, therefore,
whether identifying and filling an individuals
conceptual gaps with a more individualized ver-
sion of the same teaching is effective. A further
problem is that these interventions are effective
when there has been specialist training for teaching
assistants, but not all schools can provide this (55).
These standardized approaches depend on
curriculum-based definitions of typical arithmet-
ical development, and how children with low
numeracy differ from the typical trajectory. In con-
trast, neuroscience research suggests that rather
than address isolated conceptual gaps, remediation
should build the foundational number concepts
first. It offers a clear cognitive target for assess-
ment and intervention that is largely independent
of the learnerssocial and educational circum-
stances. In the assessment of individual cognitive
capacities, set enumeration and comparison can
supplement performance on curriculum-based
standardized tests of arithmetic to differentiate
dyscalculia from other causes of low numeracy
In intervention, strengthening the meaningful-
ness of numbers, especially the link between the
math facts and their component meanings, is cru-
cial. As noted above, typical retrieval of simple
arithmetical facts from memory elicits activation
of the numerical value of the component numbers.
Without specialized intervention, most dys-
calculic learners are still struggling with basic
arithmetic in secondary school (20). Effective
early intervention may help to reduce the later
impact on poor numeracy skills, as it does in
dyslexia (58). Although very expensive, it prom-
ises to repay 12 to 19 times the investment (10).
What Can Be Done?
Although the neuroscience may suggest what
should be taught, it does not specify how it should
be taught. Concrete manipulation activities have
been used for many decades in math remediation
because they provide tasks that make number
concepts meaningful (59), providing an intrinsic
Fig. 2. Structural abnormalities in young dyscalculic brains suggesting the critical role for the IPS. Here, we show
areas where the dyscalculic brain is different from that of typically developing controls. Both left and right IPS are
implicated, possibly with a greater impairment for left IPS in older learners. (A) There is a small region of reduced
gray-matter density in left IPS in adolescent dyscalculics (41). (B) There is right IPS reduced gray-matter density
(yellow area) in 9-year-olds (42). (C) There is reduced probability of connections from right fusiform gyrus to other
parts of the brain, including the parietal lobes (43). SCIENCE VOL 332 27 MAY 2011 1051
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relationship between a goal, the learners action,
and the informational feedback on the action (60).
Educators recognize that informational feedback
provides intrinsic motivation in a task, and that is
of greater value to the learner than the extrinsic
motives and rewards provided by a supervising
teacher (6163).
Experienced special educational needs (SEN)
teachers use these activities in the form of games
with physical manipulables (such as Cuisenaire
rods, number tracks, and playing cards) to give
learners experience of the meaning of number.
Through playing these games, learners can dis-
cover from their manipulations, for example,
which rod fits with an 8-rod to match a 10-rod.
However, these methods require specially trained
teachers working with a single learner or a small
group of learners (6466) and are allotted only
limited time periods in the school schedule.
A promising approach, therefore, is to con-
struct adaptive software informed by the neuro-
science findings on the core deficit in dyscalculia.
Such software has the potential to reduce the
demand on specially trained teachers and to tran-
scend the limits of the school sched-
ule. There have been two examples
of adaptive games based on neuro-
science findings.
The Number Race (67)targets
the inherited approximate numerosity
system in the IPS (68)thatmay
support early arithmetic (18). In dys-
calculics, this system is less precise
(17), and the training is designed to
improve its precision. The task is to
select the larger of two arrays of
dots, and the software adapts to the
learner, making the difference between
the arrays smaller as their performance
improves, and provides informational
feedback as to which is correct.
Another adaptive game, Grapho-
game-Maths, targets the inherited
system for representing and manip-
ulating sets in the IPS, which is im-
paired in dyscalculia (45). Again,
the basis of the game is the compar-
ison of visual arrays of objects, but
here the sets are small and can be
counted, and the progressive tasks
are to identify the link between the
number of objects in the sets and their
verbal numerical label, with infor-
mational feedback showing which is
The effectiveness of the two
games was compared in a carefully
controlled study of kindergarten chil-
dren (aged 6 to 7 years) who were
identified by their teachers as need-
ing special support in early maths.
After 10 to 15 min of play per school
day for 3 weeks, there was a signif-
icant improvement in the task prac-
ticed in both gamesnamely, number
comparisonbut the effect did not generalize to
counting or arithmetic. Graphogame-Maths ap-
peared to lead to slightly better and longer-lasting
improvement in number comparison (69).
Although the Number Race and Graphogame-
Maths are adaptive games based on neuroscience
findings, neither requires learners to manipulate
numerical quantities. Manipulation is critical for
providing an intrinsic relationship between task
goals, a learners actions, and informational feed-
back on those actions (60). When a learning en-
vironment provides informational feedback, it
enables the learner to work out how to adjust their
actions in relation to the goal, and they can be their
own critic,not relying on the teacher to guide
(6163). This is analogous to the actor-criticmod-
el of unsupervised reinforcement learning in neuro-
science, which proposes a critic element internal
to the learning mechanismnot a guide that is ex-
ternal to itwhich evaluates the informational
feedback in order to construct the next action (70).
A different approach, one that emulates the
manipulative tasks used by SEN teachers, has
been taken in adaptive software that, driven by
the neuroscience research on dyscalculia, focuses
on numerosity processing (Fig. 3) (56). The in-
formational feedback here is not an external critic
showing the correct answer. Rather, the visual
representation of two rods that match a given
distance, or not, enables the learner to interpret
for themselves what the improved action should
beand can serve as their own internal critic.
An additional advantage of adaptive software
is that learners can do more practice per unit time
than with a teacher. It was found that for SEN
learners (12-year-olds) using the Number Bonds
game [illustrated in Fig. 3], 411 trials per minute
were completed, while in an SEN class of three
supervised learners only 1.4 trials per minute
were completed during a 10-min observation
[(56), p. 535]. In another SEN group of 11 year
olds, the game elicited on average 173 learner
manipulations in 13 min (where a perfect perfor-
mance, in which every answer is correct, is 88 in
5 min because the software adapts the timing ac-
cording to the response). In this way, neuroscience
research is informing what should be targeted in
the next generation of adaptive software.
Stage 4: Digits and colors; the learner has to identify which rod fits the gap before the stimulus rod reaches the stack
Stage 6: Digits only; the learner has to identify which digit makes 10 before the stimulus number reaches the stack
Which number bonds make 10?
Well done
Fig. 3. Remediation using learning technology. The images are taken from an example of an interactive, adaptive
game designed to help the learner make the link between digits and their meaning. The timed version of the number
bonds game elicits many learner actions with informational feedback, and scaffolds abstraction, through stages 1, 5
colors + lengths, evens; 2, 5 colors + lengths, odds; 3, all 10 colors + lengths; 4, digits + colors + lengths; 5, digits +
lengths; and 6, digits only. Each rod falls at a pace adapted to the learners performance, and the learner has to click
the corresponding rod or number to make 10 before it reaches the stack (initially 3 s); if there is a gap, or overlap, or
they are too slow, the rods dissolve. When a stack is complete, the game moves to the next stage. The game is available
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At present, it is not yet clear whether early
and appropriately targeted interventions can turn
a dyscalculic into a typical calculator. Dyscalculia
may be like dyslexia in that early intervention can
improve practical effectiveness without making
the cognitive processing like that of the typically
What Is the Outlook?
Recent research by cognitive and developmental
scientists is providing a scientific characterization
of dyscalculia as reduced ability for understand-
ing numerosities and mapping number symbols
to number magnitudes. Personalized learning
applications developed by educational scientists
can be targeted to remediate these deficits and
can be implemented on handheld devices for
independent learning. Because there are also in-
dividual differences in numerosity processing in
the normal range (17,19,71),thesameprograms
can assist beginning mainstream learners, so one
can envisage a future in which all learners will
benefit from these developments.
Although much progress has been made, a
number of open questions remain.
(i) The possible existence of a variety of dys-
calculia behavioral patterns of impairment raises
the interesting question of whether one deficit
numerosity estimationis a necessary or suffi-
cient for a diagnosis of dyscalculia. This is critical
because it has implications for whether a single
diagnostic assessment based on numerosity is
sufficient, or whether multiple assessments are re-
quired. It also has implications for whether nu-
merosity should be the focus of remediation, or
whether other (perhaps more symbolic) activities
must also be targeted.
(ii) Does the sensitivity of neuroscience mea-
sures make it possible to identify learners at risk for
dyscalculia earlier than is possible with behav-
ioral assessments, as is the case with dyslexia (72)?
(iii) Further research is needed on the neural
consequences of intervention. Even where inter-
vention improves performance, it may not be
clear whether the learners cognitive and neural
functioning has become more typical or whether
compensatory mechanisms have developed. This
would require more extensive research, as in the
case of dyslexia, in which functional neuroimag-
ing has revealed the effects of successful behavioral
interventions on patterns of neural function (2).
(iv) Personalized learning applications enable
fine-grain evaluation of theory-based instruc-
tional interventions. For example, the value of
active manipulation versus associative learning
on one hand, and of intrinsic versus extrinsic
motivation and feedback on the other, can be as-
sessed by orthogonally manipulating these features
of learning environments. Their effects can be as-
sessed behaviorally in terms of performance on the
tasks by target learners. Their effects can also be
assessed by investigating neural changes over time
in target learners, through structural and functional
neuroimaging. Classroom-based but theory-based
testing holds great potential for the development
of educational theory and could contribute in turn
to testing hypotheses in neuroscience.
(v) At the moment, dyscalculia is not widely
recognized by teachers or educational authorities
nor, it would seem, by research-funding agencies.
Recognition is likely to be the basis for improved
prospects for dyscalculic sufferers.
There is an urgent societal need to help failing
learners achieve a level of numeracy at which
they can function adequately in the modern
workplace. Contemporary research on dyscalcu-
lia promises a productive way forward, but it is
still a poor relationin terms of funding (4),
which means there is a serious lack of evidence-
based approaches to dyscalculia intervention. An
understanding of how the brain processes under-
lying number and arithmetic concepts will help
focus teaching interventions on critical concep-
tual activities and will help focus neuroscience
research on tracking the structural and functional
changes that follow intervention. Learning more
about how to help these learners is driving, and will
continue to drive, where the science should go next.
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... 1. Phonological Dyslexia (Coltheart, 1996) 2. Directional Dyslexia (Sogame & Kubo, 1978) 3. Rapid Naming Deficit Dyslexia (Di Filippo, Zoccolotti, & Ziegler, 2008) 4. Double Deficit Dyslexia (Badian, 1997) 5. Surface Dyslexia (Coltheart, Masterson, Byng, Prior, & Riddoch, 1983) 6. Visual Dyslexia (Stein & Fowler, 1981) 7. Dyscalculia (Butterworth, Varma, & Laurillard, 2011) Phonological Dyslexia (Coltheart, 1996) is classified as Dyslexia where the patient more commonly struggles with identification of phonological sounds. With Directional Dyslexia (Sogame & Kubo, 1978), people struggle with directionality, this involves struggling with sense of direction and can most commonly be seen with the flipping of words. ...
... The most common sign of this is the use of coloured overlays to improve focus or differing reading and processing speeds when reading on differing coloured pieces of paper. Dyscalculia (Butterworth et al., 2011) is specific form of dyslexia defined as the difficulty to read and understand numbers and symbols. A table outlining the characteristics of each classification of dyslexia can be found in Appendix A. ...
... • DR -Directional Dyslexia (Sogame & Kubo, 1978) • SF -Surface Dyslexia (Coltheart et al., 1983) • PL -Phonological Dyslexia (Coltheart, 1996) • DC -Dyscalculia (Butterworth et al., 2011) • DD -Double Deficit Dyslexia (Badian, 1997) • VS -Visual Dyslexia (Stein & Fowler, 1981) • RN -Rapid Naming Deficit Dyslexia (Di Filippo et al., 2008) • NON -Non Subtype Specific Symptoms ...
A neurological phonological processing disorder affecting an estimated 9-12% of people worldwide, making it one of the most prevalent and common Specific Learning Difficulties, Dyslexia is one of the biggest challenges facing the modern education system. Most people are diagnosed with dyslexia in schooling. However, by the time they reach adulthood, only 1.82% of adults in the United Kingdom have a diagnosis. This results in over 80 percent of people with dyslexia remaining undiagnosed and as a result not receiving support in the form of assistive software packages, one-on-one tutoring or other support mechanisms, therefore putting them at a disadvantage compared to peers. Artificial Intelligence techniques provide a new and novel way of diagnosing or screening for Dyslexia allowing for a greater proportion of people to be diagnosed. This survey paper provides an overview of the different principles and methodologies that can be used for screening or diagnosing Dyslexia. A state-of-the-art survey is conducted that reviews and classifies both past and recent papers in the field. Papers are classified based on the approach taken and the results generated. Finally, principles and other approaches that could be undertaken are outlined alongside a discussion of the important future directions in this field.
... Each of these systems is supposed to rely on the specialization of sensory and associative brain areas (Dehaene, 2011), in a similar way as literacy leads to the development of brain networks for reading (Dehaene and Cohen, 2007). Understanding the development of specialized brain networks for digit and number processing could help characterize numeracy-related learning difficulties, such as dyscalculia (Butterworth et al., 2011). ...
... To achieve variability in reading and math abilities at school age, children with a broad range of familial risk for reading impairments were recruited. Given the frequent comorbidity of developmental dyslexia and dyscalculia (Butterworth et al., 2011;Peng et al., 2020) and the previously reported association of visual word sensitivity to reading skills, we were interested to additionally investigate how visual number sensitivity is related to arithmetic and reading skills in children. ...
... A limitation regarding generalizability of the current findings is that our sample consists of children with varying degree of reading skills and familial risk for dyslexia. There is evidence for comorbidity between dyslexia and dyscalculia and for shared features in the development of language and math skills (Butterworth et al., 2011;Peng et al., 2020). Although this sample may present the advantage of capturing a wider range of math achievement as it was found in our study, extrapolating these findings to the general population will require further studies with larger samples. ...
Full-text available
Number processing abilities are important for academic and personal development. The course of initial specialization of ventral occipito-temporal cortex (vOTC) sensitivity to visual number processing is crucial for the acquisition of numeric and arithmetic skills. We examined the visual N1, the electrophysiological correlate of vOTC activation across five time points in kindergarten (T1, mean age 6.60 years), middle and end of first grade (T2, 7.38 years; T3, 7.68 years), second grade (T4, 8.28 years), and fifth grade (T5, 11.40 years). A combination of cross-sectional and longitudinal EEG data of a total of 62 children (35 female) at varying familial risk for dyslexia were available to form groups of 23, 22, 27, 27, and 42 participants for each of the five time points. The children performed a target detection task which included visual presentation of single digits (DIG), false fonts (FF), and letters (LET) to derive measures for coarse (DIG vs. FF) and fine (DIG vs. LET) digit sensitive processing across development. The N1 amplitude analyses indicated coarse and fine sensitivity characterized by a stronger N1 to digits than false fonts across all five time points, and stronger N1 to digits than letters at all but the second (T2) time point. In addition, lower arithmetic skills were associated with stronger coarse N1 digit sensitivity over the left hemisphere in second grade (T4), possibly reflecting allocation of more attentional resources or stronger reliance on the verbal system in children with poorer arithmetic skills. To summarize, our results show persistent visual N1 sensitivity to digits that is already present early on in pre-school and remains stable until fifth grade. This pattern of digit sensitivity development clearly differs from the relatively sharp rise and fall of the visual N1 sensitivity to words or letters between kindergarten and middle of elementary school and suggests unique developmental trajectories for visual processing of written characters that are relevant to numeracy and literacy.
... This approach is less familiar than instruction, but it links closely to the neuroscience of learning (predictionerror learning), as well as the techniques used by special needs teachers. 6,35 It reflects the kind of learning through construction articulated by Seymour Papert at MIT. He provided a 'microworld', in which learners manipulate virtual representations of mathematical concepts linking them to the abstract symbols of formal maths in ways that are more personally meaningful to them. ...
... They therefore have to rely on counting procedures for doing arithmetic, which is highly inefficient. 35 (p1049) This is why construction games are important for dyscalculia. The repeated cycle of goal-action-result-revised action requires continual generation and modification of their concepts and practical actions and should thereby support the development of their conceptual understanding. ...
In January 2019, the Government Office for Science commissioned a series of 4 rapid evidence reviews to explore how technology and research can help improve educational outcomes for learners with Specific Learning Difficulties (SpLDs). This review examined: 1) current understanding of the causes and identification of SpLDs, 2)the support system for learners with SpLDs, 3)technology-based interventions for SpLDs 4) a case study approach focusing on dyscalculia to explore all 3 themes
... Neuroscience contributes to understanding the causes of developmental deficits, the informal development of parietal systems, which support the processing of numbers in numeracy [12,13,17], or the attention or disturbance of hyperactivity. By studying the brain's learning mechanisms and how we can intervene effectively with special teaching techniques. ...
Conference Paper
Full-text available
The purpose of this study is to examine the scientific foundations for integrating neuroscience in general and cognitive neuroscience specifically into the field of education. The scientific community has demonstrated a strong interest in recent decades in integrating neuroscience into education and the various levels of learning: cognition and emotion and precisely multisensory learning, social abilities, and personality traits based on the behavioral patterns of students. Furthermore, ethical issues have emerged upon the application of neuroscientific methods in an educational setting. The current work employs a systematic review of research articles published in the previous two decades after a keyword search of databases of acknowledged worldwide reputation. The study was designed as a systematic literature analysis and incorporates papers from Scopus, PubMed, Elsevier, and PsycINFO databases. A flowchart is designed to indicate the methodology procedure. The review's findings emphasize the critical nature of integrating neuroscience in education and raise ethical concerns about the implementation of neuroscientific methods and tools in educational environments. The novelty of this work is that the literature review on cognitive neuroscience was conducted using a combination of review articles and applied research projects illustrating both the importance of cognitive neuroscience in education and ethical considerations upon the application of neuroscientific methods in the evaluation of learning, cognitive and emotional parameters.
... Here, particularly, to solve the drawbacks of traditional teaching methods with non-routine calculations, the open calculation based on numbers (ABN) originally from the Spanish teaching methodology (abierto basado en números) can be one of numerous alternatives, permitting students to solve a problem dissimilarly, instead of the closed algorithm based on ciphers (CBC) methodology (Ablewhite, 1971;Martínez-Montero, 2011;Martínez-Montero and S anchez, 2021). Therefore, the process-based instruction must be used that it can foster an inquiry-based learning approach, which promotes more students-centered enhancing cooperative learning for mathematics activities (Butterworth et al., 2011;van Aalderen-Smeets and van der Molen, 2015). Besides, instruction process followed in a course can be the interplay of cognitive and affective domains that must foster a connection of students' learning process (Boekaerts, 2007;Li and Kulm, 2008;Jaber and Hammer, 2016). ...
Full-text available
Teaching mathematics in higher education has been followed traditionally by teacher-centered methodology. With this methodology, there are always certain difficulties in mathematics learning, revealing students are not capable of dealing properly with calculations and/or problems. This research presents the comparison and examination of two different instruction methodologies, traditional-classroom methodology (TCM) and flipped-classroom methodology (FCM) about self-belief of pre-service teacher (PST) in a mathematics course. Here, an open calculation based on numbers (ABN) method originally from the Spanish teaching methodology (abierto basado en números) was used in both teaching methodologies. The 274 PSTs participated in the course: 131 students to T-ABN and 143 students to F-ABN. The results after applying the questionnaire (Cronbach's α = 0.897) showed F-ABN had significant influences in PSTs' self-belief toward the course and made classes more interactive based on parametric-statistical tests. PSTs' self-belief for four studied groups (pre-and post-test in control and experimental group) indicated significant differences found by ANOVA test. Additionally, significant differences were only observed in educational background not in gender of PSTs' self-belief according to factorial ANVOA. In all cases, when significant differences were found, effect size and post-hoc tests were conducted. Therefore, more student-centered methodology allowed to build positive teaching/learning environment for PSTs as future teachers, which consequently expects better learning outputs for children as their future students.
... Developmental Dyscalculia (or DD) was originally described as a disorder in mathematical abilities without a deficit in general mental abilities (Kosc, 1974). More recently, DD or Mathematical Learning Disability (MLD) has been referred to as a specific learning disability characterized by a deficit in numerical and mathematical skills (Butterworth et al., 2011, for a review) that cannot be attributed to a lack of learning opportunities, inadequate education or environmental disadvantage, intellectual disabilities, global development delay, hearing/vision/motor disorders or neurological deficits American Psychiatric Association, 2013). ...
Full-text available
A longstanding debate concerns whether Developmental Dyscalculia (DD) is characterized by core deficits in processing non-symbolic or symbolic numerical information, as well as the role of domain-general difficulties. Heterogeneity in recruitment and diagnostic criteria make it difficult to disentangle this issue. Here we selected children (N=58) with severely compromised mathematical skills (2 SDs below average) but average domain-general skills from a large sample referred for clinical assessment of learning disabilities. From the same sample, we selected controls (N=42) matched for IQ, age, and visuospatial memory, but average mathematical skills. Dyscalculics showed deficits in both symbolic and non-symbolic number sense assessed with simple computerized tasks. Performance in digit comparison and in numerosity match-to-sample reliably separated children with DD from controls in cross-validated logistic regression (AUC=0.84). These results support a number sense deficit theory and highlight basic numerical abilities that could be targeted for early identification of at-risk children as well as for intervention. Statement of Relevance Developmental Dyscalculia (DD) is a neurodevelopmental disorder characterized by a deficit in the acquisition of mathematical skills, but its cognitive bases are the subject of heated debate. DD has been related to a variety of deficits, including numerosity perception, symbolic number processing, ordinality processing, as well as to a domain-general visuospatial working memory deficit. Heterogeneity in recruitment procedure and lenient diagnostic criteria make it difficult to disentangle this issue. We selected children with severe DD and controls matched on domain-general skills from a large clinical sample and tested them using computerized tasks tapping core numerical skills. Performance in comparing two Arabic digits and in the sequential comparison of sets of dots best separated children with DD from controls. These results support a number sense deficit theory of DD and highlight basic numerical abilities that should be targeted for early identification of at-risk children as well as for intervention. Highlights • We selected a group of children (N=58) with severe developmental dyscalculia (DD) but average IQ and visuospatial memory. • We selected a control group matched on IQ and visuospatial memory, but with average numeracy skills. • Both groups completed non-symbolic and symbolic number sense tasks. • Digit comparison and sequential comparison of non-symbolic quantities (dots) best separated children with DD from controls.
The foundational contributions from neuroscience regarding how learning occurs in the brain reside within one of Shulman's seven components of teacher knowledge, Knowledge of Students. While Knowledge of Students combines inputs from multiple social science disciplines that traditionally inform teacher education, teachers must also (and increasingly) know what happens inside students' brains. Neuroscience professional development provides neuroscience principles that teachers can learn and apply to distinguish among pedagogical choices, plan lessons, guide in‐the‐moment classroom decisions, and inform the views of students. Neuroscience does not directly invent new pedagogies. Rather, knowledge of neuroscience guides teachers in choosing appropriate pedagogies, pragmatically informing teaching. By providing physiological explanations for psychological phenomena relevant to education, teachers benefit from neuroscience content in their training and professional development. Understanding how learning occurs in students' brains provides teachers with insights into how to choose appropriate classroom pedagogies both in lesson planning and in‐the‐moment classroom decision‐making. Neuroscience knowledge also shapes how teachers view students' abilities and potentials. These practical applications of neuroscience illustrate the importance of including neuroscience in professional development and initial teacher education, under the component of teacher professionalism established by Shulman as Knowledge of Students.
A burgeoning body of literature in pediatric neuropsychological assessment suggests executive functioning is the foundation of many procedural learning skills as mediated by cerebellar processing. Given the neuropsychological necessity of intact procedural learning ability for efficient academic learning, the accurate identification of what we have termed “procedural consolidation deficit” (PCD) may be an underpinning of mathematical learning disorder (MLD). Thus, one aim of the present study was to perform an exploratory correlational analysis between performance on pediatric neuropsychological tasks of procedural learning and a classification of MLD. The second aim was to utilize regression analysis of measures of procedural learning for predicting a clinically useful classification of MLD. Results revealed a significant correlation between performance on tasks of procedural learning and a classification of MLD. The follow-up regression model yielded the most predictive variables in identifying individuals with MLD, which included: (a) WISC-V Coding; (b) first administration of Trail Making Test Part B; (c) slope across five serial administrations of Trail Making Test Part B. The model was highly significant and had a classification accuracy for MLD of 87.4%. Results suggest performance on procedural learning tasks significantly predict a classification of MLD. Theoretical and clinical implications are discussed.
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An important line of research related to the resolution of word problems is the study of the cognitive processes involved when subjects translate problems into the language of algebra. One of the most common errors in problem‐solving is the reversal error (RE), which occurs when students reverse the relationship between two variables when translating equations from comparison word problems. The aim of this neuroeducational study is to investigate the brain anatomy differences between two groups, one group that commits RE and a second group that does not. Magnetic resonance images of 37 normal and healthy participants between the ages of 18–25 years were acquired. Differences in gray matter were assessed using voxel‐based morphometry analysis. Our results show that the RE group has a larger volume in the putamen, suggesting that these subjects have to make a greater effort to solve problems. We investigated the brain anatomy differences involved in problem‐solving with reversal errors. The results show that the group that commits reversal error compared to the group that does not, has a larger volume in the putamen, suggesting that these subjects have to make a greater effort to solve problems. These findings could help to better understand the relationship between brain development and the development of the human capacity for mathematical cognition mediated by educational experience.
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Uzun yıllar, öğrenmede yoğunluklu olarak bilişsel süreçler üzerinde yoğunlaşılmıştır. 1950’li yıllardan bu yana yapılan araştırmalarda öğrenmede bilişsel süreçlerle birlikte duyuşsal ve psiko-motor süreçlerin de araştırmalara dâhil edildiği görülmektedir. Öğrenmedeki bilişsel olmayan süreçler içerisinde kaygı, tutum, motivasyon, öz-yeterlik ve akademik benlik gibi bileşenler yer almaktadır. Bu bileşenlerden araştırmalarda en fazla ele alınanı kaygıdır. Matematik biliminin günümüzdeki önemine ek olarak, özellikle matematik dersinin ülkemizde başarının anahtarı olarak görülmesi, bu derse karşı politika yapıcıların, öğrencilerin, öğretmenlerin ve ebeveynlerin beklentilerini farklılaştırabilmektedir. Bu beklentiler eğitimle ilişki tüm paydaşlar üzerinde matematiksel kaygılara neden olabilmektedir. Matematik kaygısı çevresel, durumsal ve psikolojik ve duygusal sebeplerden kaynaklı oluşabilmekte ve gelişebilmektedir. Bu nedenle, matematik kaygısının çok yönlü ele alınması gerekir. Bu düşüncelerden yola çıkarak yazılan kitap ülkemizde matematik kaygısını kapsamlı bir şekilde ele alan ilk kitap olma özelliği taşımaktadır. Matematik kaygısı üzerine yapılmış güncel araştırmalarla kitap dokuz bölümden oluşmaktadır. Bölüm yazarlarının hepsi matematik kaygısı üzerine araştırma deneyimlerine sahiptir. Kitabın özellikle politika yapıcılara, öğretmenlere, öğretmen adaylarına ve ebeveynlere matematik kaygısının tüm yönlerini anlama konusunda ışık tutacağına inancındayız. Kitabın ortaya çıkmasındaki katkılarından dolayı bölüm yazarlarına ve yayınevine teşekkürlerimizi sunarız. Keyifli okumalar…
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We present results of a computer-assisted intervention (CAI) study on number skills in kindergarten children. Children with low numeracy skill (n = 30) were randomly allocated to two treatment groups. The first group played a computer game (The Number Race) which emphasized numerical comparison and was designed to train number sense, while the other group played a game (Graphogame-Math) which emphasized small sets of exact numerosities by training matching of verbal labels to visual patterns and number symbols. Both groups participated in a daily intervention session for three weeks. Children's performance in verbal counting, number comparison, object counting, arithmetic, and a control task (rapid serial naming) were measured before and after the intervention. Both interventions improved children's skills in number comparison, compared to a group of typically performing children (n = 30), but not in other areas of number skills. These findings, together with a review of earlier computer-assisted intervention studies, provide guidance for future work on CAI aiming to boost numeracy development of low performing children.
Full-text available
One important factor in the failure to learn arithmetic in the normal way is an endogenous core deficit in the sense of number. This has been associated with low numeracy in general (e.g. Halberda et al. in Nature 455:665–668, 2008) and with dyscalculia more specifically (e.g. Landerl et al. in Cognition 93:99–125, 2004). Here, we describe straightforward ways of identifying this deficit, and offer some new ways of strengthening the sense of number using learning technologies.
A definition of developmental dyscalculia, stressing the hereditary or congenital affection of the brain substrate of mathematical functions, is put forth. This disorder is clearly distinguished from other forms of disturbed mathematical abilities. A classification of developmental dyscalculia is then outlined, distinguishing the following forms: verbal, practognostic, lexical, graphical, ideognostical and operational developmental dyscalculia. Finally an investigation is presented of mathematical abilities and disabilities in eleven-year-old pupils from normal schools in Bratislava, Czechoslovakia. A number of tests measuring symbolic functions were applied to 66 suspected dyscalculics with normal IQs who had neurological examinations. The tests are characterized and the results briefly described; some examples of concrete pathological solutions to test items are given. This investigation suggests that nearly 6% of children of the so-called normal population can be justifiably expected to have symptoms of developmental dyscalculia as defined in this study.
The finding that extrinsic rewards can undermine intrinsic motivation has been highly controversial since it first appeared (Deci, 1971). A meta-analysis published in this journal (Cameron & Pierce, 1994) concluded that the undermining effect was minimal and largely inconsequential for educational policy. However, a more recent meta-analysis (Deci, Koestner, & Ryan, 1999) showed that the Cameron and Pierce meta-analysis was seriously flawed and that its conclusions were incorrect. This article briefly reviews the results of the more recent meta-analysis, which showed that tangible rewards do indeed have a substantial undermining effect. The meta-analysis provided strong support for cognitive evaluation theory (Deci & Ryan, 1980), which Cameron and Pierce had advocated abandoning. The results are briefly discussed in terms of their relevance for educational practice.
I Number Words.- 1 Introduction and Overview of Different Uses of Number Words.- 2 The Number-Word Sequence: An Overview of Its Acquisition and Elaboration.- II Correspondence Errors in Counting Objects.- 3 Correspondence Errors in Children's Counting.- 4 Effects of Object Arrangement on Counting Correspondence Errors and on the Indicating Act.- 5 Effects of Object Variables and Age of Counter on Correspondence Errors Made When Counting Objects in Rows.- 6 Correspondence Errors in Children's Counting: A Summary.- III Concepts of Cardinality.- 7 Children's Early Knowledge About Relationships Between Counting and Cardinality.- 8 Later Conceptual Relationships Between Counting and Cardinality: Addition and Subtraction of Cardinal Numbers.- 9 Uses of Counting and Matching in Cardinal Equivalence Situations: Equivalence and Order Relations on Cardinal Numbers.- IV Number Words, Counting, and Cardinality: The Increasing Integration of Sequence, Count, and Cardinal Meanings.- 10 Early Relationships Among Sequence Number Words, Counting Correspondence, and Cardinality.- 11 An Overview of Changes in Children's Number Word Concepts from Age 2 Through 8.- References.- Author Index.
In order for schools to help students with learning difficulties and disabilities improve their achievement in mathematics, educators, researchers, practitioners, and policymakers need a better understanding of the evidence based on what is behind these students' difficulties in learning math. That is just what they will get with this landmark book-- the first and only definitive research volume on this important topic in education. Comprehensive and multidisciplinary, this resource gives educational decisionmakers and researchers in-depth theoretical and practical insight into mathematical learning difficulties and disabilities, combining diverse perspectives from fields such as special education, educational psychology, cognitive neuroscience, and behavioral genetics. More than 35 internationally known contributors share their expertise on: risk factors for developing difficulties with math; connections between mathematics and reading disabilities; neuropsychological factors in mathematical learning disabilities; information processing deficits; individual difference factors in mathematics difficulties, including the influences of motivation, gender, and socio-cultural background; math anxiety; the role of genetics; and effective instructional interventions. Based on the most current research available, this highly informative book gives readers the foundation they need to advance research, teaching strategies, and policies that identify struggling students-- and to begin developing appropriate practices that really help these students improve their math skills. This book divides into three parts, six sections, and nineteen chapters, as follows: PART I, contains: Section I: Characterizing Learning Disabilities in Mathematics; (1) Historical and Contemporary Perspectives on Mathematics Disabilities (Russell Gersten, Ben Clarke, and Michele M.M. Mazzocco; (2) Defining and Differentiating Mathematical Learning Disabilities and Difficulties (Michele M.M. Mazzocco); and (3) Prevalence of Developmental Dyscalculia (Ruth S. Shalev). SECTION II: Cognitive and Information Processing Features. Contains: (4) Information Processing Deficits in Dyscalculia (Brian Butterworth and Vivian Reigosa Crespo); (5) Strategy Use, Long-Term Memory, and Working Memory Capacity (David C. Geary, Mary K. Hoard, Lara Nugent, and Jennifer Byrd-Craven); (6) Do Words Count? Connections between Mathematics and Reading Difficulties (Nancy C. Jordan); (7) Individual Differences in Proportional Reasoning: Fraction Skills (Steven A. Hecht, Joseph K. Torgesen, and Kevin J. Vagi); and Cognitive Aspects of Math Disabilities: Commentary on Section II (H. Lee Swanson). PART II, SECTION III: Neuropsychological Factors, contains: (8) Mathematical Development in Children with Specific Language Impairments (Chris Donlan); (9) The Contribution of Syndrome Research to Understanding Mathematics Learning Disability (Michele M. M. Mazzocco, Melissa M. Murphy, and Michael McCloskey); (10) Mathematical Disabilities in Congenital and Acquired Neurodevelopmental Disorders (Marcia A. Barnes, Jack M. Fletcher, and Linda Ewing-Cobbs); (11) Cognitive and Behavioral Components of Math Performance in ADHD Students (Sydney S. Zentall); (12) Neuropsychological Case studies on Arithmetic Processing (Laura Zamarian, Alex Lopez-Rolon, and Margarete Delazer); and Neuropsychological Factors in Math Disabilities: Commentary on Section III (Rebecca Bull). SECTION IV: Neurobiological and Genetic Substrates, contains: (13) Neuroanatomical Approaches to the Study of Mathematical Ability and Disability (Tony J. Simon and Susan M. Rivera); and (14) Quantitative Genetics and Mathematical Abilities/Disabilities (Stephen Petrill and Robert Plomin). PART III, SECTION V: Additional Influences on Math Difficulties, contains: (15) Is Math Anxiety a Mathematics Learning Disability? (Mark H. Ashcraft, Jeremy A. Krause, and Derek R. Hopko); and (16) Influences of Gender, Ethnicity, and Motivation on Mathematics Performance (James M. Royer and Rena Walles). SECTION VI: Instructional Interventions, contains: (17) Early Intervention for Children at Risk of Developing Mathematical Learning Difficulties (Sharon Griffin); (18) Mathematical Problem Solving: Instructional Interventions (Lynn S. Fuchs and Douglas Fuchs); (19) Quantitative Literacy and Developmental Dyscalculias (Michael McCloskey); and Instructional Interventions/Quantitative Literacy: Commentary on Section VI (Herbert Ginsburg and Sandra Pappas).
This 2006 book was the first handbook where the world's foremost ‘experts on expertise’ reviewed our scientific knowledge on expertise and expert performance and how experts may differ from non-experts in terms of their development, training, reasoning, knowledge, social support, and innate talent. Methods are described for the study of experts' knowledge and their performance of representative tasks from their domain of expertise. The development of expertise is also studied by retrospective interviews and the daily lives of experts are studied with diaries. In 15 major domains of expertise, the leading researchers summarize our knowledge on the structure and acquisition of expert skill and knowledge and discuss future prospects. General issues that cut across most domains are reviewed in chapters on various aspects of expertise such as general and practical intelligence, differences in brain activity, self-regulated learning, deliberate practice, aging, knowledge management, and creativity.