Is There a Difference Between Dyscalculia and a Learning Disability That
Affects Mathematics? If So, What Is It?
In the assessment of reading, I am reluctant to use the term “dyslexia.”
Dyslexia has many different definitions. When Psychologist A uses the term,
they cannot know how Psychologist B will interpret it. In my view, it is
therefore preferable to use the conceptualization “a learning disability that affects reading.”
The learning disability lies in one of the cognitive abilities. It may
be a weakness in processing speed, auditory processing, fluid reasoning, or
another cognitive ability. The disability manifests itself in reading. In other
words, the difficulties
we observe in reading are symptoms of an underlying impairment in cognition, or
in a particular cognitive ability.
In mathematics, the situation is somewhat different. In this area, I
believe there is value in distinguishing
between “dyscalculia” and “a learning disability that affects mathematics.” Prof.
Sarit Ashkenazi and I proposed this approach in a chapter we recently wrote for
the book "Developmental Dyscalculia" edited by Avishai Henik and
Yarden Gliksman (reference below).
A Learning
Disability That Affects Mathematics
When a cognitive ability is impaired, this impairment may affect reading
as well as mathematics.
For example, weak fluid reasoning may impair reading comprehension
because it makes it difficult to draw conclusions about information that is not
stated explicitly in the text. Weak fluid reasoning may also impair
mathematical performance. It may, for example, make it difficult to solve
number-sequence problems. To complete a number sequence such as 0, 1, 1, 2, 3,
5, 8, ___, ___, the child must identify the rule connecting the elements
already provided and apply that rule to continue the sequence. The sequence
above is Fibonacci's sequence, in which each number is the sum of the two
numbers preceding it.
When processing speed is impaired, the disability may manifest itself as
non-fluent reading. Low processing speed may also affect arithmetic fluency (rapidly
solving very simple problems involving the four basic arithmetic operations).
It is entirely logical that when a particular cognitive ability is
impaired, it will affect not only reading but also mathematics. After all, we
are talking about the same child. This is why there is substantial comorbidity
between reading disabilities and mathematics disabilities.
To diagnose a learning disability that affects mathematics, we would
therefore use the same steps that we use to diagnose a learning disability
affecting reading, following Flanagan’s method.
First, the child must have persistently low achievement in mathematics,
despite having received remedial instruction.
Second, the child must have a significant
weakness in one or two of the following cognitive abilities: Fluid reasoning, Crystallized
knowledge, Processing speed, Short-term or working memory, Learning efficiency,
Retrieval fluency, Visual processing or Auditory processing.
Third, the weak cognitive ability must explain the child’s poor
mathematical performance. For example, poor working memory may explain why a
child has trouble performing calculations mentally but performs better when
calculations are written down.
Fourth, most of the child’s cognitive abilities should be intact.
Fifth, exclusionary factors, such as emotional difficulties, mathematics
anxiety, irregular school attendance, or poor instruction, should not provide a
better explanation for the child’s low mathematical achievement.
According to this model, we would recommend an intervention aimed at
improving the child’s functioning in the weak cognitive ability. Improving working
memory should have a positive effect on the child’s performance in mathematics,
as well as in reading. There is disagreement in the professional literature
about whether working memory can in fact be improved. Games and exercises such
as the N-back task may be capable of doing so.
Dyscalculia
The main characteristic of dyscalculia is difficulty with the perception
of quantity, or number sense.
Number sense is the understanding that a set of objects has the property
of quantity and that manipulating the set, by adding or removing objects,
changes that quantity.
Individuals with intact number sense intuitively understanding that adding
12 objects to 14 objects produces approximately 30 objects, not approximately
300 objects. They not only know but also sense the relationship between 4 + 2 =
6 and 4 + 3 = 7. They sense that this relationship is fundamentally different from
the relationship between the statements “Paris is the capital of France” and
“London is the capital of England.”
A difficulty with number sense is relatively uncommon, affecting only a
few percent of the population. When it is present, however, it is clearly
noticeable even in adolescents and adults.
Number sense can be assessed with computerized tests such as panamath.
Difficulties with number sense can also be observed clinically. We would
expect to see phenomena such as the following:
To calculate 21 + 7, an adolescent girl draws 21 lines, then draws
another 7 lines, and counts all the lines she has drawn, starting from 1.
To determine how many cakes costing 10 shekels each can be purchased for
100 shekels, an adolescent boy calculates:
100 - 10 = 90
90 - 10 = 80
He continues in this way and then counts how many times he subtracted
10.
An adolescent girl has great difficulty making estimates. For example,
she says that 20 + 35 is close to 1,000.
An adolescent boy counts on his fingers to solve a simple problem
involving one of the four basic arithmetic operations.
An adolescent girl has difficulty automatically retrieving
multiplication facts, not relatively difficult facts such as 9 × 7, but simple
facts involving smaller numbers.
An adolescent boy places numbers on a number line in an illogical
manner. For example, he places the number 23 close to the midpoint of a number
line ranging from 1 to 100.
In all these
examples, I deliberately used the word adolescent to emphasize that the problem
cannot be attributed to insufficient learning or inadequate practice of the
relevant material.
Naturally, we may also observe such difficulties in younger children.
However, we would attach increasing diagnostic significance to them as the
child receives more instruction and practice in the relevant area.
A child may therefore have:
- Dyscalculia alone
- Dyscalculia together with a learning disability
that affects mathematics
- A learning disability that affects mathematics
without dyscalculia
- Another difficulty that impairs mathematical
achievement, such as attention-deficit/hyperactivity disorder
Dyscalculia alone would manifest itself as low mathematical achievement
caused by an impairment in quantity perception or number sense. Such an
impairment may exist even when all the child’s other cognitive abilities are
intact, including fluid reasoning, crystallized knowledge, learning efficiency,
retrieval fluency, short-term memory, visual processing, auditory processing,
and processing speed.
To diagnose this condition, it is obviously not enough to establish that
the child has low achievement in mathematics. It is also necessary to
demonstrate that the low achievement is caused by an impairment in quantity
perception or number sense.
Sapir-Yogev, S., & Ashkenazi, S. (2025). The cognition-numeracy
model of math learning disabilities. In Developmental Dyscalculia (pp.
27-53). Academic Press. https://doi.org/10.1016/B978-0-443-22224-5.00002-3
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