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Mathematics and Dyslexia (International Dyslexia Association)
Mathematics and Dyslexia
Perspectives, Fall
1998 International Dyslexia Association
reprinted with permission
Not all individuals with dyslexia have problems with mathematics,
but many do. There are those who have a good memory for sequences
and can execute procedures in a "recipe" style,
i.e., stepbystep. They are able to remember formulas, but
may not understand why the formula makes sense. They prefer
to do paper and pencil tasks and are attentive to the details,
but do not see the big picture. Then, there are those who
see the big picture and have insight into the patterns of
mathematics, but are poor at computation and have problems
with remembering stepbystep procedures. They also understand
mathematical concepts and like to solve problems mentally
and quickly, yet their answers may be inaccurate. These individuals
may have difficulty in verbalizing and explaining their answers.
Too frequently and too readily, individuals with dyslexia
who have difficulty with mathematics are misdiagnosed as having
dyscalculia  literally trouble with calculating, a neurologically
based disability. True dyscalculia is rare (Steeves, 1983).1
We know that for individuals with dyslexia, learning mathematical
concepts and vocabulary and the ability to use mathematical
symbols can be impeded by problems similar to those that interfered
with their acquisition of the written language (Ansara, 1973).2
Additionally, we know that the learning of mathematical
concepts, more than any other content area, is tied closely
to the teacher's or academic therapist's knowledge of mathematics
and to the manner in which these concepts are taught (Lyon,
1996).3 Therefore, there are individuals with dyslexia who will
exhibit problems in mathematics, not because of their dyslexia
or dyscalculia, but because their instructors are inadequately
prepared in mathematical principles and/or in how to teach
them.
In addition, we know that individuals with dyslexia may have
problems with the language of mathematics and the concepts
associated with it. These include spatial and quantitative
references such as before, after, between, one more than,
and one less than. Mathematical terms such as numerator and
denominator, prime numbers and prime factors, and carrying
and borrowing may also be problematic. These individuals may
be confused by implicit, multiple meanings of words, e.g.,
two as the name of a unit in a series and also as the name
of a set of two objects. Difficulties may also occur around
the concept of place value and the function of zero. Solving
word problems may be especially challenging because of difficulties
with decoding, comprehension, sequencing, and understanding
mathematical concepts. In understanding the complex nature
of dyslexia, Ansara (1973)4 made
three general assumptions about learning, in particular, for
individuals with dyslexia. These assumptions affect the way
one needs to provide instruction. They are:

learning involves the recognition of patterns which
become bits of knowledge that are then organized into
larger and more meaningful units;

learning for some children is more difficult than for
others because of...deficits that interfere with the ready
recognition of patterns; (and)

some children have difficulty with the organization
of parts into wholes, due to ... a disability in the handling
of spatial and temporal relationships or to unique problems
with integration , sequencing or memory.
Therefore, teachers and academic therapists who provide remedial
instruction in mathematics to these individuals must have
an understanding of the nature of dyslexia and how it affects
learning, not only in written language, but also in mathematics.
Additionally, the instructor needs to have an understanding
of the mathematics curriculum; the ability to use a variety
of instructional techniques that are simultaneously multisensory
and which provide for explicit instruction that is systematic,
cumulative, diagnostic, and both synthetic and analytical
as well as a knowledge of current research in mathematical
instruction.
Simply just being good at mathematics is not enough. The
teacher and academic therapist need to understand that mathematics
is problemsolving which involves reasoning and the ability
to read, write, discuss and convey ideas using mathematical
signs, symbols and terms. This requires an understanding of
mathematical knowledge, both conceptual (relationships constructed
internally and connected to already existing ideas) and procedural
(knowledge of symbols used to represent mathematics, and the
rules and procedures that are used to carry out mathematical
tasks). Both are important and need to be understood. For
procedural knowledge, the most important connection is to
the conceptual knowledge that supports it; otherwise, procedural
knowledge will be learned rigidly and used narrowly. Usually,
when there is a connection to a conceptual basis, the procedure
is not only understood, but the learner will have access to
other ideas associated with the concept (Van de Walle, 1994).5 For individuals with dyslexia, this linkage is critical
and language plays an important role.
To assist individuals with dyslexia in making this linkage,
it is essential that teachers and academic therapists provide
instruction that allows the learner to work through the following
cognitive developmental stages when teaching mathematical
concepts at all grade levels: concrete, pictorial, symbolic,
and abstract. Individuals with dyslexia will learn best when
provided with concrete manipulatives with which they can work
or experiment. These help build memory as well as allowing
for revisualization when memory fails. The next stage, pictorial,
is one which may be brief, but is essential for beginning
the transition away from the concrete. This is where individuals
recognize or draw pictures to represent concrete materials
without the materials themselves. Symbols, i.e., numerals,
plus signs, etc., are introduced when individuals understand
the basic concept, thereby making the connection to procedural
knowledge. Finally, the abstract stage is where individuals
are able to think about concepts and solve problems without
the presence of manipulatives, pictures, and symbols. (Steeves
& Tomey, 1998a).6
According to Steeves and Tomey (1998a),7
it is important that the four developmental stages
are linked through language for these individuals. There are
three kinds of language which allow one to fully integrate
mathematical learning. First, is the individual's own language.
No matter how imperfect this language is, it is important
that the individual discusses, questions, and states what
she/he has learned. Second, is the language of the instructor,
or standard English, which clarifies the learner's own language,
and links to the third language, the language of mathematics.
The language of mathematics is not just the vocabulary but
the use of sign, symbols, and terms to express mathematical
ideas, such as 2 + 4=6. Also, language allows the instructor
to determine if the learner understands the concept and is
not just following steps demonstrated by the instructor to
complete a process, even at the concrete stage.
For these reasons, teachers and academic therapists who,
in mathematics, work with individuals with dyslexia, must
be welltrained in multisensory structured techniques both
in language and mathematics instruction and remediation. They
must not only demonstrate competencies in knowledge and skills
in teaching language to these individuals, but also demonstrate
the following competencies in mathematics (Steeves and Tomey,
1998b)8:
1. Understanding of the mathematics and the use of appropriate
methodology, technology, and manipulatives within the following
content:

Number systems, their structure, basic operations and
properties;

Elementary number theory, ratio, proportion and percent;

Algebra;

Measurement systems  U.S. and metric;

Geometry: geometric figures, their properties and relationships;

Probability;

Discrete mathematics: symbolic logic, sets, permutations
and combinations; and

Computer science: terminology, simple programming, and
software applications;
2. Understanding of the sequential nature of mathematics,
and the mathematical structures inherent in the content strands;
3. Understanding of the connections among mathematical concepts
and procedures and their practical applications;
4. Understanding of and the ability to use the four processes
 becoming mathematical problem solvers, reasoning mathematically,
communicating mathematically, and making mathematical connections
at different levels of complexity;
5. Understanding the role of technology, and the ability
to use graphing utilities and computers to teach mathematics;
6. Understanding of and ability to select, adapt, evaluate,
and use instructional materials and resources, including technology;
7. Understanding of and the ability to use strategies for
managing, assessing, and monitoring student learning, including
diagnosing student errors; and
8. Understanding of and the ability to use strategies to
teach mathematics to diverse learners.
The editors thank Harley A. Tomey, III (VA) and Joyce Steeves,
Ed.D. (MD) for their suggestions for and review of this article,
and especially Mr Tomey for his help in its preparation.
References and Endnotes
1Steeves, K.J. (1983). Memory
as a factor in the computational efficiency of dyslexic children
with high abstract reasoning ability. Annals of Dyslexia,
33,141152. Baltimore: International Dyslexia Association.
2, 4 Ansara A. (1973). The
language therapist as a basic mathematics tutor for adolescents.
Bulletin of the Orton Society, 23, 119138.
3 Lyon, G.R. (1996). State
of Research. In Cramer, S. & Ellis, W. (Eds.), Learning
disabilities: Lifelong issues (pp. 361). Baltimore: Brooks
Publishing.
5 Van de Walle, J. A. (1994).
Elementary school mathematics: Teachi ng developmentally (2nd
ed.). White Plains, NY. Longman.
6,7 Steeves, K. J., & Tomey,
H.A. (1998a). Mathematics and dyslexia: The individual who
learns differently may still be successful in math. Manuscript
in preparation.
8 Steeves, K. J., & Tomey,
H.A. (1998b). Personal written communications to the editors.
