|
|
|
Mathematics Disabilities |
|
a. mathematical Calculation b. Semantic Memory Type c. Visual-Spatial Based |
|
Mathematical Calculation Disability Math
calculation disability involves difficulties with arithmetic computations and
with concepts underlying different math procedures such as understanding the
base 10 system and algorithm calculations. Math procedural deficits involve
the use of counting procedures to solve simple arithmetic problems. Often, a
math calculation disabled person will commit more errors as a result of
strategies: e.g., under- or over-counting, misalignment or borrowing from one
column to the next as a result of deficits in temporal-sequential or spatial
ordering. Diagnostic Criteria ·
Scores on
computational math achievement tests are from the Low to the Much Below Average range. ·
Cognitive
abilities or IQ scores are in the Average range, sensory processes are within
normal limits, and the person has equal educational opportunities in math. ·
A significant
difference exists between cognitive abilities and scores in numerical
competencies. Differential Diagnosis There
are three subtypes of mathematics disability, each having specific cognitive
processing deficits: i.e., the first being mathematical calculation
disability (e.g., difficulties in learning, retaining, and retrieving math
facts which are essential for precise calculation), and the second disability
being semantic memory (e.g., difficulties with conceptual knowledge in math
which translates into deficits in storing, accessing and/or retrieving
arithmetic facts from long term memory), and the third disability being
visual-spatial (e.g., deficits in visuo-spatial
working memory systems or deficits in accompanying executive processes, such
as attentional or inhibitory control). Semantic Memory Math Disability A
semantic memory math disability is considered to be associated with language
difficulties; it involves difficulties in learning such as representing,
storing, accessing and/or retrieving math facts from long term memory. The representional deficits could involve quantitative,
numerical magnitude, processing speed and/or phonological representation of
numbers. These difficulties are often manifested in slow, inaccurate or
inconsistent problem-solving or math reasoning abilities. Diagnostic Criteria ·
Scores on math
reasoning or word problem achievement tests are in the Low to the Much Below Average range. ·
Cognitive
abilities are in the Average range or a significant difference exists between
cognitive abilities and scores in math reasoning. ·
Math reasoning
difficulties are often accompanied with cognitive deficits: e.g., in the use
of counting procedures, working memory, and representing and/or retrieving
basic facts from long-term memory. ·
Often, math
reasoning and reading difficulties are involved as they share comorbid features. Hence, persons who are disabled in semantic
memory for math are likely to have lower scores on verbal tests as opposed to
the nonverbal ones. Visual-spatial math disability Visual-spatial
math disability involves non-language factors; it is characterized by
difficulties in representing spatial representations and manipulations of
numerical information. Visual-spatial math disability is also characterized
by deficits of executive functions (e.g., attention, visual memory,
processing speed, temporal-sequential and spatial ordering), which affect
mathematical domains such as geometry and the solving of word problems. ·
Scores on
computational math and/or math reasoning achievement tests are in the Low to
the Much Below Average range. ·
Cognitive
abilities are in the Average range; however, there is a significant
difference which exists between verbal and nonverbal abilities, with
nonverbal abilities being much lower than verbal abilities. ·
Often, persons
who are visual-spatial math-disabled obtain lower scores on tests of
executive functions, in domains such as attentional
and inhibitory control. Intervention Strategies A
number of empirically supported interventions have been designed to help
persons with math disabilities. One strand of research focuses on implicit
instruction, targeting procedural skills as well as conceptual knowledge,
with guided peer-mediated practice. Also, research on the value of modeling
in teaching/tutoring computational skills shows that teacher demonstrations
of calculation algorithms and higher-level procedural steps are effective in
increasing both computational and problem-solving behaviors. In
addition, cognitive-behavioral models of intervention have given rise to the
development of self-instructional strategy techniques to help guide persons
with math disabilities through a variety of problem-solving contexts. A key
component of cognitive-behavioral techniques is to teach a student to first
verbalize the steps that could be used in solving particular math problems. One
line of math problem-solving intervention research that promotes competence
with arithmetic word problems, is the Self-Regulated
Strategy Development, which focuses on straightforward syntactic structures
and one-step solutions, increasing overall performance, with less probability
of applying the wrong operations. Another line of research on math models
substantiates the value of concrete materials or manipulatives,
and diagrams in helping elementary-age students master arithmetic word
problems. A
category of research for persons with math visual-spatial disabilities,
focuses on combining diagrams with methods designed to induce schemas;
instructional principles include explicit explanation, pictorial or concrete
representations, verbal rehearsal with fading, and self-regulation
strategies. Additionally, a variety of cognitive strategies which enhance
working memory, attention, temporal-sequential and spatial ordering have been
shown to be effective in developing both foundational skills and higher-order
skills involving problem-solving. Prevalence and Etiology The
findings across studies suggest that 5 to 7% of school-age children exhibit
some form of arithmetic disability. Gender ratio studies show that
males are more prone to arithmetic disability. In addition, about half of the
school children with math disabilities have reading and writing difficulties.
As with other forms of learning disability, twin and familial studies suggest
both genetic and environmental contributions to mathematics disability.
Family members (e.g., parents and siblings) of children with arithmetic
disorders are 10 times more likely to be diagnosed with an arithmetic
disorder than are members of the general population. References Feifer, S. G., & De Fina,
P.A. (2000). The neurology of reading
disorders. Fletcher, J. M., Lyon, G.
R., Fuchs, L. S., & Barnes, M. A.
(2007). Learning disabilities.
Swanson, H. L., & Saez, L. (2003). Learning disabilities in arithmetic:
Problem-solving differences and cognitive deficits. In Swanson, H. L.,
Harris, K. R., & Graham, S. (Eds). Handbook of
learning disabilities (pp. 199-212). |
|
|
