# Mathematics Disorder

# Mathematics Disorder

## Definition

Mathematics disorder, formerly called developmental arithmetic disorder, developmental acalculia, or dyscalculia, is a learning disorder in which a person’s mathematical ability is substantially below the level normally expected based on his or her individual’s age, intelligence, life experiences, educational background, and physical impairments. This disability affects the ability to do calculations as well as the ability to understand word problems and mathematical concepts.

## Description

Mathematics disorder was first described as a developmental disorder in 1937. Since then, it has come to encompass a number of distinct types of mathematical deficiencies. These include:

- difficulty reading and writing numbers
- difficulty aligning numbers in order to do calculations
- inability to perform calculations
- inability to comprehend word problems

The range and number of mathematical difficulties that have been documented suggests that there are several different causes for mathematics disorder. In addition, several known physical conditions cause mathematics disorder. Turner syndrome and fragile X syndrome, both genetic disorders that affect girls, are associated with difficulty in mathematics. Injury to certain parts of the **brain** can also cause inability to perform calculations. These conditions appear to be independent of other causes of mathematics disorder. Mathematics disorder is often associated with other **learning disorders** involving reading and language, although it may also exist independently in children whose reading and language skills are average or above average.

## Causes and symptoms

The causes of mathematics disorder are not understood. Different manifestations of the disorder may have different causes. Symptoms of the disorder, however, can be grouped into four categories: language symptoms; recognition or perceptual symptoms; mathematical symptoms; and attention symptoms.

People with language symptoms have trouble naming mathematical terms; understanding word problems; or understanding such mathematical concepts as “greater than” or “less than.” People with recognition symptoms have difficulty reading numbers and such operational signs as the plus or minus signs, or aligning numbers properly in order to perform accurate calculations. Mathematical symptoms include deficiencies in the ability to count; to memorize such basic arithmetical data as the multiplication tables; or to follow a sequence of steps in problem solving. Attention symptoms are related to failures in copying numbers and ignoring operational signs. Sometimes these failures are the result of a person’s carelessness. At other times, however, they appear to result from a lack of understanding of the factors or operations involved in solving the problem.

In practical terms, parents and teachers may see the following signs of mathematics disorder in a child’s schoolwork:

- problems counting
- difficulty memorizing multiplication tables
- inability to grasp the difference between such operations as addition and subtraction
- poor computational skills; many errors in simple arithmetic
- slowness in performing calculations
- difficulty arranging numbers in order (from smallest to largest, for example)
- inability to grasp information on graphs
- difficulty copying numbers or problems
- inability to grasp the concept of place value
- inability align two or three digit numbers to do calculations
- difficulty understanding word problems
- inability to understand mathematical symbols

These symptoms must be evaluated in light of the person’s age, intelligence, educational experience, exposure to mathematics learning activities, and general cultural and life experience. The person’s mathematical ability must fall substantially below the level of others with similar characteristics. In most cases several of these symptoms are present simultaneously.

## Demographics

The number of children with mathematics disorder is not entirely clear. The *Diagnostic and Statistical Manual of Mental Disorders-IV (DSM-IV),*which is the basic manual consulted by mental health professionals in assessing the presence of mental disorders, indicates that about 1% of school age children have mathematics disorder. Other studies, however, have found higher rates of arithmetical dysfunction in children. Likewise some studies find no gender difference in the prevalence of mathematics disorder, while others find that girls are more likely to be affected. Mathematics disorder, like other learning disabilities, however, does appear to run in families, suggesting the existence of a genetic component to the disorder.

## Diagnosis

Mathematics disorder is not usually diagnosed before a child is in the second or third grade because of the variability with which children acquire mathematical fluency. Many bright children manage to get through to fourth- or fifth-grade level in mathematics by using memorization and calculation tricks (such as counting on fingers or performing repeated addition as a substitute for multiplication) before their disability becomes apparent. Requests for testing usually originate with a teacher or parent who has observed several symptoms of the disorder.

To receive a **diagnosis** of mathematics disorder according to the criteria established by the American Psychiatric Association, a child must show substantially lower than expected ability in mathematics based on his or her age, intelligence, and background. In addition, the child’sdeficiencies must cause significant interference with academic progress or daily living skills.

In addition to an interview with a child **psychiatrist** or other mental health professional, the child’s mathematical ability may be evaluated with such individually administered diagnostic tests as the Enright Diagnostic Test of Mathematics, or with curriculum-based assessments. If the results of testing suggest mathematics disorder, such other causes of difficulty as poor vision or hearing, **mental retardation** , or lack of fluency in the language of instruction, are ruled out. The child’s educational history and exposure to opportunities for learning mathematics are also taken into account. On the basis of this information, a qualified examiner can make the diagnosis of mathematics disorder.

## Treatments

Children who receive a diagnosis of mathematics disorder are eligible for an individual education plan (IEP) that details specific accommodations to learning. Because of the wide variety of problems found under the diagnosis of mathematics disorder, plans vary considerably. Generally, instruction emphasizes basic mathematical concepts, while teaching children problem solving skills and ways to eliminate distractions and extraneous information. Concrete, hands-on instruction is more successful than abstract or theoretical instruction. IEPs also address other language or reading disabilities that affect a child’s ability to learn mathematics.

## Prognosis

Progress in overcoming mathematics disorder depends on the specific type of difficulties that the child has with mathematics; the learning resources available; and the child’s determination to work on overcoming the disorder. Some children work through their disability, while others continue to have trouble with mathematics throughout life. Children who continue to suffer from mathematics disorder may develop low self-esteem and social problems related to their lack of academic achievement. Later in life they may be more likely to drop out of school and find

### KEY TERMS

**Individual education plan (IEP)** —A plan of instruction drawn up for an individual student who is having specific difficulties with mathematics, reading, or other skills necessary to progress beyond elementary school.

themselves shut out of jobs or occupations that require the ability to perform basic mathematical calculations.

## Prevention

There is no known way to prevent mathematics disorder.

*See also*Reading disorder; Disorder of written expression.

## Resources

#### BOOKS

American Psychiatric Association. *Diagnostic and Statistical Manual of Mental Disorders.* 4th ed., text revised. Washington DC: American Psychiatric Association, 2000.

Sadock, Benjamin J. and Virginia A. Sadock, eds. *Comprehensive Textbook of Psychiatry.* 7th ed. Vol. 2. Philadelphia: Lippincott Williams and Wilkins, 2000.

#### PERIODICALS

Jordan, Nancy, and Laurie B. Hanich. “Mathematical Thinking in Second-Grade Children with Different forms of LD.” *Journal of Learning Disabilities* 33 (November 2000): 567-585.

#### ORGANIZATIONS

Learning Disabilities Association of America. 4156 Library Road Pittsburgh, PA 15234-1349. (412) 341-1515. <www.ldanatl.org>

National Center for Learning Disabilities. 381 Park Avenue South, Suite 1401, New York, NY 10016. (888) 575-7373 (toll-free) or (212) 545-7510. <www.ncld.org>

Tish Davidson, A.M.

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#### NEARBY TERMS

**Mathematics Disorder**