eMedicine Specialties > Pediatrics: Developmental and Behavioral > Medical Topics

Learning Disorder: Mathematics

Author: Vidhu V Thaker, MB, BCh, MD, Instructor in Pediatrics, Albert Einstein College of Medicine; Consulting Staff, Department of Pediatrics, Jacobi Medical Center
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Updated: Dec 17, 2008

Introduction

Background

Neurologic in origin, learning disorders impede a person's ability to store, process, and/or produce information. Learning disorders can affect the ability to read, write, speak, or compute mathematics and can impair socialization skills. The central clinical feature of a learning disorder is the lack of normal developmental skill, either cognitive or linguistic.

Definitions

Mathematical learning disorder (MD) also known as dyscalculia is a term used for a wide range of disorders caused by abnormalities in one or more of the basic psychological processes involved in understanding or use of math. Several manifestations of the disorder may occur throughout the life of the individual. Mathematical learning disorder does not include children who have learning problems caused primarily by (1) visual, hearing, or motor impairments; (2) mental retardation; (3) emotional disturbance; or (4) environmental, cultural, or economic disadvantages.

US clinicians should become familiar with the federal Individuals with Disabilities Education Act (IDEA), which defines learning disorders as "processing disorders that result in a significant discrepancy between potential and acquisition of various academic or language skills."^1,2 Although this definition has raised several questions, it remains important in current clinical practice. Mathematical learning disorder is among the disabilities that qualify children for special education programs under IDEA.

Frequency

United States

Assessing the exact incidence of mathematical learning disorder is difficult due to paucity of studies that focus specifically on basic number and arithmetic skills.

Collectively, learning and language disorders comprise a very common set of problems. An estimated 10-20% of children and adolescents have a language disorder, a learning disorder, or both. Reading disorders (RDs) comprise a large portion of this group. An estimated 6-7% of elementary school children have been recognized with mathematical disorder. However, children often have more than one disorder; 56% of children with a reading disorder also showed poor mathematics achievement, and 43% of children with a mathematical learning disorder showed poor reading skills.

The estimated incidence may not accurately reflect the presence of the disorder. Some children may have narrow deficits in certain aspects of arithmetic (eg, counting) and perform well in all other aspects. However, standardized tests will still record a poor performance.

Mathematical learning disorder incidence among American children is higher than in Japanese, German, or French children. This higher incidence may be linked to the instructional course design.

Clinical

History

Children with learning disorders typically present at primary school age or later. Often, mathematical learning disorder (MD) is associated with reading disorder (RD), although mathematical learning disorder is noticed later because of language's permeating influence in everyday life. Mathematical learning disorder often goes unrecognized until the child begins schooling.

Causes

• Learning facts
  • Virtually all mathematical procedures involve a body of underlying factual givens. Mathematical facts include the multiplication tables, simple addition and subtraction, and a range of numerical equivalencies.
  • Early stages of elementary school mathematical learning generally place heavy reliance on rote memory as a child seeks to incorporate an immense volume of mathematical facts. Once these facts are memorized, the child then must engage in convergent retrieval; facts must be recalled precisely on demand.
  • An elementary school student then must progress to fully automated recall of mathematical facts. For example, while performing an algebra problem, a student is required to recall principals of addition, subtraction, division, and multiplication accurately and in precise detail.
  • Elementary school students who face difficulty are those who have problems initially memorizing mathematical facts; those with divergent, imprecise patterns of retrieval memory; and those who have difficulty recalling mathematical facts, which slows their ability to count. These students later have difficulty with more sophisticated problem solving, resulting in mathematics underachievement at middle school level.
• Understanding details
  • Mathematics computations laden with fine detail (eg, order of numbers in a problem, precise location of a decimal, appropriate operational signs [+, -]) comprise the heart of a mathematics problem. High attention to detail is needed throughout the operation of mathematics.
  • The children most likely to face problems with mathematical computations at this level are those who have attention deficits and those who are impulsive and lack self-monitoring.
  • A student with attention deficit hyperactivity disorder (ADHD) may appear to understand facts, but that student's lack of attention to detail creates poor overall performance.
• Mastering procedures
  • In addition to mastering mathematical facts, a student must be able to recall specific procedures (eg, mathematical algorithms). These algorithms include the processes involved in multiplication, division, reducing fractions, and regrouping.
  • A good understanding of their underlying logic enhances recall of such procedures.
  • At this level of functioning, children with sequencing problems have significant difficulty accessing and applying mathematical algorithms.
• Using manipulations
  • With increasing experience and skill, school-aged children should be able to manipulate facts, details, and procedures to solve more complex mathematical problems, a process that requires integrating several facts and procedures in the same problem-solving task.
  • The act of manipulation requires a substantial amount of thinking-space or active-working memory. For example, solving a problem often requires students to remember numbers and use them later. Students should be able to understand why they are using the numbers and then use them. Students should also be able to manipulate task subcomponents.
  • Students with limited active-working memory experience considerable difficulty using manipulations.
• Recognizing patterns
  • Mathematics confronts students with a wide range of recurring patterns. These patterns may consist of keywords or phrases that continually emerge from word problems and yield significant hints about the procedures required.
  • Students often must be able to discard superficial differences and recognize the underlying pattern, a process that creates problems for students with a pattern recognition disability.
• Relating to words
  • Without question, mastery of mathematics requires the acquisition of a rather formidable mathematical vocabulary (eg, denominator, numerator, isosceles, equilateral). Much of this vocabulary is not part of everyday conversation and, hence, must be learned without the assistance of contextual clues.
  • Children who slowly process words and who are weak in language semantics falter at this level.
• Analyzing sentences
  • The language of mathematics is unique in the sense that a student is expected to draw inferences from word problems expressed in sentences. Keen sentence comprehension and knowledge of mathematics vocabulary are needed to understand explanations from books and instructors.
  • Children with language disabilities may feel disoriented and confused by verbal instructions and by written assignments and tests.
• Processing images
  • Much mathematical subject matter is presented in images and in a visual-spatial format. Geometric figures require keen interpretation of differences in shapes, sizes, proportions, quantitative relationships, and measurements.
  • Students must also be able to correlate language and figures; the terms trapezoid and square should evoke design patterns in students' minds.
  • Children with weaknesses in visual perception and visual memory may have trouble with these subcomponents of mathematics.
• Performing logical processes
  • At middle school level, use of logical processes and proportional reasoning increase. Word problems (eg, if...then, either...or) require considerable reasoning and logic. These concepts are also used in other subjects such as chemistry and physics.
  • Children who lag in acquiring propositional and proportional reasoning skills may be less able to perform direct computation and word problems that demand reasoning. These students may excessively rely on rote memory.
• Estimating solutions
  • An important part of the reasoning process, and a problem for children lacking this skill, is the ability to estimate answers to problems.
  • The ability to estimate solutions to a mathematical problem often indicates the child's understanding of the concepts needed to solve the problem.
• Conceptualizing and linking
  • Understanding concepts forms the basis of several mathematical problems (eg, 2 sides of an equation should be equal, fractions and percentages are frequently equal).
  • Children with poor conceptualization abilities frequently have difficulty in middle school mathematics; they may be unable to link concepts and have only fragmentary knowledge of applicable mathematics.
• Approaching the problem systematically
  • Problem-solving skills are complex abilities that require a systematic strategic approach, entailing the following steps:
    • Identify the question
    • Discard irrelevant information
    • Devise possible strategies
    • Choose the best strategy
    • Try that strategy
    • Use alternative strategies, if required
    • Monitor the entire process
  • Impulsive children who fail to use this systematic approach and do not self-monitor throughout the process are unlikely to perform the task in a coordinated, executive-functioning manner.
• Accumulating abilities
  • Mathematics is intensely cumulative. A hierarchy of knowledge and skills must be constructed over time. Information learned in lower grades must be retained for future use. Students can appreciate the Pythagorean theorem only to the extent that they recall the definition of a right triangle.
  • Some children apparently encounter difficulties developing cumulative memory and recall. They may have problems in subjects other than mathematics that also require cumulative recall (eg, science, foreign language).
• Applying knowledge
  • Children should be able to realize the relevance of mathematics to learning and use in day-to-day life.
  • Students unable to perceive this relevance may find mathematics alien or irrelevant.
• Fearing the subject
  • Apprehensions, anxieties, or phobias are common complications of disabilities in mathematics.
  • These reactions can be caused by any of the above disabilities or may be rooted in fear of repeated humiliation in class.
• Having an affinity for the subject
  • Some children have natural affinity to mathematics. These children may have strong role models with an affinity for mathematics, or the children themselves have strong conceptualization abilities.
  • Students with a natural affinity for mathematics may be keenly aware of the subject's cohesion and can perceive mathematics' beauty and elegance.
• Mathematical subcomponents and the principal neurodevelopmental function(s) each requires
  • Facts - Memorization, retrieval memory
  • Details - Attention, retrieval memory
  • Procedures - Conceptualization, sequencing procedural recall
  • Manipulations - Conceptualization, active-working memory
  • Patterns - Conceptualization, recognition memory
  • Words - Language, conceptualization, verbal memory
  • Sentences - Language conceptualization
  • Images - Visual processing, visual retrieval memory
  • Logical processes - Reasoning skills, procedural skills
  • Estimating - Attention (ie, planning, previewing skills), nonverbal and verbal conceptualization
  • Concepts - Nonverbal and verbal conceptualization

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