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Pediatrics: Developmental and Behavioral > MEDICAL TOPICS
Learning Disorder: Mathematics
Article Last Updated: Jun 5, 2006
AUTHOR AND EDITOR INFORMATION
Section 1 of 9  
Author: Vidhu V Thaker, MB, BCh, MD, Instructor in Pediatrics, Albert Einstein College of Medicine; Consulting Staff, Department of Pediatrics, Jacobi Medical Center
Vidhu V Thaker is a member of the following medical societies: American Academy of Pediatrics
Editors: Angelo P Giardino, MD, PhD, Clinical Associate Professor, Department of Pediatrics, Baylor College of Medicine; Medical Director, Texas Children's Health Plan, Inc; Mary L Windle, PharmD, Adjunct Assistant Professor, University of Nebraska Medical Center College of Pharmacy, Pharmacy Editor, eMedicine.com, Inc; Carrie Sylvester, MD, MPH, Director of Education in Child and Adolescent Psychiatry, Professor, Departments of Psychiatry and Pediatrics, Northwestern University Medical School; Caroly Pataki, MD, Professor of Clinical Psychiatry, Department of Psychiatry and Biobehavioral Sciences, Division Chair of Child and Adolescent Psychiatry, Director of Training, Child and Adolescent Psychiatry Residency Program, University of Southern California Keck School of Medicine
Author and Editor Disclosure
Synonyms and related keywords:
mathematic learning disorder, MD, reading disorder, RD, learning disability, cognitive development, linguistic development, perceptual disabilities, brain injury, dyslexia, developmental aphasia
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) is a disorder in one or more of the basic psychological processes involved in understanding or in using language (spoken or written), which may manifest as an imperfect ability to perform mathematical calculations or to listen, think, speak, read, write, or spell. The term includes such conditions as perceptual disabilities, brain injury, dyslexia, and developmental aphasia. MD 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." Although this definition has raised several questions, it remains important in current clinical practice. MD is among the disabilities that qualify children for special education programs under IDEA.
Frequency
United States
Assessing the exact incidence of MD 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 and/or learning disorder. RDs comprise a large portion of this group. An estimated 6.4% of elementary school children have been recognized with MD. However, children often have more than 1 disorder; 56% of children with RD also showed poor mathematics achievement, and 43% of children with MD 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.
MD incidence among American children is higher than in Japanese, German, or French children. This higher incidence may be linked to the instructional course design.
History
Children with learning disorders typically present at primary school age or later. Often, mathematical learning disorder (MD) is associated with RD, although MD is noticed later because of language's permeating influence in everyday life. MD often goes unrecognized until the child begins schooling.
Causes
A multitude of developmental pathways converge when children strive to comprehend and apply mathematics in school. Over time, the demands of the mathematics curriculum impose increasing strain on a developing and differentiating nervous system. Levine and associates' 16-subcomponent model helps clarify the causes of problems performing mathematics and helps evaluate MD. Subcomponents of the model include the following:
- 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 also should 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 process words slowly 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 also must 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 also are 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 rely excessively 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 frequently are 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
Learning Disorder: Reading
Other Problems to be Considered
Mathematical learning disorder may be associated with other neurodevelopmental or neuropsychological abnormalities; recognizing and simultaneously treating these disorders is as important as treating the principal disability.
Procedures
- Tests and other assessment strategies: Mathematics assessments play a valuable role in identifying students' strengths and weaknesses and in developing and monitoring instructional practices. The following assessment strategies are the most popular in use today:
- Portfolios: The term portfolio refers to collections of students' work that exhibit their efforts, progress, and achievements in single or multiple subjects. In mathematics assessment, a portfolio can be a useful tool to monitor student learning and the effectiveness of instructional programs. In assembling a portfolio, it is important to ensure that content a valid representation of curricular goals, content is collected within a time frame, and content represents a variety of situations. Documented analysis of the student's portfolio that incorporates the following points can be used to monitor student progress on a regular basis:
- Answer correct or incorrect
- Computational skills demonstrated or lacking
- Reading errors that may have contributed to the incorrect solution
- Syntactical errors made
- Strategy used to solve problem
- Visual aids (eg, pictures, graphs) used
- Criterion-referenced test results demonstrate student knowledge of specific content that is unrelated to peer performance. These tests present a sufficient number of items to measure various aspects of mathematics skills. The tests are conducted within a specified time period (usually 1.5 times that of an average child's performance time) to identify specific skill deficiencies.
- Curriculum-based measurement (CBM) is a validated version of curriculum-based assessment. CBM involves ongoing measurement of a student's actual performance in comparison to the school curriculum's planned outcomes. Because CBM uses the school's curriculum as a basis for comparison, CBM provides great help to teachers on a daily basis by evaluating each student's learning rates, by determining what instruction is needed, and by ascertaining the effectiveness of interventions with individual students.
- Calculation error analysis, using structured interviews and checklists/rating scales, is an efficient way to identify a student's calculation strategies. Checklists and/or rating scales can be used to note strategies used during the interview or strategies observed while the student performs a calculation. Checklists can be dichotomous (yes/no) responses or can use Likert scale (ie, sliding scales ranging from never to always). One approach is for the interviewer to give a student a problem and then ask the student to "think out loud" while working on the solution.
- Observations provide valuable data, which should be combined with data accumulated via other strategies to assess the overall effectiveness of instructional efforts. Within the instructional context, teachers continually make informal judgments about student progress.
- Student perceptions: Gathering information about a student's motivation and confidence level during an instructional activity sometimes proves helpful. Students may respond to a brief survey of questions about their confidence level and any difficulties they encounter.
Medical Care
Management of mathematics disability Mathematical learning disorder (MD) management should begin early in a child's educational career. Unfortunately, MD usually is not recognized early enough or management is delayed until other problems (eg, language disabilities) are addressed. Many children perceive mathematics as a subject confined strictly to mathematics class and homework. Early remediation of MD is crucial to ensure the child's recognition of mathematics' significance not just in the classroom but also in everyday life. Remediation demands close collaboration between regular classroom teachers and those involved in remedial support. Many children with underachievement in mathematics are eligible for legally mandated special education services in public schools. Wide differences exist in service eligibility requirements, and the quality and intensity of services vary markedly between communities. General remediation guidelines follow:
- Underdeveloped subcomponents
- Intervening at the level of the individual subcomponents is essential (see Causes).
- A tutor, a regular or resource classroom teacher, and, under certain circumstances, a parent can help the student work on the specific underdeveloped subcomponent. The concept is for the child to work more on the underdeveloped subcomponent than on getting the correct answer. (Examples include supervised practice for a student with poor pattern recognition, designed to review word problems and to identify the key words or patterns that suggest a particular procedure. In another example, a child whose automatic recall of mathematics facts is delayed should practice recalling facts under timed conditions.)
- Whenever possible, exploit a child's developmental strengths and subject area affinities. A good visualizer should study correctly solved problems and make use of diagrams and other graphic material. A highly verbal child should learn mathematics by trying to teach the subject. In some instances, use of educational software can facilitate learning at the level of the deficient subcomponent.
- Bypass techniques
- Within regular classroom settings, an often desirable teaching method is to circumvent the deficient mathematical task component. This bypass technique enables a child to learn mathematics despite the presence of a deficient subcomponent. Examples include allowing students who are weak at recalling mathematical facts to use calculators when solving word problems.
- Time may be used as another bypass strategy. Students with delayed automatization may take an extremely long time to finish a problem. The bypass strategy for these students may consist of giving them more time to complete the problems or expecting them to solve fewer problems.
- Teaching real-life mathematics
- Children who have too many deficient components or who have deficient curricular abilities require consistently innovative teaching methods.
- Sameness analysis and real-life situations are examples of innovative methods that enable children to learn basic mathematics techniques.
- Management of neurodevelopmental dysfunctions
- Mathematics performance may be impaired by other neurodevelopmental dysfunctions (eg, ADHD, language disabilities). Treating these respective problems may greatly enhance mathematics skills.
- Selected modes of cognitive training may help improve concept formation, problem solving skill, and, most importantly, memory.
- Improving curriculum
- Research has revealed that, on average, poor mathematics performance in the US may be linked to a deficient curriculum in comparison to curricula used in other nations.
- In-depth analysis of the curriculum, together with incorporation of various suggested new changes, might improve overall national performance in mathematics.
Consultations
- Neurodevelopmental or neuropsychological testing can yield valuable information about the underlying dysfunctions that may impede mathematical learning. These dysfunctions include the following:
- Attention deficits
- Visual-spatial weaknesses
- Language disabilities
- Memory problems
- Poor sequential organization
- An education diagnostician or psychoeducational specialist should examine all areas of academic performance. Educational testing of a child with mathematics underachievement should be performed on a 1-to-1 basis. Other academic difficulties (eg, spelling, writing) often lead to mathematics underachievement.
- Evaluation of a child's mathematics performance should be calibrated specifically to that child's age and grade level. Identification of specific developmental subcomponents may have significant implications for remediation efforts. Include the following parameters in a standard examination:
- Speed and accuracy of factual recall
- Appreciation of quantity (ie, quantity in relation to number concepts)
- Recall and appreciation of algorithms
- Ability to interpret and solve word problems
- Level of concept mastery
- Quality of attention to detail
- Work pace
- Child's affect
- Student's approach to problem solving
- Extent of automatization
Prognosis
- Individuals With Disabilities Education Act (IDEA)
Originally approved by the US Congress in 1975, and subsequently amended in 1997, IDEA is an attempt to remedy problems that contribute to the barriers faced by children with disabilities. IDEA aims to strengthen academic expectations of, and accountability for, the United States' 5.4 million children with disabilities and to bridge the too common gap between the regular school curriculum and what these children learn. IDEA strives to effect changes with the following goals: - To raise expectations for children with disabilities: Each individualized education program (IEP) must relate more clearly to the general curriculum designed for children in regular classrooms. IEPs are plans enumerating educational goals for individual children and the education-related services each is to receive.
- To increase parental involvement: IDEA's goal is to increase parental involvement in the education of children with disabilities. Parents in all states must now be included in groups that make eligibility and placement decisions about children with disabilities. Previously, in some states, parents had the right to be included only in IEP meetings. Parents now have a right to consent to periodic reevaluations of their child's programs and the initial evaluations. IDEA also requires regular progress reports to parents.
- To ensure regular education teachers' involvement: IDEA requires the involvement of regular education teachers in planning and assessing children's progress.
- To include children with disabilities in educational plans: IDEA strives to add children with disabilities to school measurements of children without disabilities in state and district assessments and in setting and reporting school performance goals.
- To support quality professional development: Professional development initiatives to inform educators about advancements in research benefit all personnel involved in educating children with disabilities.
With passage of the 1997 IDEA amendments, the US government acknowledged that: "Disability is a natural part of the human experience and in no way diminishes the right of individuals to participate in or contribute to society. Improving educational results for children with disabilities is an essential element of our national policy of ensuring equality of opportunity, full participation, independent living, and economic self-sufficiency for individuals with disabilities." - Prior to the implementation of IDEA in 1975, approximately 1 million children with disabilities were shut out of schools and hundreds of thousands more were denied appropriate services. Since then, IDEA has changed the lives of children with disabilities.
- Many children now learn and achieve at levels previously thought impossible. As a result, and in unprecedented numbers, these children are graduating from high school, going to college, and entering the workforce as productive citizens.
- In the past, as many as 90% of children with serious developmental disabilities were housed in state institutions. Today, 3 times as many young people with disabilities are enrolled in colleges or universities; twice as many 20-year-olds with disabilities are working.
- While significant progress has occurred, the status of children with disabilities still falls short of expectations. The following facts reflect this status:
- Twice as many children with disabilities drop out of school, compared to children without disabilities.
- Dropouts do not return to school, have difficulty finding jobs, and often end up in the criminal justice system.
- Girls who drop out often become young unwed mothers at a much higher rate than their peers without disabilities.
- Many children with disabilities are excluded from the curriculum and from assessments used with classmates without disabilities, actions that limit their possibilities of excelling and achieving higher standards of performance.
- The 1997 IDEA legislation attempts to remedy these and other problems that contribute to the barriers faced by children with disabilities. IDEA aims to strengthen academic expectations and accountability for the United States' 5.4 million children with disabilities and to bridge the gap that too often has existed between the regular curriculum and what these children learn. IDEA strives to effect changes based on the following premises:
- Raising expectations for children with disabilities is important.
- Parental involvement in the education of their children (by teachers making regular progress reports to parents) and inclusion of parents in groups making eligibility and placement decisions about children with disabilities should be increased. Previously, parents in some states only had a right to be included in IEP meetings. Parents also have a right to consent to periodic reevaluations of their child's program, in addition to initial evaluations.
- Regular education teachers should be involved in planning and assessing children's progress. Ensuring that the IEP relates more clearly to the general curriculum that children in regular classrooms receive also is important.
- Including children with disabilities in assessments, performance goals, and reports to the public is necessary.
- Quality professional development for all personnel involved in educating children with disabilities should be supported. Professional development initiatives help teachers benefit from advancements in research.
Patient Education
- The following nonprofit organizations provide information, referrals to professionals, and contacts to local groups:
- Failure to educate and provide awareness of IDEA and its provisions has implications similar to that of depriving a patient of appropriate medical or surgical therapy.
- Failure to refer a suspected case of learning disability to appropriate agencies for evaluation and then appropriate placement in an IEP, considered the therapy for disabilities, may constitute malpractice.
Special Concerns:
- Many students who underachieve in mathematics perceive the subject as hostile and perpetually threatening. Because parents and teachers seriously value mathematics performance, students who underachieve in mathematics must not develop an adversarial relationship with the subject. To prevent such intimidation, students should not be publicly humiliated for their performance.
- Students with mathematic learning disorder (MD) should not be required to answer questions in class.
- Teachers must not have other students correct, or even see, papers of students with MD.
- At home, parents must be aware of the profound feelings of sadness that can overcome a child who is having trouble learning mathematics. Parents must be supportive and as nonjudgmental as possible.
- Teachers and parents should collaborate to make mathematics fun whenever possible. The use of games and rewards sometimes may facilitate this effort.
- All children with mathematics difficulties require demystification. They should understand the reasons for MD. The strengths of these students should be supported. They should be told that mathematics is but 1 of many forms of intelligence and reassured that they are competent individuals.
- At the same time, students with MD must sustain a degree of optimism toward the subject, while perceiving mathematics as a challenge. Encourage students to foresee a reasonable level of proficiency as an attainable goal.
- AACAP. Practice parameters for the assessment and treatment of children and adolescents with language and learning disorders. AACAP. J Am Acad Child Adolesc Psychiatry. Oct 1998;37(10 Suppl):46S-62S. [Medline].
- Badian NA. Dyscalculia and nonverbal disorders of learning. In: Myklebust HR, ed. Progress in learning disabilities. Vol 5. New York, NY: Stratton;235-64.
- Brainerd CJ. Young children's mental arithmetic errors: A working memory analysis. Child Dev. 1983;812-16.
- Bryant BR, Rivera DP. Educational assessment of mathematics skills and abilities. J Learn Disabil. Jan-Feb 1997;30(1):57-68. [Medline].
- Carnine D. Instructional design in mathematics for students with learning disabilities. J Learn Disabil. Mar-Apr 1997;30(2):130-41. [Medline].
- Challinor J, Moore IK, Kramer R, et al. Development and testing of the School Competency Assessment Scale. J Pediatr Oncol Nurs. Mar-Apr 2003;20(2):56-64. [Medline].
- Earp NW, Tanner FW. Mathematics and Language. Arithmetic Teacher. 1980;28:32-38.
- Engelmann S, Carnine D, Steely DG. Making connections in mathematics. J Learn Disabil. May 1991;24(5):292-303. [Medline].
- Geary DC. Mathematical disabilities: cognitive, neuropsychological, and genetic components. Psychol Bull. Sep 1993;114(2):345-62. [Medline].
- Goldman SR, Hasselbring TS. Achieving meaningful mathematics literacy for students with learning disabilities. Cognition and Technology Group at Vanderbilt. J Learn Disabil. Mar-Apr 1997;30(2):198-208. [Medline].
- Hallahan DP, Kauffman JM. Exceptional learners: Introduction to Special Education. 7th ed. Boston: Allyn & Bacon;1997.
- Hammill DD, Bryant BR. Standardized assessment and academic intervention. In: Swanson HL, ed. Handbook on the Assessment of Learning Disabilities: Theory, Research and Practice. Pro Ed;1991:373-406.
- IDEA '97 page. Office of Special Education Programs Web site. Available at: http://www.ed.gov/offices/OSERS/IDEA/regs.html. Accessed 2000. [Full Text].
- Kosc L. Developmental dyscalculia. J Learn Disabil. 1974;7:46.
- LD Online. Available at: http://www.ldonline.org/. Accessed February 23, 2006. [Full Text].
- Levine MD, Lindsay RL, Reed MS. The wrath of math. Deficiencies of mathematical mastery in the school child. Pediatr Clin North Am. Jun 1992;39(3):525-36. [Medline].
- Levine MD. Developmental Variations and Learning Disabilities. Cambridge MA, Educators Pub. 1987.
- Patton JR, Cronin ME, Bassett DS, Koppel AE. A life skills approach to mathematics instruction: preparing students with learning disabilities for the real-life math demands of adulthood. J Learn Disabil. Mar-Apr 1997;30(2):178-87. [Medline].
- Rivera DP. Mathematics education and students with learning disabilities: introduction to the special series. J Learn Disabil. Jan-Feb 1997;30(1):2-19, 68. [Medline].
- US Department of Education. Seventeenth Annual Report to Congress on the Implementation of the Individuals With Disabilities Education Act. Washington DC: US office of Special Education Programs;1995.
- Yell ML, Shriner JG. The IDEA amendments of 1997: Implications for special and general education teachers, administrators, and teacher trainers. 1997;30:1-20.
Learning Disorder: Mathematics excerpt Article Last Updated: Jun 5, 2006
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