What is Dyscalculia?
Mathematics is the major area of difficulty for many youngsters with Learning disabilities. Learning disabilities in mathematics may be classified in at least three different groupings.
One of these groups is characterized by an overall deficiency in mathematics such that progress is slow and labored, but steady.
A second group displays deficiencies in specific mathematics topics such as fractions, or within a subtopic such as division.
A third group is characterized by comprehensive disorders of thinking, reasoning and problem solving such that performance in both concepts and skills in mathematics is bizarre, distorted and illogical. A severe mathematics learning disability and related conceptual disturbances in learning quantitative elements are sometimes referred to as dyscalculia.
Dyscalculia has a medical connotation suggesting a central nervous system involvement. McLeod and Crump (1978) found that about one half of students with learning disabilities require supplemental work in mathematics, although only ten percent were seriously deficient in mathematics. According to Bliss (2000), “mathematics learning disabilities do not often occur with clarity and simplicity. Rather they can be combination of difficulties which may include language processing problems, visual spatial confusion, memory and sequence difficulties and or unusually high anxiety.”
How Common is Dyscalculia?
Between 3 and 8% of schoolaged children show persistent gradetograde difficulties in learning some aspects of number concepts, counting, arithmetic, or in related math areas.^{1,7} These and other studies indicate that these learning disabilities, or dyscalculia, are not related to intelligence, motivation or other factors that might influence learning. The finding that 3 to 8% of children have dyscalculia is misleading in some respects. This is because most of these children have specific deficits in one or a few areas, but often perform at grade level or better in other areas. About half of these children are also delayed in learning to read or have a reading disability, and many have attention deficit disorder.^{8}
Common Features of Dyscalculia
Some general conclusions can be made about the basic number, counting and arithmetic skills of children with dyscalculia. As stated, screening measures that predict which preschool children will have these problems in school are not yet available. However, as stated, it is likely that preschoolers who do not know basic number names, quantities associated with small numbers (< 4), how to count small sets of objects, or do not understand simple addition and subtraction are at risk.^{5}
Research Context and Recent Research Results
Number
In first grade, children with dyscalculia often do not know basic number names (e.g. “9” = “nine”), and have difficulty discriminating which number is larger or smaller. They will typically know that 3 is more than 2, but not know that 9 is more than 8. However, many of these children catch up in these areas of number understanding, at least for simple numbers.
Counting
Learning the basic counting sequence, "one, two, three and four …" is not difficult; almost all children learn this sequence, including most children with dyscalculia. What is important is that children learn the basic rules that underlie the ability to count effectively.
Children’s understanding of these rules emerges during the preschool years, but they also must come to understand that counting can be done correctly in ways that differ from the typical. For instance, children will often observe adults counting from lefttoright and counting each item in order. As a result, many children come to believe that you must count in exactly this way. By second grade, most children understand that counting is more flexible, but for children with dyscalculia this understanding is delayed by one or two years.
Arithmetic
The basic arithmetic skills of children with dyscalculia have been extensively studied.^{3, 6} These studies, which have focused on how children solve simple arithmetic problems (e.g. 4 + 5 =?), such as finger counting or remembering the answer, have revealed several very consistent patterns:
First, many children with dyscalculia have difficulties remembering basic arithmetic facts, such as the answers to 5+3.^{6} It is not that these children do not remember any arithmetic facts, but rather that they cannot remember as many facts as other children do and appear to forget facts rather quickly. Second, many of these children use immature problemsolving strategies. For example, they rely on finger counting for more years than other children, and they make more mistakes when counting.^{3}
In Conclusion
Between 3 and 8% of schoolaged children will show evidence of dyscalculia. The early signs of this form of disability include a poor understanding of number magnitude (e.g. that 8 < 9), a rigid understanding of counting, and use of immature strategies during problemsolving. One of the most common and longterm problems is difficulty remembering basic arithmetic facts (e.g. 4+2 = “6”). These children are likely to be at risk for development of math anxiety, which will lead to avoidance of mathematics and make the acquisition of basic skills in this area even more difficult.
References

Badian NA. Dyscalculia and nonverbal disorders of learning. In: Myklebust HR, ed. Progress in learning disabilities. Vol 5. New York, NY: Grune & Stratton; 1983:235264.

Geary DC. Children's mathematical development: research and practical applications. Washington, DC: American Psychological Association; 1994.

Geary DC. Mathematics and learning disabilities. Journal of LearningDisabilities 2004;37(1):415.

Geary DC. Development of mathematical understanding. In: Kuhl D, Siegler RS, eds. Cognition, perception, and language. New York, NY: John Wiley and Sons. Damon W, ed. Handbook of child psychology. 6^{th} ed; vol 2. In press.

Gersten R, Jordan NC, Flojo JR. Early identification and interventions for students with mathematics difficulties. Journal of Learning Disabilities 2005;38(4):293304.

Jordan NC, Hanich LB, Kaplan D. Arithmetic fact mastery in young children: A longitudinal investigation.Journal of Experimental Child Psychology 2003;85(2):103119.

Kosc L. Developmental dyscalculia. Journal of Learning Disabilities 1974;7(3):164177.

Shalev RS, Manor O, GrossTsur V. The acquisition of arithmetic in normal children: Assessment by a cognitive model of dyscalculia. Developmental Medicine and Child Neurology 1993;35(7):593601.