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Math LD: Identifying Basic Number Processing Difficulties

Math Learning Disability – DyscalculiaMany elementary and middle school students find math challenging, but an estimated 5 to 9% experience difficulties severe enough to be categorized as having a mathematical learning disability (MLD). An emerging consensus, at least among researchers, is that such students must exhibit comparatively poor performance on a standardized mathematics achievement test (at or below the 10th percentile) over at least a successive two-year period to be properly identified as having MLD (also known as dyscalculia). As a consequence, children who meet such criteria are typically not identified prior to first grade. And while research in this field is at least 10 years behind research on reading disabilities, progress is being made in:

  • Screening children at risk for developing MLD.
  • Identifying the neurocognitive mechanisms that contribute to their poor performance, and
  • Designing remedial techniques to strengthen basic numerical and arithmetic skills.

Let’s consider what researchers are discovering about some of the most basic foundations of numerical thinking. Children with MLD often lack fluency in translating numerical information from one notational form to another. This process, called “transcoding,” takes place when, for example, a student is asked to write down the Arabic numeral “7” upon hearing the spoken word “seven.” Third- and fourth-graders who don’t have MLD take relatively little time to mentally convert a spoken number word to an Arabic numeral before starting to write it down. Furthermore, they need no additional time to do so for larger single-digit numbers (8, 9) than smaller ones (1, 2). In contrast, their peers with MLD not only need more time to make such mental conversions, but also take increasingly longer to do so the larger the number. Rather than automatically retrieving the correct quantity from long-term memory, they figure it out by moving from left to right along a “mental number line” until they reach the correct value.

Another problem students with MLD experience at this basic level of numerical thinking is in quickly naming the number of randomly arrayed dots in small subsets, known as “subitizing.” Building on some of my own research findings, others have verified that while most third- and fourth- graders successfully accomplish this for up to four dots before having to count, many children with MLD can do so only up to three dots (and sometimes just two).

Finally, when asked to make comparative judgments of relative quantities of randomly arrayed colored dots too numerous to subitize and presented too briefly to count (e.g., “Are there more blue dots or more yellow dots?”), children with MLD make more errors than their peers without MLD. More importantly, researchers at Baltimore’s Kennedy Krieger Institute and Johns Hopkins University have shown that the accuracy with which children make such approximate judgments correlates with their performance on standardized math tests.

Taken together, these findings illustrate that in making even the most basic exact and approximate judgments, elementary school children with MLD find themselves lagging behind their peers. As school math builds upon these foundational skills, moving on to increasingly complex math problems will prove to be even more difficult if these children don’t become fluent in such skills.

Fortunately, help is available for children with the math difficulties I've described here. In my next blog post [to be featured on May 17th] I'll explain how researchers, teachers, and parents can make a positive difference.

Additional Resources


Dr. Daniel B. Berch, is Professor of Special Education and Applied Developmental Science and Senior Advisor to the Dean at the University of Virginia's Curry School of Education. He has authored various articles and book chapters on mathematical learning disabilities, and is senior editor of the book,

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