Math disabilities are notoriously difficult to specifically diagnose because math processing and problem solving often require the cooperation of many cognitive abilities. Our understanding of the biological basis of developmental dyscalculias greatly lags the dyslexias, but this latest review by Dehaene and his colleagues is a step in the right direction.
The figure below shows three candidate locations for different subtypes of dyscalculia. I can add a little personal knowledge to this discussion too, because I have a deficits in both "number sense" and "multiplication facts" retrieval. My visual perception of number is absolutely fine, however.
A math disability can be absolutely mind-boggling to a person doesn't have one. How is it possible that I still count on fingers, but managed to graduate from Harvard and place out of math because of getting a 5 on the AP Calculus exam? Answer: the brain has main opportunities to compensate. In my case, I struggled in my early elementary school years (if nobody knows how to specifically diagnose math disabilities, you can bet that few teachers or parents know how to customize teaching for them), but eventually got along pretty well by brute force of memorization, reasoning, and of course finger counting.
Poor performances in math also commonly occur for other reasons such as dysgraphia, limitations in attention or working memory, problems in rote, visual, spatial, or sequential memory, and inadequate or other types of poor teaching. Students with mild visual or auditory problems may overload when too much information is presented at once; and uni-taskers struggle for the same reason when spatial and verbal aspects of math become more complex.
Often math interventions require a combination of accommodations (scribing, work with a printed example of math facts chart in view), one-on-one tutoring, and more time. An error log can be helpful getting students to recognize the patterns of their errors, and the need to check and double-check answers if a problem-solving approach has been mislearned or forgotten, or faulty execution is to blame wrong results.
Developmental Dyscalculia Review 2007 pdf
Math Disabilities at SchwabLearning
Common Math Mistakes
Dyscalculia at MislabeledChild.com
Problem solving strategies in math at About.com
Eide Neurolearning Blog: Dyscalculia & Two Brain Pathways for Math
Eide Neurolearning Blog: East meets West: Fundamental Differences in Math Teaching
Eide Neurolearning Blog: Math Software Resources for Dyslexia & Dysgraphia
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