Difficulties in learning math seldom lead to referrals for learning disabilities evaluation, despite being specified in both federal and state LD definitions. School systems provide assessment and special services mostly on the basis of difficulties learning to read (dyslexia). So perhaps math difficulties are uncommon, not particularly serious, or maybe they don’t impact adult functioning significantly?
Wrong, on all counts.
Contrary to the widespread neglect of math learning disabilities among children identified as LD, math dilemmas are common. Of course, there are LD students who excel in math. Interestingly, those with strong underlying math potential may stumble in the elementary years, but then soar once they enter higher realms of mathematics (after the language-heavy branch known as arithmetic).
Severe math disabilities exist across ability and achievement levels, even among strong readers successful in other areas—many not identified as LD.
Tragically, these are largely ignored until later years, by which time they have exacted a terrible toll. Despite the commonplace, “I-was-terrible-in-math-ha-ha,” adults with serious math difficulties cite painful effects on their professional, practical, and emotional lives.
Sadly, neglect of math disabilities is reflected in teacher preparation. Both special educators and math teachers exit their preparation programs with little understanding of LD students’ math needs—and no clue about students with severe math disabilities. The status quo, over decades now, remains: Even when math learning disabilities are noticed, there is little expertise to deal with them.
Profiles of Math LD
Students with LD affecting math experience differing intensities and kinds of difficulty. The profiles below reflect the different foundational math needs of two broad subgroups. Some students fit one profile, some the other (to mild, moderate or severe degrees), while others present with mixed profiles.
Profile 1: Language-Based LD “Glitches”
Students with language-based LD commonly have difficulties with elementary arithmetic procedures and basic facts, along with their reading/writing problems. Their struggles are not from serious math weakness, but are related to underlying language-based disabilities that affect verbal memory, procedural learning, sequential processing, and/or cognitive slippage, and sometimes distractibility and impulsivity.
Teachers assume these students’ basic counting skills are intact, when often they are not. Math learners must become adept at a range of counting skills: counting-on, counting-back, counting-by, counting-on-by, and swinging with easy up-ten or back-ten from any number, to name a few. Such counting gymnastics comprise early “mental math” and reflect foundational understanding of the number system. Exercising counting arouses delight in young learners, tickling that sense of “I can” and promoting flexible math thinking.
While a foundational need for many LD youngsters, agility with the count/number system does not encompass all the arithmetic “glitches” they experience, which commonly include slow/inaccurate “basic facts,” unreliable computing procedures, bedevilment with “careless” errors, and confusion from their teachers’ math-language. All of these require sorting out and attentive, creative compensation.
Profile 2: Severe Math LD
A smaller LD math subgroup experiences spatially based math difficulties, often, though not always, accompanied by weaknesses in writing, interpreting graphs/maps/graphic organizers, along with some social misperception, and navigation confusion.
Students with “severe math-disability” or dyscalculia may (or may not) display neurological deficits and can demonstrate tremendous academic strength and talent, commonly in verbal areas, making it hard for the unskilled observer to catch the seriousness of their math needs.
Math conceptual understanding is grounded in spatial relations. For some learners, this spatial underpinning is underdeveloped or dysfunctional, resulting in their not “getting it” when math teaching attempts to connect with their underlying spatial-numerical substructure.
These students need to be guided back to vivid physical representations, constructing the foundation anew and relying on their relatively well-developed language in the process. Even though they may seem too old or too smart for this basic instruction, the key to securing a math foothold is returning to physical-numerical concrete representations (things), firmly connecting these to verbal representations (words) and to written symbols (numerals), and then linking these to actions on the number line (our number system).
All children benefit from concrete math materials; these students require them. The teacher models combining, separating, feeling/noticing, and comparing, while narrating their actions/thoughts aloud, followed by the student’s show and tell.
This basic work proceeds, usually slowly, to connecting actions-and-words with concrete materials to written numerals, the number system (counting, number lines, and number grids), and then written algorithms. Students with severe math disabilities require highly concrete, language-intensified instruction, tailored to their particular needs.
As youngsters lose their mathematical footing, not only do they lag behind classmates, they also learn lessons that are often hard to unlearn: “My brain doesn’t work.” “Effort doesn’t pay.” “I can’t do this.”
Kids that need to “go back” to math basics are sensitive to putdowns and often raise barriers to learning. They may dig in their heels (resisting to tread where they’ve already fallen), derail instruction, or quickly give up.
Such self-protective moves require skilled handling and use of the powerful tools of charting and feedback.
Charting shows real progress, even in small steps, and is a potent motivator. Charting math progress makes it visible, providing evidence that the effort is worth it.
Feedback—descriptive acknowledgment—provides support. Specific descriptive feedback captures attention, confirms the step-just-taken (i.e., teaches), and invites the child to congratulate him/herself: “Yes, I did do that, and you noticed!” Unfortunately, we fall easily into empty praise (“Good! Good! Excellent!”). Such generic hoopla does not teach (point towards, focus, underscore, reinforce), and eventually backfires as our smart youngsters learn not to believe it. On the other hand, skillful acknowledgment, descriptive feedback that points, is one of our most powerful teaching tools, fueling a child’s courage to take the next math step.
Kate Garnett is a professor in the Department of Special Education, Hunter College, CUNY and a well-known expert on math learning disabilities.