While learning disabilities (LD) broadly encompass disorders in mathematics, it’s notable that difficulties specifically in math often receive less attention compared to reading disabilities. In educational settings, evaluations and special education services are frequently centered around reading challenges, sometimes overshadowing the equally significant needs of children with Learning Disability Mathematics. Even when a learning disability is identified, targeted assessment and intervention for arithmetic difficulties can be limited.
This disparity in focus might lead to a misconception that math learning problems are uncommon or less severe. However, statistics reveal a different picture. Approximately 6% of school-aged children experience significant deficits in mathematics. Among students diagnosed with learning disabilities, arithmetic difficulties are as prevalent as reading problems. This underscores that while not all reading disabilities co-occur with math learning problems, deficits in mathematics are widespread and demand comparable attention, concern, and effective educational strategies.
Ignoring or downplaying challenges in learning disability mathematics can have long-lasting consequences. The societal myth that being “bad at math” is acceptable is contradicted by the realities faced by adults with math learning disabilities. Years of struggling with math in school, culminating in math illiteracy in adulthood, can significantly impede daily living skills and limit vocational opportunities. In today’s increasingly quantitative world, proficiency in mathematical knowledge, reasoning, and skills is just as critical as reading ability for navigating personal and professional life.
Exploring the Spectrum of Math Learning Problems
Similar to reading disabilities, the severity of learning disability mathematics varies widely, ranging from mild to profound. Research also suggests that children exhibit diverse profiles of math disabilities. While classifications are still under investigation and require careful interpretation, it’s becoming increasingly clear that students encounter not only different intensities of math struggles but also distinct types of challenges. This necessitates varied instructional approaches, classroom accommodations, and sometimes, fundamentally different teaching methodologies to effectively address learning disability mathematics.
Mastering Basic Number Facts: Strategies for Support
A common hurdle for students with learning disability mathematics is the persistent difficulty in memorizing basic number facts across all four operations (addition, subtraction, multiplication, division). Despite understanding the underlying concepts and investing considerable effort, these students struggle to automatically recall that 5+7=12 or 4×6=24. Instead, they may rely on inefficient strategies like finger counting, drawing marks, or making scribbled circles, even over extended periods, seemingly unable to develop effective memory strategies independently.
For some students, this difficulty with basic facts may be their primary math learning challenge. In such cases, it’s crucial to avoid holding them back solely due to fact retrieval difficulties. Instead, a practical approach is to allow them to use a pocket-sized fact chart as a tool to access basic facts, enabling them to progress to more complex computation, applications, and problem-solving. As students demonstrate increased speed and accuracy in recalling a specific number fact, it can be removed from their personal chart. Addition and multiplication charts can also be adapted for subtraction and division, respectively. For quick reference, a portable chart is often more effective than an electronic calculator. Having the entire set of answers visible aids recall, and consistent location of answers on the chart can further enhance memory. To prevent over-reliance, mastered facts can be marked or blackened out on the chart, encouraging motivation to learn more. For students who struggle with locating answers at intersections on the chart, a cutout cardboard L-shape can be a helpful visual aid.
Several educational resources offer specific methods designed to facilitate the mastery of basic arithmetic facts for students with learning disability mathematics. These approaches are built on the fundamental assumption that students already possess a solid understanding of quantity concepts and operations. This implies that the student can demonstrate and explain the meaning of a math problem using objects or drawings. Effective teaching strategies often include:
- Interactive and Intensive Practice: Engaging practice sessions using motivational materials like games. Focus on attentiveness during practice is as crucial as the duration of practice itself.
- Distributed Practice: Short, frequent practice sessions are more effective than infrequent, long sessions. For example, two 15-minute sessions daily are preferable to a single hour-long session every other day.
- Small Fact Groupings: Introduce and focus on mastering a small number of facts at a time before moving to mixed groups.
- Emphasis on “Reverses” or “Turnarounds”: Practice fact pairs like 4+5 and 5+4, or 6×7 and 7×6 in vertical, horizontal, and oral formats to reinforce commutative properties.
- Student Self-Charting of Progress: Students track their mastered facts and remaining facts, promoting ownership and motivation.
- Instructional Strategies: Teaching thinking strategies to derive unknown facts from known facts. For example, using “doubles facts” (5+5, 6+6) to learn “double-plus-one” facts (5+6, 6+7).
(For detailed information on these thinking strategies, refer to Garnett, Frank & Fleischner, 1983, Thornton.1978; or Stern, 1987).
Arithmetic Weakness and Math Talent: Recognizing Divergent Profiles
It’s important to recognize that learning disability mathematics can manifest in diverse ways. Some students with LD may exhibit a strong grasp of mathematical concepts yet struggle with computational accuracy. They might be inconsistently reliable in paying attention to operational signs, borrowing or carrying correctly, and sequencing steps in multi-step calculations. Interestingly, these students might also experience difficulties mastering basic number facts.
Paradoxically, some students who struggle with computation in elementary grades, where accuracy is heavily emphasized, can excel in higher-level math courses in later grades when conceptual understanding becomes paramount. These students should not be confined to low-level secondary math classes where their computational inconsistencies are continually highlighted, while being denied access to advanced math where their conceptual strengths can flourish. Mathematics is far more than just accurate calculation. It’s crucial to assess the broader spectrum of math abilities and avoid judging intelligence or understanding solely based on weaker lower-level computational skills. A balanced approach when working with students with learning disability mathematics often involves:
- Acknowledging their computational weaknesses openly and honestly.
- Providing consistent and persistent support to strengthen these inconsistent skills.
- Collaborating with the student to develop self-monitoring strategies and compensatory techniques.
- Simultaneously providing access to a full and enriched math curriculum that goes beyond basic computation.
Bridging the Gap: Written Symbols and Concrete Materials
Many young children entering school with learning disability mathematics actually possess a solid foundation of informal mathematical understanding gained from everyday experiences. Their difficulties often arise when connecting this informal knowledge to the formal procedures, language, and symbolic notation of school mathematics. This transition can be likened to a musically inclined child encountering written music notation as something disconnected from their innate musical abilities. Mapping the abstract world of written math symbols onto the familiar world of quantities and actions, while simultaneously learning the specific language of arithmetic, is a complex undertaking. Students benefit significantly from repeated experiences and diverse concrete materials to solidify these connections.
Teachers can inadvertently exacerbate these difficulties by prematurely asking students to match pictures of groups with number sentences before they have adequate experience relating physical representations to math symbols and mathematical language. Concrete materials, which can be physically manipulated, grouped, and separated, offer a more tangible and vivid teaching tool compared to pictorial representations. Pictures are semi-abstract symbols and can be confusing if introduced too early, potentially disrupting the formation of connections between existing concepts, new math vocabulary, and written number problems.
Cuisenaire Rods
Structured concrete materials are beneficial for concept development across all grade levels and math topics when addressing learning disability mathematics. Research indicates that students who utilize concrete materials often develop more precise and comprehensive mental representations, exhibit increased motivation and engagement, gain a deeper understanding of mathematical ideas, and are better equipped to apply these concepts to real-world situations. Concrete materials have proven effective in developing concepts and clarifying early number relations, place value, computation, fractions, decimals, measurement, geometry, money, percentage, number bases, word problems, probability, statistics, and even algebra.
Different types of concrete materials are suited to different instructional purposes. It’s crucial to remember that materials alone do not teach; they are most effective when used in conjunction with teacher guidance, student interaction, and repeated demonstrations and explanations from both teachers and students.
Workbooks and worksheets filled with problems can sometimes reinforce confusion with written math notation. In these formats, students may focus on finding answers rather than demonstrating mathematical understanding. Students who struggle with ordering math symbols in conventional vertical, horizontal, and multi-step algorithms require extensive practice translating between different forms of representation. For example, teachers can provide solved addition problems and ask students to write the two related subtraction problems. Dictating problems (with or without answers) for students to translate into pictorial form, vertical notation, and horizontal notation can also be beneficial. Structuring worksheets with designated boxes for each representation format can provide helpful scaffolding.
Students can also work in pairs, translating solved problems into different verbal expressions. For instance, 20 x 56 = 1120 can be expressed as “twenty times fifty-six equals one thousand, one hundred and twenty” or “twenty multiplied by fifty-six is one thousand, one hundred twenty.” Another paired activity involves students using materials (e.g., bundled sticks for carrying problems) to demonstrate or “prove” solved problems presented on individual cards. To increase engagement, some cards can contain incorrectly solved problems, and the goal becomes identifying the “bad eggs.”
These suggestions aim to shift students away from viewing math solely as finding correct answers or giving up when challenged. They foster a mindset that connects understanding with symbolic representation and appropriate mathematical language.
The Language of Math: Addressing Verbal Processing Challenges
Some students with learning disability mathematics are significantly impacted by the language aspects of math. This can manifest as confusion with mathematical terminology, difficulty following verbal instructions, and/or weak verbal skills for monitoring the steps in complex calculations. Teachers can provide support by adjusting their verbal delivery: slowing down the pace, maintaining natural phrasing, and presenting information in smaller, discrete segments. This “chunking” of verbal information is particularly important when asking questions, giving directions, introducing concepts, and providing explanations.
Equally important is frequently prompting students to verbalize their mathematical thinking process. Too often, math instruction is dominated by teacher explanations or silent written practice. Students with language processing challenges benefit from demonstrating their understanding with concrete materials and explaining their actions at all grade levels and across all math topics, not just in early grades. Having students regularly take on the role of “teacher” can be both enjoyable and crucial for developing a deeper understanding of the complexities of math language. Furthermore, all students tend to achieve more complete understanding when they are required to explain, elaborate on, or justify their reasoning to others. The act of explaining often provides the necessary impetus to connect and integrate knowledge in meaningful ways.
Typically, children with language deficits may perceive math problems on a page as mere signals to perform an operation rather than as meaningful sentences requiring comprehension. It’s as if they actively avoid verbalizing their math processes. Both younger and older students need to cultivate the habit of reading or saying problems aloud before and/or after solving them. By consciously engaging in self-verbalization, they can better monitor attentional lapses and careless errors. Therefore, teachers should encourage these students to:
- Pause after arriving at each answer.
- Read aloud the problem and their answer.
- Listen to themselves and ask, “Does this make sense?”
For students with language weaknesses, establishing this habit may require repeated teacher modeling, patient reminders, and consistent practice, possibly utilizing a cue card as a visual prompt.
Visual-Spatial Aspects of Math: Supporting Students with Perceptual Challenges
A smaller subset of students with learning disability mathematics experience difficulties rooted in visual-spatial-motor organization. This can lead to weak or absent conceptual understanding, poor “number sense,” specific challenges with pictorial representations, and/or poorly controlled handwriting and disorganized arrangement of numerals and symbols on the page. Students with profound conceptual deficits often exhibit significant perceptual-motor difficulties, potentially indicative of right hemisphere dysfunction.
This specific subgroup may benefit significantly from a strong emphasis on precise and clear verbal descriptions. They seem to learn more effectively by substituting verbal constructs for the intuitive/spatial/relational understanding they lack. Pictorial examples or diagrammatic explanations can be particularly confusing and should be minimized or avoided when teaching or clarifying concepts. In fact, remediation for this subgroup should specifically target picture interpretation, diagram and graph reading, and nonverbal social cues. To foster understanding of math concepts, repeated use of concrete teaching materials (e.g., Stern blocks, Cuisenaire rods) is recommended, with careful attention to developing stable verbal descriptions for each quantity (e.g., “five”), relationship (e.g., “five is less than seven”), and operation (e.g., “5+2=7”). Since visual relationships and organization are challenging for these students, anchoring verbal constructions in repeated experiences with structured materials that can be physically manipulated and observed while being verbally described is crucial. For instance, they might learn to identify triangles more effectively by holding a triangular block and verbally stating, “A triangle has three sides. When drawn, it has three connected lines.” This verbal self-description can become a necessary tool for students with visual-spatial deficits to understand and internalize mathematical concepts.
The primary goal for these students is to build a robust verbal model for quantities and their relationships to compensate for the visual-spatial mental representations that most individuals develop naturally. Consistent and descriptive verbalizations are also essential for establishing when to apply math procedures and how to execute the steps of written computation. Developing these skills requires considerable patience and verbal repetition, with progress often occurring in small increments.
It is crucial to recognize that students of average, high average, and even very high intelligence can experience severe visual-spatial organization deficits that make developing fundamental math concepts extremely difficult. When these deficits are coupled with strong verbal abilities, there is a risk of underestimating the severity of the impairment. Parents and teachers might mistakenly attribute the difficulties to lack of effort, inattention, math phobia, or emotional problems. However, these math difficulties often coexist with challenges in body awareness in space, interpreting nonverbal social cues, and general disorganization. Misinterpreting these challenges as primarily emotional or behavioral can delay appropriate interventions in both mathematics and related areas.
In Summary: Addressing Learning Disability Mathematics for Enhanced Outcomes
Math learning difficulties are prevalent, significant, and deserve serious instructional attention in both general and special education settings. Repeated math failure can lead to student disengagement, decreased self-esteem, and avoidance behaviors. Furthermore, significant math deficits can negatively impact everyday life management and limit future career prospects.
Learning disability mathematics presents in various forms and severities. Common challenges include inefficient recall of basic arithmetic facts and inconsistent accuracy in written computation. When these computational difficulties are coupled with strong conceptual understanding, it’s vital to avoid solely focusing on computation remediation. While addressing computational skills is important, it should not restrict access to a comprehensive math education for otherwise capable students.
Language disabilities, even subtle ones, can impede math learning. Many students with LD tend to avoid verbalizing in math activities, a tendency often reinforced by typical math teaching approaches. Encouraging verbalization of math problems and procedures can significantly improve success in mainstream math settings.
Bridging the gap between informal math knowledge and formal school math is crucial for many children. This process requires time, experience, and carefully guided instruction. The use of structured concrete materials plays a vital role in solidifying these connections, not only in early elementary grades but also during concept development in higher-level math. Some students particularly benefit from explicit instruction in translating between different written forms, verbal expressions, and representations (objects or drawings) of mathematical concepts.
A less common but profoundly impactful form of learning disability mathematics stems from significant visual-spatial-motor disorganization. This can impair the development of foundational math concepts. Effective strategies include minimizing the use of pictures or graphics for concept delivery, emphasizing verbal explanations of math ideas, and utilizing concrete materials as anchors for understanding. The organizational and social challenges that often accompany this type of math disability also require ongoing and appropriate remedial attention to support successful adult life adjustment.
In conclusion, as educators, particularly special educators, there is a significant opportunity and responsibility to provide greater attention and more effective interventions for learning disability mathematics than has been traditionally offered. By understanding the diverse nature of these challenges and implementing appropriate strategies, we can empower students with learning disability mathematics to achieve their full potential.
