Math Learning Disability, often termed dyscalculia, is a specific learning disorder that affects an individual’s ability to understand and work with numbers. While learning disabilities in reading often receive significant attention and resources in educational settings, difficulties in mathematics are frequently overlooked. Despite being explicitly included under the umbrella of Learning Disabilities, math learning disabilities often lead to fewer referrals for evaluation and subsequently, less targeted support within school systems. In fact, special education services are sometimes disproportionately focused on reading disabilities, overshadowing the critical needs of students struggling with math. Even when identified as learning disabled, a smaller proportion of children receive comprehensive assessment and intervention specifically designed to address their arithmetic challenges.
This relative lack of focus can mistakenly lead parents and educators to underestimate the prevalence and severity of math learning problems. However, the reality is that approximately 6% of school-age children grapple with significant math deficits. Among students already classified as learning disabled, arithmetic difficulties are just as common as reading problems. This does not imply that all students with reading disabilities also have math learning disabilities, but it underscores the widespread nature of math deficits and the urgent need for comparable attention, concern, and effective interventions.
The societal notion that it’s acceptable to be “bad at math” is a harmful myth, particularly when considering the long-term implications for adults with math learning disabilities. Years of academic struggle in mathematics, coupled with adult math illiteracy, can severely impact daily living skills and limit vocational opportunities. In today’s increasingly complex and data-driven world, mathematical knowledge, reasoning, and skills are unequivocally as vital as reading ability for navigating life and career paths successfully.
Different Types of Math Learning Problems
Similar to reading disabilities, math learning difficulties manifest across a spectrum, ranging from mild to severe. Research also indicates that children experience diverse types of disabilities in math. While the classification of these different types is still evolving and requires further validation, it’s evident that students face not only varying degrees of math challenges but also qualitatively different kinds of difficulties. This diversity necessitates tailored classroom approaches, adaptations, and sometimes, fundamentally different teaching methodologies to effectively address the specific nature of each student’s math learning disability.
Mastering Basic Number Facts: A Foundational Hurdle
A common struggle for students with math learning disabilities is the persistent difficulty in “memorizing” basic number facts across all four operations (addition, subtraction, multiplication, division). This occurs despite possessing adequate conceptual understanding and significant effort invested in memorization. Instead of automatically recalling that 5+7=12 or 4×6=24, these children may continue to rely on laborious counting methods, such as using fingers, pencil marks, or drawn circles, even after years of practice. They often appear unable to independently develop efficient memory strategies for basic facts.
For some students, this struggle with basic facts may be their primary math learning difficulty. In such cases, it is crucial to avoid holding them back academically solely because they haven’t mastered their facts. Instead, a more effective approach is to allow them to use a portable facts chart as a tool to access basic facts, enabling them to progress to more complex computation, applications, and problem-solving tasks. As students demonstrate increasing speed and accuracy in recalling specific number facts, those facts can be gradually removed from their personal chart. Addition and multiplication charts can also be effectively used as reference tools for subtraction and division, respectively, by understanding the inverse relationships between these operations.
For basic fact reference, a pocket-sized chart is often more beneficial than an electronic calculator. Having the complete set of answers visually accessible is valuable, as is the consistent spatial location of each answer, as spatial memory can aid recall. To discourage over-reliance and encourage mastery, students can black out or mark off facts as they become memorized, fostering motivation to learn more. For students who struggle to locate answers at the intersections of rows and columns on a chart, using a cutout cardboard L-shape can help isolate specific facts.
Numerous curriculum resources offer targeted methods to aid in mastering basic arithmetic facts. A fundamental principle underlying these materials is the assumption that the student has already established a firm understanding of the concepts of quantities and operations. This means the student can demonstrate and explain the meaning of a problem using concrete objects, drawings, or other representations. Effective teaching suggestions often include:
- Interactive and intensive practice: Utilizing motivational materials such as games. The quality of attentiveness during practice is as important as the duration.
- Distributed practice: Employing frequent practice in short sessions, such as two 15-minute sessions daily, rather than infrequent longer sessions.
- Small fact groups: Focusing on mastering a small number of facts at a time, followed by frequent practice with mixed groups to ensure retention and generalization.
- Emphasis on reverses/turnarounds: Practicing fact families and commutative properties (e.g., 4 + 5/5 + 4, 6×7/7×6) in vertical, horizontal, and oral formats to build flexibility and understanding of number relationships.
- Student self-charting of progress: Having students track their mastered facts and remaining facts to promote ownership and motivation.
- Instruction, not just practice: Explicitly teaching thinking strategies to derive facts from known facts (e.g., using doubles facts like 5 + 5 and 6 + 6 to learn near-doubles facts like 5 + 6 and 6 + 7).
(For detailed information on thinking strategies, refer to Garnett, Frank & Fleischner, 1983, Thornton, 1978; or Stern, 1987).
Arithmetic Weakness/Math Talent: A Dichotomy
Interestingly, some students with math learning disabilities exhibit a strong grasp of mathematical concepts but struggle with consistent and accurate calculation. They may be reliably unreliable in attending to operational signs, borrowing or carrying appropriately, and sequencing steps in multi-step operations. These students may also experience difficulties mastering basic number facts.
It’s noteworthy that some students with these seemingly contradictory profiles may be placed in remedial math during elementary school, where computational accuracy is heavily emphasized. However, they may later excel in honors-level higher mathematics courses where conceptual understanding and reasoning are paramount. It is crucial to avoid tracking these students into low-level secondary math classes based solely on their computational inconsistencies. Such placement would deny them access to higher-level mathematical content they are capable of mastering, focusing instead on their areas of weakness. Mathematics encompasses far more than simply accurate calculation. Therefore, a comprehensive assessment of math abilities is essential, moving beyond a narrow focus on lower-level computational skills to gauge true mathematical potential.
Working effectively with math learning disabled students often requires a delicate balance, encompassing:
- Acknowledging their computational weaknesses: Recognizing and validating their struggles with calculation accuracy.
- Persistently strengthening inconsistent skills: Providing targeted and ongoing support to improve computational skills.
- Partnering with students: Collaboratively developing self-monitoring strategies and compensatory techniques to manage computational errors.
- Providing enriched math teaching: Simultaneously offering access to the full breadth and depth of mathematics, fostering conceptual understanding and higher-order thinking.
Bridging the Gap: Written Symbol Systems and Concrete Materials
Many young children entering school with math learning difficulties actually possess a solid foundation of informal mathematical understanding gained through everyday experiences. Their challenges often arise when connecting this intuitive knowledge to the formal procedures, language, and symbolic notation system of school mathematics. This transition can be likened to a musically inclined child encountering written music notation as something disconnected from their existing musical abilities. Indeed, mapping the abstract world of written math symbols onto the familiar world of quantities and actions, while simultaneously learning the specialized language of arithmetic, is a complex cognitive task.
Students require numerous and varied experiences with concrete materials to build strong and stable connections between their informal understanding and formal math. Teachers can inadvertently compound difficulties at this stage by prematurely asking students to match pictorial representations with number sentences before they have adequately connected physical representations with math symbols and related verbal language. Concrete materials, due to their tangible and manipulable nature, serve as more effective teaching tools than pictorial representations, especially in the initial stages of concept development. Pictures, being semi-abstract symbols, can easily confuse the delicate connections being formed between pre-existing concepts, new math vocabulary, and the formal system of written math problems if introduced too early.
Structured concrete materials remain beneficial for concept development across all grade levels and math topics. Research evidence consistently demonstrates that students who utilize concrete materials develop more precise and comprehensive mental representations of mathematical concepts. They often exhibit increased motivation and on-task behavior, achieve deeper understanding of mathematical ideas, and demonstrate improved ability to apply these concepts to real-world situations. Structured concrete materials have proven effective in teaching a wide range of mathematical concepts, from early number relations and place value to computation, fractions, decimals, measurement, geometry, money, percentage, number bases, story problems, probability, statistics, and even algebraic concepts.
It is important to note that different types of concrete materials are best suited for different teaching purposes. Materials themselves do not teach; their effectiveness relies on teacher guidance, student interaction, and repeated demonstrations and explanations from both teachers and students.
The common practice of relying heavily on workbooks and worksheets filled with abstract problems can perpetuate student confusion regarding written math notation conventions. These formats often encourage students to become “answer-finders” rather than active demonstrators and explainers of mathematical ideas. Students who struggle with ordering math symbols in conventional vertical, horizontal, and multi-step algorithms benefit greatly from activities that involve translating between different forms of representation. For instance, teachers can provide solved addition problems and ask students to translate them into related subtraction problems. Similarly, teachers can dictate problems (with or without answers) for students to represent pictorially, then in vertical notation, and finally in horizontal notation. Structuring worksheets with designated boxes for each representation format can provide valuable visual support.
Collaborative activities, such as students working in pairs to translate solved problems into multiple representations or verbal explanations, can also be highly effective. For example, students can translate a problem like 20 x 56 = 1120 into different verbal expressions (e.g., “twenty times fifty-six equals one thousand, one hundred and twenty” or “twenty multiplied by fifty-six is one thousand, one hundred, twenty”). In another paired activity, students can be given cards with solved problems and alternate demonstrating or proving each example using concrete materials like bundled sticks for carrying in addition. To add engagement, some problems can be intentionally answered incorrectly, turning the activity into a “bad egg” hunt to identify errors.
These suggestions aim to shift students away from viewing math solely as a pursuit of right answers or a source of frustration. They help cultivate a mindset that connects conceptual understanding with symbolic representation, while simultaneously reinforcing appropriate mathematical language variations.
Decoding the Language of Math
Language aspects of mathematics can pose significant barriers for some students with learning disabilities. This can manifest as confusion with mathematical terminology, difficulty following verbal explanations, and/or weak verbal skills for internally monitoring the steps of complex calculations. Teachers can provide crucial support by adjusting their verbal delivery: slowing down the pace, maintaining natural phrasing, and breaking down information into smaller, manageable segments. This “chunking” of verbal information is particularly important when asking questions, giving instructions, presenting new concepts, and providing explanations.
Equally important is consistently prompting students to verbalize their mathematical thinking and actions. All too often, math instruction is dominated by teacher explanations or silent written practice. Students with language processing challenges need opportunities to demonstrate their understanding using concrete materials and articulate their reasoning at all ages and across all levels of math work, not just in the early grades. Regularly having students “play teacher” can be both engaging and essential for developing proficiency in the complex language of mathematics. Furthermore, understanding for all students tends to deepen when they are required to explain, elaborate on, or defend their approaches to others. The act of explaining often provides the necessary cognitive push to connect and integrate knowledge in meaningful ways.
Typically, children with language deficits may perceive math problems on a page merely as signals to perform operations, rather than as meaningful sentences requiring comprehension. They may even actively avoid verbalizing their mathematical thinking. Both younger and older students benefit from developing the habit of reading or saying problems aloud before and after computation. By consciously engaging in self-verbalization, they can enhance their self-monitoring skills and reduce attentional slips and careless errors. Therefore, teachers should actively encourage these students to:
- Stop briefly after arriving at an answer.
- Read aloud the entire problem along with their answer.
- Listen to themselves and ask, “Does this answer make sense in the context of the problem?”
For students with language weaknesses, establishing this self-verbalization routine may require repeated teacher modeling, patient reminders, and the use of cue cards as visual prompts.
Navigating Visual-Spatial Aspects in Math
A smaller subset of students with learning disabilities experience challenges related to visual-spatial-motor organization. These difficulties can lead to weak or absent conceptual understanding of mathematical ideas, impaired “number sense,” specific problems with pictorial representations, and/or poor handwriting and disorganized arrangement of numerals and symbols on the page. Students with profound conceptual understanding deficits often exhibit significant perceptual-motor challenges, potentially indicating right hemisphere dysfunction.
This particular subgroup may benefit significantly from a strong emphasis on precise and clear verbal descriptions in math instruction. They tend to learn more effectively by substituting verbal frameworks for the intuitive/spatial/relational understanding they lack. Pictorial examples or diagrammatic explanations can be highly confusing and should be minimized or avoided when teaching or clarifying concepts with these students. In fact, remediation for this subgroup may need to specifically target picture interpretation, diagram and graph reading, and even nonverbal social cues, areas that rely heavily on visual-spatial processing.
To foster understanding of math concepts, repeated use of concrete teaching materials, such as Stern blocks or Cuisenaire rods, is highly recommended. Conscientious attention should be given to developing stable verbal representations for each quantity (e.g., “five”), relationship (e.g., “five is less than seven”), and action (e.g., “five plus two equals seven”). Because understanding visual relationships and spatial organization is inherently difficult for these students, it is crucial to anchor verbal constructions in repeated, multi-sensory experiences with structured materials that can be physically felt, seen, and manipulated while being verbally described. For example, they may learn to identify triangles more effectively by holding a triangular block and verbalizing, “A triangle has three sides. When we draw it, it has three connected lines.” This verbal anchoring helps create a cognitive framework to compensate for their visual-spatial processing deficits.
The goal for these students is to build a robust verbal model for quantities and their relationships, effectively substituting for the visual-spatial mental representations that most individuals develop naturally. Consistent descriptive verbalizations also need to be firmly established to guide the application of math procedures and the execution of written computation steps. Progress for these students often requires great patience, verbal repetition, and small, incremental steps in learning.
It’s crucial to recognize that students with average, bright, and even very high overall intelligence can experience severe visual-spatial organization deficits that make developing even basic math concepts extremely challenging. When these deficits are coupled with strong verbal abilities, there can be a tendency to underestimate or dismiss the impaired area of functioning. Consequently, parents and teachers may mistakenly attribute the student’s struggles to lack of effort, inattention, math anxiety, or emotional problems. Accompanying difficulties often include a poor sense of body in space, challenges in interpreting nonverbal social cues like gestures and facial expressions, and general disorganization in managing physical objects and their environment. Misinterpreting these interconnected challenges as primarily emotional or behavioral can significantly delay appropriate interventions in mathematics and related areas.
In Summary: Addressing the Critical Need for Math Learning Disability Support
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 have serious negative consequences on everyday life management, future job prospects, and career advancement.
Math learning problems exhibit a wide range, from mild to severe, and manifest in diverse ways. Common challenges include inefficient recall of basic arithmetic facts and inconsistent accuracy in written computation. When these computational difficulties coexist with strong conceptual understanding of mathematical and spatial relations, it is vital to avoid solely focusing on computation remediation. While addressing computational skills is important, these efforts should not limit access to a comprehensive math education for otherwise capable students.
Language disabilities, even subtle ones, can significantly hinder math learning. Many students with learning disabilities tend to avoid verbalizing in math activities, a tendency often reinforced by traditional math instruction methods. Actively developing students’ habits of verbalizing math problems and procedures can be a powerful strategy to overcome obstacles to success in mainstream math classrooms.
Many children experience difficulty bridging their informal, intuitive math knowledge to the formal system of school mathematics. Building these crucial connections requires time, varied experiences, and carefully guided instruction. The strategic use of structured, concrete materials is essential for solidifying these links, not only in the early elementary grades but also during concept development stages in higher-level mathematics. Some students particularly benefit from explicit instruction in translating between different written forms of math problems, different verbal expressions of math, and various representations (using objects or drawings) of mathematical concepts.
A profoundly impactful, though less common, math learning disability stems from significant visual-spatial-motor disorganization. This condition impairs the formation of foundational math concepts in a small subgroup of students. Effective intervention strategies include minimizing the use of pictures or graphics for concept conveyance, emphasizing verbal descriptions of math ideas, and utilizing concrete materials as anchors for understanding. The organizational and social challenges that often accompany this type of math learning disability also require sustained, targeted remedial attention to support successful life adjustment in adulthood.
In conclusion, as educators and especially as special educators, we have a significant and often unmet responsibility to provide greater attention and targeted support for math learning disabilities. By understanding the diverse nature of these challenges and implementing evidence-based strategies, we can empower students with math learning disabilities to achieve their full mathematical potential and lead successful lives.
About the author
Dr. Garnett received her doctorate from Teachers College, Columbia University. Over the last 18 years Dr. Garnett has been on the faculty of the Department of Special Education, Hunter College, CUNY where she directs the masters program in Learning Disorders. She is currently with The Edison Project, where she is the architect of their Responsible Inclusion/Special Edison Support.
