Table of Content
- What is dyscalculia
- Etiology and Prevalence
- Subtypes of Dyscalculia
- Math Anxiety
- Intervention and Strategies
- Assistive Technology
- LIving with Dyscalculia- video
Dyscalculia (/ˌdɪskælˈkjuːliə/), is a disability resulting in difficulty learning or comprehending arithmetic, such as difficulty in understanding numbers, learning how to manipulate numbers, performing mathematical calculations and learning facts in mathematics. It is sometimes informally known as “math dyslexia”, though this can be misleading as dyslexia is a different condition from dyscalculia.
Dyscalculia does not reflect a general deficit in cognitive abilities or difficulties with time, measurement, and spatial reasoning. Estimates of the prevalence of dyscalculia range between 3 and 6% of the population. In 2015, it was established that 11% of children with dyscalculia also have ADHD. Dyscalculia has also been associated with people who have Turner syndrome and people who have spina bifida. (Wikipedia/dyscalculia, n.d)
A range of terms are used to refer to problems in learning mathematical concepts and skills, including Math Difficulties, Math Disability, Mathematical Learning Disability, Mathematics Disorder, Specific Disorder of Arithmetic Skills, Math Anxiety, and Developmental Dyscalculia ( DD). These terms are similar in that all implicate low numeracy skills. However, they are not synonymous Here we differentiate general Mathematics Disorder [MD: e.g., DSM-IV: from Developmental Dyscalculia in several important ways.
In Developmental Dyscalculia the learning problem:
1) is specific to the domain of arithmetic (reading and spelling skills are within the normal range);
2) manifests partly as problems in learning and remembering simple arithmetic facts (such as single-digit sums or products; e.g., 3+4 = 7), rather than more general problems in computation;
3) is typically defined by very low scores on standardized tests of arithmetic achievement, e.g., below the 8th or even 5th percentile, which is equivalent to standard scores below 78
4) reflects a specific impairment in brain function that gives rise to unexpected problems in basic numerical processing, such as automatic or implicit processing of quantities or numbers
(Rubinsten & Tannock, 2010)
- An important distinction between Developmental Dyscalculia and Mathematical deficits stemming from external factors.
Mathematical performance deficits, Developmental Dyscalculia, may arise because of a wide range of factors, from poor teaching to low socio-economic status, to behavioral attention problems. However, a subset of children with math difficulties, possibly with the most-severe impairments, appears to suffer from a developmental learning disorder that undermines the ability to process basic numerical magnitude information, and that impairment in turn undermines the acquisition of school-level arithmetic skills. This disorder, “primary developmental dyscalculia,” should not be confused with “secondary developmental dyscalculia,” which refers to mathematical deficits stemming from external factors such as those described above. Instead, primary DD is associated with impaired development of brain mechanisms for processing numerical magnitude information and is thus driven by endogenous neurodevelopmental factors. (Gaven & Ansari, 2013)
The term ‘dyscalculia’ was coined in the 1940s, but it was not completely recognized until 1974 by the work of Czechoslovakian researcher Ladislav Kosc. Kosc defined dyscalculia as “a structural disorder of mathematical abilities.” His research proved that the learning disability was caused by impairments to certain parts of the brain that control mathematical calculations and not because symptomatic individuals were ‘mentally handicapped’. Researchers now sometimes use the terms “math dyslexia” or “math learning disability” when they mention the condition. Cognitive disabilities, specific to mathematics were originally identified in case studies with patients who experienced specific arithmetic disabilities as a result of damage to specific regions of the brain. More commonly, dyscalculia occurs developmentally as a genetically linked learning disability which affects a person’s ability to understand, remember, or manipulate numbers or number facts (e.g., the multiplication tables). The term is often used to refer specifically to the inability to perform arithmetic operations, but is also defined by some educational professionals and cognitive psychologists such as Stanislas Dehaene and Brian Butterworth as a more fundamental inability to conceptualize numbers as abstract concepts of comparative quantities (a deficit in “number sense”), which these researchers consider to be a foundational skill upon which other mathematics abilities build. Symptoms of dyscalculia include the delay of simple counting, inability to memorize simple arithmetic facts such as adding, subtracting, etc. There are few known symptoms because little research has been done on the topic. (Wikipedia/dyscalculia, n.d)
At its most basic level, dyscalculia is a learning disability affecting the normal development of arithmetic skills. A consensus has not yet been reached on appropriate diagnostic criteria for dyscalculia.
Other than using achievement tests as diagnostic criteria, researchers often rely on domain-specific tests (i.e. tests of working memory, executive function, inhibition, intelligence, etc.) and teacher evaluations to create a more comprehensive diagnosis. Alternatively, fMRI research has shown that the brains of the neurotypical children can be reliably distinguished from the brains of the children with dyscalculia based on the activation in the prefrontal cortex. (Wikipedia/dyscalculia, n.d)
Etiology and Prevalence
Developmental Dyscalculia (DD) describes a specific and severe deficit in the ability to process numerical information that cannot be ascribed to sensory difficulties, low IQ or inadequate education, and that results in a failure to develop fluent numerical computation skills. Untreated, DD typically persists beyond the school-age years into late adolescence and adulthood. Epidemiological studies indicate that DD is as common as reading disorders and affects 3.5% – 6.5% of the school-age population. Moreover, DD runs in families and is heritable, which implicates genetic factors in its etiology, though to date, none have been reported, (Rubinsten & Tannock, 2010)
The earliest appearance of dyscalculia is typically a deficit in subitizing, the ability to know, from a brief glance and without counting, how many objects there are in a small group. Children as young as five can subitize six objects, especially looking at a die. However, children with dyscalculia can subitize fewer objects and even when correct take longer to identify the number than their age-matched peers. Dyscalculia often looks different at different ages. It tends to become more apparent as children get older; however, symptoms can appear as early as preschool. Common symptoms of dyscalculia are having difficulty with mental math, trouble analyzing time and reading an analog clock, struggle with motor sequencing that involves numbers, and often they will count on their fingers when adding numbers.
Dyscalculia is characterized by difficulties with common arithmetic tasks. These difficulties may include:
- Difficulty reading analog clocks
- Difficulty stating which of two numbers is larger
- Inability to comprehend financial planning or budgeting, sometimes even at a basic level; for example, estimating the cost of the items in a shopping basket or balancing a checkbook
- Visualizing numbers as meaningless or nonsensical symbols, rather than perceiving them as characters indicating a numerical value (hence the misnomer, “math dyslexia”)
- Difficulty with multiplication, subtraction, addition, and division tables, mental arithmetic, etc.
- Inconsistent results in addition, subtraction, multiplication and division
- When writing, reading and recalling numbers, mistakes may occur in the areas such as: number additions, substitutions, transpositions, omissions, and reversals
- Poor memory (retention and retrieval) of math concepts; may be able to perform math operations one day, but draw a blank the next; may be able to do book work but then fails tests
- Ability to grasp math on a conceptual level, but an inability to put those concepts into practice
- Difficulty recalling the names of numbers, or thinking that certain different numbers “feel” the same (e.g. frequently interchanging the same two numbers for each other when reading or recalling them)
- Problems with differentiating between left and right
- A “warped” sense of spatial awareness, or an understanding of shapes, distance, or volume that seems more like guesswork than actual comprehension
- Difficulty with time, directions, recalling schedules, sequences of events, keeping track of time, frequently late or early
- Difficulty reading maps
- Difficulty working backwards in time (e.g. What time to leave if needing to be somewhere at ‘X’ time)
- Difficulty reading musical notation
- Difficulty with choreographed dance steps
- Having difficulty mentally estimating the measurement of an object or distance (e.g., whether something is 3 or 6 meters (10 or 20 feet) away)
- Inability to grasp and remember mathematical concepts, rules, formulae, and sequences
- Inability to concentrate on mentally intensive tasks
- Mistaken recollection of names, poor name/face retrieval, may substitute names beginning with same letter.
[The National Center for Learning Disabilities],(2021, May 11). What is Dyscalculia, [Video file]. from https://youtu.be/HVf_OHK2hHQ (7:46 minutes)
Persistence in children
Although many researchers believe dyscalculia to be a persistent disorder, evidence on the persistence of dyscalculia remains mixed.
Persistence in adults
There are very few studies of adults with dyscalculia who have had a history of it growing up, but such studies have shown that it can persist into adulthood. It can affect major parts of an adult’s life. Most adults with dyscalculia have a hard time processing math at a 4th grade level. For 1st-4th grade level, many adults will know what to do for the math problem, but they will often get them wrong because of “careless errors”, although they are not careless when it comes to the problem. The adults cannot process their errors on the math problems or may not even recognize that they have made these errors. Visual-spatial input, auditory input, and touch input will be affected due to these processing errors. People with dyscalculia may have a difficult time adding numbers in a column format because their mind can mix up the numbers, and it is possible that they may get the same (wrong) answer twice due to their mind processing the problem incorrectly. People with dyscalculia can have problems determining differences in different coins and their size or giving the correct amount of change and if numbers are grouped together, it is possible that they cannot determine which has less or more. If a person with dyscalculia is asked to choose the greater of two numbers, with the lesser number in a larger font than the greater number, they may take the question literally and pick the number with the bigger font. Adults with dyscalculia have a tough time with directions while driving and with controlling their finances, which causes difficulties on a day-to-day basis.
College students and other adult learners
College students, particularly may have a tougher time due to the fast pace and change in the difficulty of the work they are given. As a result of this, students may develop a lot of anxiety and frustration. After dealing with their anxiety for a long time, students can become averse to math and try to avoid it as much as possible, which may result in lower grades in math courses. However, students with dyscalculia often do exceptionally well in writing, reading, and speaking. (Wikipedia/dyscalculia, n.d)
Research on subtypes of dyscalculia has begun without consensus; preliminary research has focused on comorbid learning disorders as subtyping candidates. The most common comorbidity in individuals with dyscalculia is dyslexia. Most studies done with comorbid samples versus dyscalculic-only samples have shown different mechanisms at work and additive effects of comorbidity, indicating that such subtyping may not be helpful in diagnosing dyscalculia. But there is variability in results at present.
Due to high comorbidity with other disabilities such as dyslexia and ADHD, some researchers have suggested the possibility of subtypes of mathematical disabilities with different underlying profiles and causes. Whether a particular subtype is specifically termed “dyscalculia” as opposed to a more general mathematical learning disability is somewhat under debate in the scientific literature.
- Semantic memory: This subtype often coexists with reading disabilities such as dyslexia and is characterized by poor representation and retrieval from long-term memory. These processes share a common neural pathway in the left angular gyrus, which has been shown to be selective in arithmetic fact retrieval strategies and symbolic magnitude judgments. This region also shows low functional connectivity with language-related areas during phonological processing in adults with dyslexia. Thus, disruption to the left angular gyrus can cause both reading impairments and difficulties in calculation. This has been observed in individuals with Gerstmann syndrome, of which dyscalculia is one of a constellation of symptoms.
- Procedural concepts: Research by Geary has shown that in addition to increased problems with fact retrieval, children with math disabilities may rely on immature computational strategies. Specifically, children with mathematical disabilities showed poor command of counting strategies unrelated to their ability to retrieve numeric facts. This research notes that it is difficult to discern whether poor conceptual knowledge is indicative of a qualitative deficit in number processing or simply a delay in typical mathematical development.
- Working memory: Studies have found that children with dyscalculia showed impaired performance on working memory tasks compared to neurotypical children. Working memory problems are confounded with domain-general learning difficulties, thus these deficits may not be specific to dyscalculia but rather may reflect a greater learning deficit. Dysfunction in prefrontal regions may also lead to deficits in working memory and other executive function, accounting for comorbidity with ADHD. (Wikipedia/dyscalculia, n.d)
According to the data Rubinsten and Tannock, there is clear evidence that, for Developmental Dyscalculia (DD), math words had an anxious influence mainly when it comes to addition and multiplication arithmetic problems. What may be some of the reasons for this phenomenon? Normally developing children enter school with informal knowledge about numbers and arithmetic; knowledge that is based on their daily experiences of counting and calculation. Once entering school, however, much educational training is focused on basic multiplication and addition arithmetic facts. Consider, however, a child with DD who is innately deficient in his/her ability to process numbers, to count and to calculate. This child, from a very young age, has to answer addition and multiplication questions for which there is almost always only one correct answer. This situation, combined with the culture of solving these problems quickly, can lead students with DD towards a negative attitude style and ultimately learned helplessness to arithmetic in general (i.e., the affectively related influence that negative affective words had on solving simple arithmetic problems). Also, this situation can lead to a specific and accentuated fear and avoidance when it comes to the retrieval of addition and multiplication problems from memory (i.e., the affectively related influence that math words had on solving mainly multiplication and addition problems).
Hembree showed that cognitive-behavioral interventions for math anxiety had a positive influence on math achievement test scores. These findings are quite significant in terms of the relationship between math anxiety and math achievement, and specifically in relation to DD. For people with DD, childhood difficulties with numerical processes and poor math achievement intensify math anxiety, which further impedes math achievement. As educators come to appreciate the key role played by math anxiety, interventions that reduce it may become a key part of the math educational system. It might be that one of the most effective ways to reduce math anxiety is to improve math achievement from an early age through interventions focused on children with DD thus turning the cycle of failure-fear-failure to one of success-confidence-success. This is especially true if the assumption that DD is an innate condition is correct. Such programs would be an important way of helping students cope with the frustrations inherent in the learning of mathematics, and thereby improve math achievement.
(Rubinsten & Tannock, 2010)
To date, very few interventions have been developed specifically for individuals with dyscalculia. Concrete manipulation activities have been used for decades to train basic number concepts for remediation purposes. This method facilitates the intrinsic relationship between a goal, the learner’s action, and the informational feedback on the action. A one-to-one tutoring paradigm designed by Lynn Fuchs and colleagues which teaches concepts in arithmetic, number concepts, counting, and number families using games, flash cards, and manipulatives have proven successful in children with generalized math learning difficulties, but intervention has yet to be tested specifically on children with dyscalculia. These methods require specially trained teachers working directly with small groups or individual students. As such, instruction time in the classroom is necessarily limited. For this reason, several research groups have developed computer adaptive training programs designed to target deficits unique to dyscalculic individuals.
Software intended to remediate dyscalculia has been developed. While computer adaptive training programs are modeled after one-to-one type interventions, they provide several advantages. Most notably, individuals are able to practice more with a digital intervention than is typically possible with a class or teacher. As with one-to-one interventions, several digital interventions have also proven successful in children with generalized math learning difficulties
Several digital interventions have been developed for students with dyscalculia specifically. Each attempts to target basic processes that are associated with math difficulties. Digital interventions for dyscalculia adapt games, flash cards, and manipulatives to function through technology.
While each intervention claims to improve basic numeracy skills, the authors of these interventions do admit that repetition and practice effects may be a factor involved in reported performance gains. An additional criticism is that these digital interventions lack the option to manipulate numerical quantities. While the computer game provides the correct answer, the individual using the intervention cannot actively determine, through manipulation, what the correct answer should be. Butterworth and colleagues argued that games like The Number Bonds games, should be the direction that digital interventions move towards. Such games use manipulation activities to provide intrinsic motivation towards content guided by dyscalculia research. (Wikipedia/dyscalculia, n.d)
Instructional strategies for students with Dyscalculia from DO-IT
Rochelle Kenyon lists the following strategies for teaching a student with math-related learning disabilities.
- Avoid memory overload. Assign manageable amounts of work as skills are learned.
- Build retention by providing review within a day or two of the initial learning of difficult skills.
- Provide supervised practice to prevent students from practicing misconceptions and “misrules.”
- Make new learning meaningful by relating practice of subskills to the performance of the whole task.
- Reduce processing demands by preteaching component skills of algorithms and strategies.
- Help students to visualize math problems by drawing.
- Use visual and auditory examples.
- Use real-life situations that make problems functional and applicable to everyday life.
- Do math problems on graph paper to keep the numbers in line.
- Use uncluttered worksheets to avoid too much visual information.
- Practice with age-appropriate games as motivational materials.
- Have students track their progress.
- Challenge critical thinking about real problems with problem solving.
- Use manipulatives and technology such as tape recorders or calculators.
This list was adapted from the following source: Garnett, K., Frank, B., & Fleischner, J. X. (1983). A strategies generalization approach to basic fact learning (addition and subtraction lessons, manual #3; multiplication lessons, manual #5). Research Institute for the Study of Learning Disabilities. New York, NY: Teacher’s College, Columbia University.
Dyscalculia: Teaching Strategies and Modifications From [Teachings in Education] (3:05 minutes)
For more math accommodations and teaching strategies to, consult some of the following online articles:
Kenyon, R, (2000) Accommodating Math Students with Learning Disabilities From https://www.ncsall.net/index.html@id=325.html
Manitoba.ca.(n.d.) Supporting Students with Mathematics Disability. From https://www.edu.gov.mb.ca/k12/docs/support/learn_disabilities/module5.pdf
Assistive technology does not “cure” a specific learning disability. These tools compensate rather than remedy, allowing a person with an LD to demonstrate their intelligence and knowledge. Adaptive technology for the person with an LD is a made-to-fit implementation. Trial and error may be required to find a set of appropriate tools and techniques for a specific individual. Ideally, a person with an LD plays a key role in selecting their technology. The teacher should help to determine what works and what does not. Once basic tools and strategies are selected, they can be “test driven,” discarded, adapted, and/or refined. (DO-IT, n.d.)
Living with Dsycalculia
[BBC The Social], (2019, Mar. 11), Living with Dyscalculia (It’s Not Just “Number Dyslexia” [Video File] From https://youtu.be/_djdPIZrFno (3:04 minutes)
DO-IT, University of Washington, (2021) What are strategies for teaching a student with a math related learning disability? From https://www.washington.edu/doit/what-are-strategies-teaching-student-math-related-learning-disability (CC BY SA)
DO-IT, University of Washington, (2021), Why is accessible math important? From https://www.washington.edu/doit/why-accessible-math-important?3= (CC BY SA)
Price, Gavin R., and Daniel Ansari. “Dyscalculia: Characteristics, Causes, and Treatments.” Numeracy 6,
Iss. 1 (2013): Article 2. DOI: http://dx.doi.org/10.5038/1936-46188.8.131.52 (CC BY-NC 4.0)
Rubinsten, O., Tannock, R. Mathematics anxiety in children with developmental dyscalculia. Behav Brain Funct 6, 46 (2010). https://doi.org/10.1186/1744-9081-6-46 (CC BY 2.0) https://behavioralandbrainfunctions.biomedcentral.com/articles/10.1186/1744-9081-6-46#citeas
Wikipedia, (n.d.) Dyscalculia From https://en.wikipedia.org/wiki/Dyscalculia (CC SA)
Grigore, M. (2020). Towards a standard diagnostic tool for dyscalculia in school children. CORE Proceedings, 1(1). https://doi.org/10.21428/bfdb1df5.d4be3454 https://core.pubpub.org/pub/ttoew31a/release/1
Rubinsten O (2015) Link between cognitive neuroscience and education: the case of clinical assessment of developmental dyscalculia. Front. Hum. Neurosci. 9:304. doi: 10.3389/fnhum.2015.00304 https://www.frontiersin.org/articles/10.3389/fnhum.2015.00304/full