Some children take to numbers quickly, while others seem to struggle with math concepts from early childhood on. If you’re concerned that your child’s math difficulties stand apart from those of her peers, learn about the symptoms, diagnostic process, and effective interventions for dyscalculia.
Difficulty with mathematical concepts is a struggle that educators and parents alike may overlook in the expectation that children will “just catch up.” Read on to learn more about what characterizes dyscalculia and how to advocate for your child’s learning needs if you suspect she shows symptoms of the disorder.
Dyscalculia (formerly known as “Mathematics Disorder” or “Mathematics Learning Disability”) is diagnosed as a “Specific Learning Disorder” relating to math. Researchers have described it as a disability with “the representation or processing of specifically numerical information.” It can manifest in the following ways:
- Difficulty with math calculations (e.g., basic math operations)
- Difficulty with “number sense” (e.g., estimation, counting, place value)
- Difficulty with math concepts (e.g., the notion of fractions)
- Difficulty with “numerosity” (e.g., how many dots are in an array)
- Difficulty with some combination of these math aptitudes
Math is multifaceted, so the potential learning challenges are diverse. An initial clue that your child may have difficulty with math is if she struggles to learn how to count or with a notion known as “number sense” — that is, the ability to just “get” numbers, how they relate to one another, and how you can manipulate them using mathematical operations.
By first grade, children should know how to count reliably without skipping numbers and be able to differentiate which of two numbers is larger. More important still is whether a child has significant trouble learning how to add. If your child does struggle with addition, she may rely on her fingers to count or even on her memory to compensate for her difficulty with the underlying concept.
Children with dyscalculia may be inconsistent in their ability to answer math problems. They are also often slower to respond to math problems than their peers, and they may not be able to answer the range of math problems that their classmates can.
Children who have a math-based specific learning disorder tend to exhibit:
- Difficulty with addition in the early years
- Difficulty with memorizing multiplication facts in later years
- Slowness or inaccuracy in guessing how many items are in an array (i.e., a pattern of numbers)
- Avoidance of math-based tasks
- Slowness in arriving at the answers to math problems relative to their peers (although this may also be a symptom of an underlying processing disorder)
- Difficulty with generalizing math facts to unfamiliar problems
- Difficulty noticing patterns
- Difficulty with problem-solving
- A noticeable difference between their verbal and math skills (with relatively strong verbal skills)
These are factors to consider if you believe your child may be struggling with symptoms of dyscalculia.
Diagnostician and Testing
Dyscalculia can be diagnosed by a neuropsychologist or by a clinical, school, or educational psychologist. An evaluation of dyscalculia will include information about family history, developmental milestones, and academic history, as well as intelligence and academic achievement tests that examine a variety of math skills and question types. A psychologist also needs to look at previous school work to determine if the math skills being assessed have already been taught. Information about the school’s math curriculum, homework, and tests, as well as a conversation with your child’s math teacher will help clarify the concepts that have been covered and the teaching approaches that have been used.
As with all types of testing, task familiarity — that is, how familiar a child is with a type of question or activity — will influence achievement. A child may understand fractions and be able to demonstrate this knowledge visually, but she may not know how to express her understanding algorithmically. She may also know how to calculate partial sums in math, but not be familiar with the traditional “scratch” method (which is a particular approach to solving math calculations); the approach that a child has learned, in short, should align with how the evaluator assesses each skill. That way, the evaluator will reach an accurate diagnosis of a math learning disability.
See Noodle's guide to learning disabilities in children for a more detailed description of the diagnostic process.
Age of Diagnosis
The American Psychiatric Association’s DSM-V states that Specific Learning Disorders — such as dyscalculia — can be diagnosed once a child reaches school age. If, however, parents or preschool teachers notice that a child is struggling to learn to count, it would be beneficial to begin providing early math learning supports, even before a formal diagnosis.
Research from Dr. Nathlie Badian has shown that just above two percent of children have a “persistent disability in arithmetic only,” whereas another 3.4 percent of children have a “persistent disability with arithmetic plus reading.” These findings align with more current research demonstrating the prevalence range of math combined with reading disorders to be between three and six percent. There is a slightly greater prevalence of math-only disorders among boys than girls.
The Brain and Dyscalculia
Within the brain, numerical information is stored in the parietal lobe, which is the area located behind the frontal lobe (more or less on the top of your head). Within the parietal lobe, number understanding is housed in the intraparietal sulcus, an area located on the outer part of the parietal lobe. In addition to numerical skills, this area is responsible for eye movements and visual attention; people with dyscalculia also tend to struggle with pattern recognition.
While we sometimes see both math and language difficulties in a single individual, most current research supports the idea that people who have difficulties with arithmetic and reading have two distinct disorders. Information relating to numbers and that relating to language are stored in different neurological areas. This understanding of the brain is also supported by research on adults who, following a stroke, have no problem with language but develop difficulty comprehending or manipulating numbers. Brain scans show damage to particular neurological regions that are responsible for numeracy skills, but the same patients have no disruptions to their language abilities.
Recognition of the Positives
Research has demonstrated that as a group, children with dyscalculia alone (and no other learning disabilities) have high-average performance on IQ tests and non-verbal intelligence tests as well as vocabulary tests. Children with dyscalculia also tend to have average to above-average working memories, motor skills, and language skills. Researchers note, moreover, that high verbal skills persist in these children as they get older.
With the development of increasingly sophisticated assistive technology (AT), people with math impairments are better able than ever before to compensate for some of their math difficulties. (Read on to learn more about effective AT tools for children with dyscalculia.)
As with all interventions, adapting support mechanisms to a child’s particular struggles — as well as strengths — leads to better outcomes in meeting the challenges of the dyscalculia. That said, there are certain kinds of supports that tend to be especially effective. Math specialists, special education and other classroom teachers, and learning specialists have found that the most effective instructional approaches include:
- Consistent and frequent practice
- Breaking up of topics into separate components
- Small-group settings in which students interact with each other
- Use of cues in strategy instruction (i.e., how to learn particular sets of skills)
Development of Number Sense
Number sense refers to a range of math abilities involved in making estimations, knowing which of two numbers is greater, and understanding the relationships among numbers. It is applied when students move from concrete math practices, such as counting blocks, to conceptual math skills, such as using algorithms to answer math questions on a worksheet. In other words, students rely on number sense as they move from the physical application to the abstract use of math skills.
So, what about students who don’t develop this skill on their own? Number sense can be taught through the explicit use of mini-strategies. For example, we can teach children that it is easier to begin with the larger number when adding two small numbers (e.g., 9 + 2 is easier to compute than 2 + 9 because you can begin with 9 and simply “count up” 2).
Providing frequent opportunities to verbalize and discuss math is another strategy that benefits students with math disorders, since it allows them to use their relatively strong verbal skills to help internalize math concepts.
Dr. Jo Baeler, a math professor at Stanford University’s Graduate School of Education, has done research focusing on the most effective approaches to avoid rote memorization when teaching conceptual math knowledge. She has found that the use of arrays (or patterns) and visual representations of math facts help students with dyscalculia to develop number sense.
Real-world problems, or “anchor problems,” help students understand and apply a variety of math concepts simultaneously. There are a number of concrete applications of math ideas — from creating a budget for a business to developing a scaled drawing for an architecture project to tracking the growth of a class plant — that offer students opportunities to apply multiple math skills to a single problem, while simultaneously engaging their particular interests and helping them appreciate the importance of math.
For additional tools, check out Noodle’s free math resources for children at all learning levels. Other websites like Math Munch, which has weekly examples of math “in the news,” are also effective tools for enticing learners with dyscalculia to practice their skills in number-based activities.
The Center for Integrating Technology in Education (CITEd) notes the efficacy of using consistent cues when working with students with dyscalculia. To that end, technology can prompt students to employ the strategies they have been taught through more traditional means — and help provide “next steps” when a student becomes stuck.
Since the organization of math concepts can be particularly difficult for students with dyscalculia, tools such as graphic organizers can provide an effective means for practicing the proper steps of math functions and for imposing structure on abstract concepts. Calculators, too, are an assistive technology that help students problem-solve and apply mathematical concepts.
These specific technologies can help students with math strategies, visualization, and organization:
- Cymath is a website and app that helps you solve math problems. While some have criticized it for supplying the correct answer, this tool allows students to use a model answer to follow a mathematical algorithm. Students are able to work backward through their mistakes — as in a maze — to understand the concepts they may have misapplied or omitted.
- Tinkerplots and SketchPad assist with organizing and visualizing math concepts (especially of Data and Statistics for Tinkerplots and Geometry for Sketchpad).
- PhET is a University of Colorado–based site that has simulations for math and science. This tool allows students to manipulate numbers and objects, and to strengthen their understanding through exploration and play.
- Modmath is an iPad app originally created to help students with dyslexia and dysgraphia meet the challenges of language-based disabilities in completing math work. It is useful for students with dyscalculia, as well, as it offers tool to organize math notes, practice mathematical organization, and strengthen facility with basic math problem-solving.
Noodle’s range of resources on dyscalculia and math support, including:
- 5 Ways to Help Your Child with Dyscalculia Master Math
- Dyscalculia: What Parents Need to know about Diagnosis and Intervention
- 6 Apps That Help Elementary Schoolers Master Math
- 6 Apps to Help Your Middle School Child Master Math
- 6 Apps to Help High Schoolers Excel at Math Sneak Learning Into Everyday Life: The Math Edition
- Noodle’s video libraries of real-world math problems and their solutions
The following outside resources are from well-established authorities in the field of dyscalculia. You will find in-depth coverage here:
- LD Online’s math and dyscalculia articles
- The Center for Implementing Technology in Education’s Technology-Supported Math Instruction for Students with Disabilities
- Dr. Carol Dweck’s research on Mindset Theory
- Understood.org’s series of articles about dyscalculia
Badian, N. (1999). Persistent Arithmetic, Reading, or Arithmetic and Reading Disability. Annals of Dyslexia, 49(1), 43-70. Retrieved March 17, 2015, from Springer Link.
Boaler, J. (2013). Ability and Mathematics: The Mindset Revolution That Is Reshaping Education. Forum, 55(1), 143-152. Retrieved March 20, 2015, from Jo Boaler.
Boaler, J. (2015, January 28). Fluency Without Fear: Research Evidence on the Best Ways to Learn Math Facts. Retrieved March 22, 2015, from You Cubed.
Dyscalculia. (2007, January 1). Retrieved March 20, 2015, from LD Online.
Geary, Ph.D., D. (2006, March 6). Dyscalculia at an Early Age: Characteristics and Potential Influence on Socio-Emotional Development. Retrieved March 20, 2015, from University of Missouri.
Gersten, R., & Chard, D. (n.d.). Number Sense: Rethinking Arithmetic Instruction for Students with Mathematical Disabilities. Retrieved March 21, 2015, from LD Online.
Hasselbring, T., Lott, A., & Zydney, J. (n.d.). Technology-Supported Math Instruction for Students with Disabilities: Two Decades of Research and Development. Retrieved March 20, 2015, from CITEd.
Kaufmann, L., & Von Aster, M. (2012). The Diagnosis and Management of Dyscalculia. Deutches Arzteblatt International, 109(45), 767-778. Retrieved March 19, 2015, from NCBI.
Landerl, K., Bevan, A., & Butterworth, B. (2004). Developmental Dyscalculia and Basic Numerical Capacities: A Study of 8–9-Year-Old Students. Cognition, 93, 99-125. Retrieved March 20, 2015, from Science Direct.
Misleading Graphs: Real Life Examples. (n.d.). Retrieved March 20, 2015, from Statistics How To.
Nelson, C., & Williams, N. (2008). A Fair Game? The Case of Rock, Paper, Scissors. Mathematics Teaching in the Middle School, 14(5), 311-319. Retrieved March 20, 2015, from Springlake Park Schools.
Ramsden, S., Richardson, F., & Josse, G. (2011). Verbal and Non-Verbal Intelligence Changes in the Teenage Brain. Nature, 479, 113-116. Retrieved March 20, 2015, from Nature.
Ranpura, A., Isaacs, E., & Edmonds, C., et al. (2013). Developmental Trajectories of Grey and White Matter in Dyscalculia. Trends in Neuroscience and Education. Retrieved March 22, 2015, from Mathematical Brain.
Shalev, R., Auerbach, J., & Manor, O., et al. (2000). Developmental Dyscalculia: Prevalence and Prognosis. Eur. Child. Adolesc. Psychiatry. Retrieved March 21, 2015, from NCBI.