Dyscalculia

Developmental Dyscalculia: A New Understanding of Early Warning Signs

This math learning disability is nearly as common as dyslexia, however it’s studied far less, understood far worse, and diagnosed inconsistently. At its core, developmental dyscalculia is an inability to process and represent numerals in a typical way. Here is what educators and clinicians need to know about symptoms, complicating factors, comorbid conditions, and useful screening tools.

Numbers on an adding machine represent the challenges of diagnosing dyscalculia in children

Though nearly as common as dyslexia, dyscalculia is neither well-known nor well-understood among educators and clinicians. Roughly 5%-7% of students in the United States have this math-based learning disability.1, 2 Still, dyslexia is studied and discussed in scientific journals nearly 14 times more frequently than is dyscalculia.3

In other words, children with developmental dyscalculia are quite likely slipping through the cracks at school and at the doctor’s office. What’s more, our new understanding of dyscalculia suggests that educators and caregivers can detect its symptoms long before a child fails at arithmetic; it is possible to test and improve foundational skills beginning at an early age.

What Is Developmental Dyscalculia?

Individuals with developmental dyscalculia experience a specific deficit: They struggle to represent and process numerical magnitude in a typical way.

This is a development disorder and begins long before kindergarten; early struggles lead to difficulties in learning numerical expressions such as calculation problems and retaining them in memory. A poor understanding of underlying quantities may also mean an individual needs more working memory to complete a calculation, which taxes the brain in observable ways. This means the risk of dyscalculia can — and should — be screened before a child even learns arithmetic.

In the Diagnostic and Statistical Manual of Mental Disorders (DSM-5), dyscalculia appears underneath the umbrella term “specific learning disorder,” which is defined as a neurodevelopmental disorder with biological origins that manifests in “learning difficulty and problems in acquiring academic skills markedly below age level and manifested in the early school years, lasting for at least six months, not attributed to intellectual disabilities, developmental disorders, or neurological or motor disorders.”4

Specific hallmarks of a mathematics learning disability include difficulty with number sense, fact and calculation, and mathematical reasoning. A child can present with multiple impairments, but to merit a diagnosis of developmental dyscalculia, he or she must experience persistent (not transient) difficulty in acquiring basic mathematical concepts. A child who is not paying attention in a specific class or not understanding one specific concept would likely not qualify.

[Self-Test: Could Your Child Have Dyscalculia?]

What Are the Signs of Developmental Dyscalculia?

Early studies of developmental dyscalculia focused on symptoms such as a child’s counting knowledge and working memory. David C. Geary, Ph.D., a professor at the department of psychological sciences at the University of Missouri, who pioneered research in this field, showed consistently that children who experience math difficulty have poor working memory, which compromises their ability to carry out calculation procedures and to hold intermediary solutions in mind. This, in turn, affects their ability to encode arithmetic facts into long-term memory.5

Two hallmarks of developmental dyscalculia are:

  • The use of immature counting procedures to solve simple arithmetic problems.6
  • A persistent inability to retrieve arithmetic facts from memory.5

For example, children with developmental dyscalculia typically take longer than their peers to complete standardized math tests and use “crutches” such as counting on their fingers long after their peers have begun drawing math facts from memory. They struggle to graduate from counting-based strategies to memory-based strategies, and they make frequent counting procedure errors.7, 8, 9

Children with developmental dyscalculia may not struggle in all domains of math; calculation is the most prevalent sticking point. More recently, research has begun to probe beyond working memory to understand the domain-specific causes of number-processing problems, which I discuss below.

[Self-Test: Could Your Child Have a Working Memory Deficit?]

What Contributes to Poor Number Processing?

Modern research on dyscalculia has worked to identify core readiness skills in the domain of math. We know that early readers, for example, who lack foundational skills have poor decoding skills will continue to lag behind peers with good phonological awareness for some time. This is referred to as the “Matthew effects” in reading, and the implication is that early deficits in core competencies lead to subsequent difficulties in acquiring higher-level skills.

The first influential study of the foundational competencies of number processing was conducted by researchers at the University College London.10 Four groups of children were recruited for this study: a group with dyscalculia, a group with dyslexia, a group with dyscalculia and dyslexia, and a control group with none of the above. In a number-comparison task, researchers asked the children in the 4 groups to judge 2 sets of numbers wherein one digital was either numerically or physically larger.

This task succinctly allowed the researchers to assess core math deficits because any child who struggled with the physical size comparison and the number comparison likely had a core difficulty perceiving numbers, the researchers said. On the other hand, a child who stumbled over the number-comparison task but glided through the size-comparison task almost certainly had trouble with a specific math skill: retrieving the quantity associated with a numeral.

The results of the study showed that children with dyscalculia (and comorbid dyscalculia and dyslexia) struggled to associate a symbol with a quantity, and then use that association in a number comparison task. This suggests that dyscalculia is a deficit related to the representation and processing of numerical magnitudes in a typical way. This, in turns, leads to difficulties in learning numerical expressions such as multiplication tables — and retaining them in memory.

If this finding holds true, the risk for dyscalculia can be assessed before a child even learns arithmetic.

[Free Download: The Teacher’s Guide to Common Learning Challenges]

Important Considerations When Diagnosing Developmental Dyscalculia

1. Developmental Dyscalculia Is Heterogeneous and Commonly Comorbid

There is no single cause of developmental dyscalculia, a learning disability with multiple components11 and subtypes. A recent cluster analysis shows that developmental dyscalculia is very heterogeneous and has at least six different clusters.12

Moreover, developmental dyscalculia rarely occurs in isolation. It is diagnosed often in children with comorbid conditions such as dyslexia and ADHD, and there is no clear evidence of a common cause.

2. Quantitative vs Qualitative Gauges of Competency

Like dyslexia, developmental dyscalculia is diagnosed quantitatively using an arbitrary cutoff score. “One of the major problems is that there’s no specific blood test or brain imaging result that can provide a diagnosis,” writes Linda Siegel in an article on dyslexia.13 The DSM-5 reflects this arbitrariness: “Academic skills are distributed along a continuum, so there is no natural cut-off point that can be used to differentiate individuals with and without specific learning disorders. Thus, any threshold used to specify what constitutes significantly low academic achievement is to a large extent arbitrary.”

3. Is It Math Anxiety or Dyscalculia?

Mathematics anxiety and dyscalculia often go hand in hand but they are not the same thing. The former is quite prevalent, and its hallmarks are emotional factors — not necessarily cognitive ones. According to a study by the Program for International Student Assessment,14 up to 60% of students say things like, “I often worry that it will be difficult for me in mathematics classes” or “I worry that I will get poor grades in mathematics.”

Clinicians should also consider a student’s aptitude and emotions, since math anxiety can affect performance dramatically. This is a bit of a chicken and egg problem because we don’t yet fully understand whether poor math competency leads to math anxiety or vice versa. Regardless, research suggests some level of correlation between math performance and math anxiety.

We also know that math anxiety can be reflected in the brain. A study from Stanford University showed that students with math anxiety activate brain regions like the amygdala and the medial prefrontal cortex that are associated with fear and coping negative emotions when working on math problems. Students without math anxiety, on the other hand, activate carriers in and around the parietal cortex that are involved in mathematics achievement.

[Related Reading: 6 Things You Didn’t Know About the ADHD Brain]

4. Role of Teachers in Students’ Math Anxiety

Teachers and parents may contribute to students’ math anxiety. A study from the University of Chicago showed essentially that a teacher’s math anxiety may impact her students’ achievement.15 Researchers measured first- and second-grade female teachers’ math anxiety, students’ beliefs about math, and students’ math achievement over the first year of schooling. Measuring gender-related attitudes toward math, researchers read children a story about a child who was good at reading or good at math, and then asked the students to draw a picture of the child in the story.

The children were more likely to draw a girl when depicting a student who was good at reading and more likely to draw a boy when depicting a student who excelled at math. In the beginning of the school year, there was no relationship between a teacher’s math anxiety and her students’ math achievement. By the school year’s end, however, the more anxious a teacher was about math, the more likely her female (but not male) students were to endorse the stereotype that “boys are good at math, and girls are good at reading” — and the lower these girls’ math achievement scores were.

5. Role of Parents in Students’ Math Anxiety

Research also shows that parents’ math anxiety may negatively impact their kids, particularly when they work on homework together.16 Findings from a 2015 study showed that, when parents (with either low or high math anxiety) did very little homework with their children, the students’ math growth was not impacted. However, when parents with high math anxiety did a lot of homework with their children, those students’ math scores tended to decline.

Do children with high math anxiety inherently make homework time more stressful? This needs to be further examined, however the findings suggest that a parent’s attitude toward math may seriously influence their child’s learning and achievement.

6. Combat Negative Effects of Math Anxiety with Expressive Writing

Some educators work to alleviate math anxiety by engaging their students in an exercise of expressive writing. A 2011 study showed that students, given the opportunity to reflect on their anxieties with expressive writing before a high-stakes exam, experienced significantly improved scores.17 The simple task of writing down worries, it seems, has great academic impact — particularly for students with frequent test-taking anxiety. Researchers believe that anxiety consumes an individual’s processing resources, which translates into weaker working memory and compromised performance.

Screening Tools for Math Learning Disabilities

Educational psychologists are typically best equipped to assess a child for developmental dyscalculia, however no single diagnostic protocol exists. That said, the following screening tools may indicate if a child has problems with basic math understanding.

1. NumeracyScreener.org tests a child’s ability to judge which of two numbers is larger. A simple paper-and-pencil tool that can be administered without technology, this tool was designed and implemented by Nadia Nosworthy, PhD, under my supervision in the Numerical Cognition Laboratory in the Department of Psychology at Western University.

2. Number Sense Screener™ is a teacher-friendly kindergarten number sense screener and an intervention program for high-risk children based on the research of Nancy C. Jordan, a professor in the School of Education at the University of Delaware.

Intervention Programs and Tools

1. What Works Clearinghouse focuses on the results from high-quality research to answer the question “What works in education?” From the U.S. Department of Education, this resource reviews existing research on different programs, products, practices, and policies in education and provides educators with the information they need to make evidence-based decisions.

2. The Number Race is a fun computer game primarily designed for children aged 4 to 8. Younger players use this tool to learn the basic concepts of numbers and arithmetic. Older children may use it to build their fluency in arithmetic and number sense — that is, mapping numbers to quantities.

3. The Number Catcher, designed by the creator of The Number Race, is primarily designed for children aged 5 to 10 but its higher levels can be fun for adults, too!

This article came from the ADDitude webinar “Understanding Dyscalculia: How to Recognize & Address Math Learning Disabilities” with Daniel Ansari, Ph.D., which is available for free replay now.


References

1 von Aster MG, Shalev RS. Number development and developmental dyscalculia. Dev Med Child Neurol. 2007 Nov;49(11):868-873. https://www.ncbi.nlm.nih.gov/pubmed/17979867

2 Butterworth B, Varma S, Laurillard D. Dyscalculia: from brain to education. Science. 2011 May 27; 332(6033): 1049-1053. doi: 10.1126/science.1201536. https://www.ncbi.nlm.nih.gov/pubmed/21617068

3 Berch DB, Mazzocco MMM, eds. Why is math so hard for some children? the nature and origins of mathematical learning difficulties and disabilities. Baltimore, MD: Paul H Brookes Publishing Co.; 2007.

4 American Psychiatric Association. Diagnostic and statistical manual of mental disorders. 5th ed. Washington, DC: American Psychiatric Association; 2013. https://www.psychiatry.org/psychiatrists/practice/dsm

5 Geary DC. Mathematical disabilities: cognitive, neuropsychological, and genetic components. Psychol Bull. 1993 Sep;114(2):345-362. https://www.ncbi.nlm.nih.gov/pubmed/8416036

6 Geary DC, Bow-Thomas CC, Yao Y. Counting knowledge and skill in cognitive addition: a comparison of normal and mathematically disabled children. J Exp Child Psychol. 1992 Dec;54(3):372-91. https://www.ncbi.nlm.nih.gov/pubmed/1453139

7 Siegel LS, Ryan EB. The development of working memory in normally achieving and subtypes of learning disabled children. Child Dev. 1989 Aug;60(4):973-980. https://www.ncbi.nlm.nih.gov/pubmed/2758890

8 Geary DC. A componential analysis of an early learning deficit in mathematics. J Exp Child Psychol. 1990 Jun:49(3):363-383. https://www.ncbi.nlm.nih.gov/pubmed/?term=Geary+DC.+A+componential+analysis+of+an+early+learning+deficit+in+mathematics.+Journal+of+Experimental+Child+Psychology

9 Hitch GJ, McAuley E. (1991). Working memory in children with specific arithmetical learning disabilities. Br J Psychol. 1991 Aug;82(pt 3):375-386. https://www.ncbi.nlm.nih.gov/pubmed/?term=Working+memory+in+children+with+specific+arithmetical+learning+disabilities.+British+Journal+of+Psychology

10 Landerl K, Bevan A, Butterworth B. Developmental dyscalculia and basic numerical capacities: a study of 8-9 year old students. Cognition. 2004 Sep;93(2):99-125. https://www.ncbi.nlm.nih.gov/pubmed/?term=Developmental+dyscalculia+and+basic+numerical+capacities%3A+a+study+of+8-9+year+old+students

11 Fias W, Menon V, Szucs D. Multiple components of developmental dyscalculia. Trends Neurosci Educ. 2013 Jun;2(2):43-47. [study highlighting that there is no single cause] https://www.sciencedirect.com/science/article/pii/S2211949313000203

12 Bartelet D, Ansari D, Vaessen A, Blomert L. Cognitive subtypes of mathematics learning difficulties in primary education. Res Dev Disabil. 2014 Mar;35(3):657-670. doi: 10.1016/j.ridd.2013.12.010 https://www.ncbi.nlm.nih.gov/pubmed/?term=Cognitive+subtypes+of+mathematics+learning+difficulties+in+primary+education.

13 Siegel LS. Perspectives on dyslexia. Paediatr Child Health. 2006 Nov;11(9):581-587.
https://www.ncbi.nlm.nih.gov/pubmed/?term=Siegel+LS.+Perspectives+on+dyslexia.

14 Program for International Student Assessment (PISA). OECD. http://www.oecd.org/pisa/ Accessed July 31, 2018. http://www.oecd.org/pisa/

15 Beilock SL, Gunderson EA, Ramirez G, Levine SC. Female teachers’ math anxiety affects girls’ math achievement. Proc Natl Acad Sci U S A. 2010 Feb 2;107(5):1860-1863. doi: 10.1073/pnas.0910967107 https://www.ncbi.nlm.nih.gov/pubmed/?term=Female+teachers%27+math+anxiety+affects+girls%27+math+achievement

16 Maloney EA, Ramirez G, Gunderson EA, Levine SC, Beilock SL. Intergenerational effects of parents’ math anxiety on children’s math achievement and anxiety. Psychol Sci. 2015 Sep;26(9):1480-1488. doi: 10.1177/0956797615592630
https://www.ncbi.nlm.nih.gov/pubmed/?term=Intergenerational+effects+of+parents%27+math+anxiety+on+children%27s+math+achievement+and+anxiety

17 Ramirez G, Beilock SL. Writing about testing worries boosts exam performance in the classroom. Science. 2011 Jan 14;331(6014):211-213. doi: 10.1126/science.1199427 https://www.ncbi.nlm.nih.gov/pubmed/?term=Ramirez+G%2C+Beilock+SL.+Writing+about+testing+worries+boosts+exam+performance+in+the+classroom.

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