Dyscalculia: understanding and supporting mathematics disorders

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Dyscalculia: understanding and supporting mathematical learning difficulties

Dyscalculia is a specific learning disorder that affects the acquisition of mathematical skills. Affecting 3 to 7% of children, it impacts number sense, calculation, logical-mathematical reasoning and problem solving. This comprehensive guide presents the scientific foundations, clinical manifestations and effective intervention strategies.

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Number line
Number decomposition
Problem solving

What is dyscalculia?

Developmental dyscalculia is a neurodevelopmental disorder that specifically affects the acquisition of numerical and mathematical skills. According to the DSM-5, it is a specific learning disorder with impairment in mathematics, characterized by persistent difficulties in mastering number sense, arithmetic facts, calculation or mathematical reasoning.

This disorder is not the consequence of an intellectual deficit, sensory impairment, lack of instruction or adverse psychosocial factors. Children with dyscalculia have normal intelligence but mathematical performance significantly below what would be expected given their age, grade level and intellectual abilities.

🔬 Prevalence and comorbidities

Dyscalculia affects 3 to 7% of the population, with similar prevalence in boys and girls (unlike dyslexia). It is frequently associated with other disorders: dyslexia (30-70% comorbidity), ADHD (25%), developmental coordination disorder, and math anxiety (which can be both cause and consequence).

Number sense: neuroscientific basis

Number sense (or basic numerical cognition) is an innate ability, present from birth, that allows perception and manipulation of quantities in an approximate way. Neuroscience research has identified the intraparietal sulcus as the key brain region for quantity processing.

Components of number sense

Component	Description	Example
Subitizing	Immediate perception of small quantities (1-4) without counting	Instantly seeing that there are 3 dots
Estimation	Approximate evaluation of large quantities	Estimating there are "about 50" people
Comparison	Determining which quantity is larger	8 is greater than 5
Mental number line	Ordered spatial representation of numbers	Placing 7 between 5 and 10 on a line

In dyscalculia, one or more of these basic components may be deficient, compromising the construction of subsequent mathematical learning. This is why remediation must often return to the foundations of number sense.

Manifestations by age

In preschool (3-6 years)

Difficulty counting in a stable and ordered manner
Does not understand that the last number said represents the total quantity (cardinality)
Difficulty comparing collections (more/less/same)
Does not recognize small quantities without counting (no subitizing)
Confusion with spatial terms (before/after, more/less)
Difficulty with number rhymes

In elementary school (6-11 years)

Difficulty memorizing arithmetic facts (addition and multiplication tables)
Frequent errors in counting
Confusion with place value (tens/units)
Use of immature strategies (counting on fingers late)
Difficulty with word problems
Inversion of digits (12/21) or signs (+/-)
Significant slowness in calculation
Anxiety about mathematics

In middle school and beyond

Difficulty with fractions, decimals, percentages
Proportional reasoning problems
Difficulty in geometry and measurement
Inability to estimate if a result is plausible
Difficulties in daily life: money, time, distances

Differential diagnosis

⚠️ What is NOT dyscalculia

Many children have difficulties in mathematics without being dyscalculic. We must distinguish:

Mathematical difficulties related to inadequate or insufficient teaching
Math anxiety that blocks performance (can coexist with dyscalculia)
Secondary difficulties to a language disorder (comprehension of statements)
Attention difficulties (ADHD) impacting concentration in calculation
Global intellectual deficit affecting all learning

The diagnosis of dyscalculia requires a comprehensive neuropsychological assessment including evaluation of general intellectual level, cognitive functions (attention, working memory, executive functions) and specific mathematical skills. The speech-language pathologist can also perform a logical-mathematical assessment.

Different profiles of dyscalculia

Profile	Main difficulties	Relative strengths
Number sense deficit	Estimation, comparison, quantity representation	Calculation procedures once learned
Procedural deficit	Learning and applying calculation procedures	Preserved number sense
Fact retrieval deficit	Memorizing tables, arithmetic facts	Conceptual understanding
Visuo-spatial deficit	Alignment, geometry, spatial representation	Mental calculation

Remediation principles

1. Strengthen number sense

Before any work on calculation, it is essential to consolidate the foundations: subitizing, estimation, comparison, number line. Regular activities involving quantity manipulation, estimation games, number line placement help strengthen these foundations.

2. Use concrete manipulation

Respect the progression Concrete → Visual → Abstract. Use manipulative material (cubes, Cuisenaire rods, tokens, base-10 material) before moving to representations then symbols. This progression must be maintained even for older children if necessary.

3. Make strategies explicit

Children with dyscalculia do not spontaneously discover effective strategies. They must be explicitly taught: decomposition, bridging through 10, doubles and near-doubles, checking strategies. Verbalize reasoning aloud.

4. Gradually automatize

Once strategies are understood, aim for automatization through spaced repetition. The goal is to free up cognitive resources for more complex tasks. But beware: automatizing too early, before understanding, is counterproductive.

Practical strategies by domain

For numeration

Use the number line as a permanent visual support
Work with base-10 material (physical units, tens, hundreds)
Play decomposition/recomposition games with numbers
Verbalize place value: "42 is 4 tens and 2 units"

For calculation

Teach calculation strategies explicitly (8+5 = 8+2+3 = 10+3)
Use visual supports for tables (Pythagorean tables, cards)
Allow compensation tools (calculator, tables)
Work with fact families (3+4=7, 4+3=7, 7-3=4, 7-4=3)

For problem solving

Use a structured methodology: read, identify data, understand the question, choose the operation, calculate, check
Systematically diagram problems
Work on key words (beware of traps: "more" is not always addition)
Have students estimate the result before calculating

Our downloadable tools

🔢 Manipulable number line

Essential visual support for visualizing the number sequence, making comparisons and calculations by jumps. Several formats available (0-20, 0-100).

Download

🧩 Decomposition cards

Cards illustrating the decomposition of numbers from 1 to 20, with representation in dots, fingers and numerical writing. Ideal for working on complements.

Download

📝 Problem-solving aid

Methodological sheet with resolution steps, pictograms for operations and space for diagramming. Guides the child towards autonomy.

Download

📊 Visual multiplication tables

Tables with visual representation in dot arrays to understand the meaning of multiplication. Aids memorization through images.

Download

School accommodations

Students with dyscalculia can benefit from a PAP (Personalized Accommodation Plan) or a PPS (Personalized Schooling Project) depending on the severity of the disorder. Here are frequently recommended accommodations:

Domain	Possible accommodations
Time	One-third extra time, reduction in quantity of exercises
Supports	Operation tables allowed, calculator, number line
Presentation	Spaced exercises, one operation per line, adapted font
Evaluation	Adapted scoring (valorize reasoning even if calculation is wrong)
Method	Allow personal strategies, finger counting

Frequently asked questions

📌 Is dyscalculia as common as dyslexia?

Yes, dyscalculia has a similar prevalence to dyslexia (3-7% of the population). However, it is much less known and less diagnosed. Mathematical difficulties are often wrongly attributed to a "lack of work" or the false idea that "math is not for everyone".

📌 Who makes the diagnosis of dyscalculia?

The diagnosis is generally made by a neuropsychologist after a comprehensive assessment. The speech-language pathologist can perform a logical-mathematical assessment and contribute to the diagnosis. The physician (neuropediatrician, school physician) validates the diagnosis and can direct towards accommodations.

📌 Does dyscalculia get cured?

Like other DYS disorders, dyscalculia is a lasting disorder but progress is possible with appropriate remediation. The goal is not to "cure" but to develop effective compensatory strategies and strengthen basic skills. With appropriate support, people with dyscalculia can develop sufficient mathematical functionality for their daily and professional lives.

📌 Can my child use a calculator?

Yes! The calculator is a legitimate compensation tool for children with dyscalculia, like glasses for a nearsighted person. It allows bypassing calculation difficulties to access mathematical reasoning. This does not mean abandoning work on calculation, but that the calculator can be used when calculation is not the main objective of the exercise.