What is Dyscalculia?

Clarifications / Implications

Domain specific abilities

Domain specific abilities refer to abilities processing the magnitude of sets or numerical symbols.

Babies have an approximate number system (ANS) that allows them to differentiate between two collections of objects if they differ from one another by a sufficient ratio (i.e., a ratio of 1:2 such as between a collection of 8 versus 16 items). They are also able to see the difference between two very small sets of 1, 2 or sometimes 3 objects based on a mechanism called the object tracking system (OTS). The ANS is used later in development when required to estimate, without counting, the number of elements in a set and the OTS, to subitize, i.e., to precisely and very quickly determine the number of items of a very small set (up to 3 or 4).

Preschoolers learn number words (“one”, “two”, “three”,…) and develop an exact number representation based on the successor function (a number (n) has the same value as the preceding one in the counting list plus one (n+1) e.g., “six” refers to the same quantity as “five”, plus one). This exact number representation is progressively modified to incorporate the base-10 representation of numbers (now “twenty-five” is not solely understood as “twenty-four plus one” but as corresponding to “two times ten plus five”). Later, new symbolic systems are integrated in the magnitude representation: fractions, percentages, decimals, negative numbers ….

Domain general abilities

Domain general abilities refer to cognitive skills that are not specific to the processing of numbers but which play a significant role in several number processing or math skills, as well as other domains.

Working memory is a key factor for most learning, including mathematics learning. Working memory predicts the extent of the young child’s number vocabulary, the ability to learn the count sequence, the ability to solve simple additions and then to store in memory the solution of these calculations. Even solving the problem 5+4 by counting 6,7,8,9 requires working memory. It is obviously involved when doing mental calculation as solutions of intermediate calculations must be kept active in working memory. It is important when solving a mathematics problem: holding all the information to find a way to create the mathematical model of the problem.

Visuo-spatial processing or reasoning is important to differentiate between symbols such as 5 and 2, 6 and 9, < and >, to use visual representations of number (e.g. number lines), to detect and differentiate the positions of digits in multi-digit numbers (24 and 42 are not the same), to correctly position digits in written calculations, to interpret graphs, to visualize situations presented in a word problem and obviously, to solve most geometrical exercises.

The first symbolic system that the child encounters is number words and language impairment leads to difficulties in learning these words and their order. Learning the times tables also uses language as multiplication facts are stored as verbal routines. Sufficient language capacities are also important for understanding word problems presented, but also, the teacher’s explanation or instructions for an exercise. More globally, language supports our thinking. Consequently, language impairment will often lead to very broad (but not specific) difficulties in mathematics. Therefore, in addition to the math skills described above, language impairments (dyslexia or even more strongly, developmental language impairments) can negatively affect any mathematical activity that requires verbal retrieval of facts, rules and procedures, or relies on verbal understanding.

Inhibition is the cognitive ability to deliberately suppress impulsive or automatic responses, particularly those involving dominant, familiar, or overlearned strategies, when they are inappropriate for the task at hand. For example when:

• dealing with the comparison or the addition of rational numbers as one needs to resist the natural number bias, i.e., the tendency to process the numbers of fractions or decimals as if they were natural numbers.
• using keywords in problem solving blindly for example seeing “more” and impulsively choosing addition, even if the problem requires subtraction or comparison.
• simplifying an arithmetic expression: you should resist doing the first operation presented on the left hand side and respect the order of mathematical operations
• applying vertical subtraction, students must resist subtracting the smaller digit from the larger and instead use the borrowing rule. Vertical addition—where digit size doesn’t matter—is taught first and becomes the dominant habit and students need to resist that instinct.
• in geometry, students should resist automatically applying the Pythagorean Theorem or right-angled triangle ratios to non-right-angled triangles, suppressing familiar but inappropriate strategies.
• when simplifying an algebraic expression, failure to suppress the overlearned response “if there’s an equals sign, I must solve for x” and continuing as if it’s an equation, trying to “solve” it.

Hypersensitivity to interference in memory refers to the difficulty in filtering out competing, irrelevant, or overwhelming information, which disrupts the formation and retrieval of accurate memory traces. This can hinder the ability to encode distinct pieces of information—for example:

• distinguishing between similar arithmetic facts, such as 3×8 = 24 and 4×8 = 32, which involve the same digits (2, 3, 4, and 8) but represent different operations and outcomes
• differentiating between similar but conceptually distinct mathematical facts or procedures such as 3×2 from 32 or (a+b)x2 from (a+b)2 or x+x from x∙x
• correctly beginning to solve a multi-step equation, but midway forgetting which step they’re on or mixing steps together, due to mental interference from prior steps or unrelated thoughts.
• given a geometric figure with many labels, auxiliary lines, or extra shapes, difficulty distinguishing/isolating the part they need to answer the question.
• distinguish the competitive formula of the area of a triangle (½ × b × h) and the area of the trapezoid (½ × (a+b) × h) or confusing the formula for the area of a circle (πr2) with that of the circumference (2πr) — not due to misunderstanding, but because both formulas compete in memory and they can’t block one out.
• mixing up minus signs with dashes or misreading the variable “l” as the number “1” because too many similar visual forms compete.
• in functions problems like f(g(x)), forgeting which function to apply first or reversing the order, not due to a lack of knowledge, but because both operations are held in mind and interfere with each other.

Shifting/flexibility refers to a student’s ability to switch between tasks, strategies, rules, representations, or perspectives when a problem changes or requires a new approach – for example:

• in a worksheet that mixes addition and subtraction, continuing to use the same operation (e.g., adds even when a subtraction sign is clearly present).
• difficulties perceiving different representations of the same number e.g. 0.5 and ½
• in calculations, struggling to choose the most efficient strategy based on the problem’s structure—for example, solving 99 + 27 with vertical addition instead of rounding 99 to 100 and adjusting mentally.
• in problems involving parallel and intersecting lines, struggling to switch to the appropriate angle type—such as alternate, corresponding, or vertically opposite angles—depending on the context.
• when solving quadratic equations, always using the quadratic formula—even for simpler cases like x2−3x=0, instead of choosing a more efficient method like factorisation.
• in function problems that include both the graph and the corresponding equation, students may understand them separately, but struggle to connect them or move fluidly between the two representations to solve the problem.