How the brain learns to count: the triple-code model and dyscalculia

A number isn't one thing in the brain

Three apples on a table, the word “three,” and the digit 3 are three different formats of the same number. And the brain processes them differently, in different areas and by different mechanisms.

Neuropsychologist Stanislas Dehaene described the triple-code model — one of the most influential theories in the neuroscience of mathematics. This model explains why a child may know the word “five” but not recognize the digit 5 — or the other way around.

The three codes of number

The analog code — a sense of quantity

You see three slices of cake and immediately perceive “three” — without counting. Even infants have this mechanism: six-month-old babies react when the number of objects behind a screen changes.

Instantly recognizing small quantities (up to 4) without counting is called subitizing. It's a basic “building block” of math — if it's weak, the child has to count everything one by one.

The verbal code — number as a word

“Three,” “twelve,” “one hundred five” — counting out loud, memorizing the multiplication table. This code relies on the brain's language mechanisms. That's exactly why children with speech disorders often have difficulties with math too.

The visual code — the digit as a symbol

Writing a number, reading a digit, telling the signs + and − apart. This code develops as the child learns to write and requires visuospatial processing.

How the links between the codes are built

In an adult, all three codes are so tightly linked that they fire at the same time. You see the digit 5 — and you immediately sense the quantity and “hear” the word in your head.

In a child, this network is still being built — through repeated experience of working with number in different formats. That's exactly why it's important to use all three codes at once during lessons: show a dot card, say the number out loud, and write the digit.

What happens in dyscalculia

In children with dyscalculia, the links between the codes form more slowly or with gaps. This explains patterns that seem strange at first glance: a child counts well out loud — but doesn't recognize the same digit on paper. Or works easily with objects — but gets lost when writing down a problem.

Research shows that in children with difficulties in counting, subitizing is limited to 2–3 objects and is significantly slower than in their peers (Schleifer & Landerl, 2011). Where other children instantly see “four,” a child with dyscalculia has to count.

Why fingers matter for math

In the brain, the areas responsible for fingers and for numbers are located next to each other. That's no accident. Finger counting is a normal stage that helps build analog images of numbers.

There is a concept called “finger agnosia” — when a child can't tell which finger is being touched if the hand is hidden from view. Children with this trait more often have difficulties with math. Banning finger counting deprives the child of an important tool for building images of numbers.

What this means in practice

If a child has difficulties with math, look at which of the three codes the problem is in:

• Doesn't recognize digits, confuses similar ones → visual code
• Confuses number words, doesn't understand instructions → verbal code
• Can't see a quantity without counting → analog code

Each case points to a different part of the developing network and calls for a different approach. The atlas on dyscalculia-help.com has specific exercises for each case.