← Atlas of Difficulties
S-01
The child can't see a quantity without counting (impaired subitizing)
Type: practognostic
What the research says
Among the characteristic symptoms of dyscalculia are a poorly formed sense of the quantitative relationships between numbers and difficulty determining the number of objects simultaneously. Children struggle to compare numbers of beats, to count the beats in a given rhythm, and to determine the number of objects simultaneously.
Lalaeva R.I. Dyscalculia in Children, p. 23 (2005)
An insufficient level of development of simultaneous analysis and synthesis, which is what makes it possible to master the concept of number and the structure of number, is one of the leading mechanisms of dyscalculia.
Lalaeva R.I. Dyscalculia in Children, pp. 24–25 (2005)
Simultaneous determination of the number of objects is impaired in dyscalculia — children find it hard to determine the number of objects all at once and to establish the order and place of each element within a class.
Baryaeva L.B., Kondratyeva S.Yu. Dyscalculia in Children, p. 31 (2013)
The three codes of number (the triple-code model) — analog, verbal-phonological and visual-Arabic — are so tightly linked neurofunctionally in competent adults that they are activated simultaneously and automatically. In children, this network forms gradually through repeated experience with different formats of number.
Dehaene, 2012, cited in: Austrian Federal Ministry of Education. A school-based approach to difficulties with arithmetic., p. 7 (2023)
In children with difficulties in arithmetic, subitizing (quickly recognizing small quantities without counting) is limited to two or three objects; when reaction times are measured precisely, the process is statistically significantly slower than in their peers.
Schleifer & Landerl, 2011, cited in: Austrian Federal Ministry of Education. A school-based approach to difficulties with arithmetic., p. 9 (2023)
Finger counting is an important stage in forming the neurocognitive representation of numbers: in the brain, fingers and numbers are represented in neighboring areas. Finger agnosia (the inability to match the tactile sensation of a finger with its image) is linked to difficulties in building number knowledge. Finger counting should not be forbidden in primary school.
von Aster, Kaufmann & Lipka, 2015; Reeve & Humberstone, 2011, cited in: Austrian Federal Ministry of Education. A school-based approach to difficulties with arithmetic., p. 9 (2023)
To count correctly, a child has to master three principles: one-to-one correspondence (one number word for each object), a stable order of number words, and the cardinality principle (the last number said = the size of the whole set).
Gelman & Gallistel, 1978, cited in: Austrian Federal Ministry of Education. A school-based approach to difficulties with arithmetic., p. 8 (2023)
Exercises at home — free
How many without counting
Builds: Instant perception of quantity (subitizing)
You need: dice or dot cards (1–6), a stopwatch
- Show a dot card for 1–2 seconds and take it away.
- The child says how many there are — not counting one by one, but “grabbing” the amount with a glance.
- If it doesn't work, show the card for longer and let them study the arrangement of the dots.
- Gradually shorten the showing time.
- Harder: show two dice at once — how many dots in total?
Lalaeva R.I. Dyscalculia in Children, 2005, ch. 3
Find the same amount
Builds: Matching quantities without counting
You need: domino tiles or dot cards, coins or counters
- Show one half of a domino tile.
- The child lays out the same number of coins next to it — by eye, without counting.
- Check together: do they match? If not, where are there more?
- Harder: both halves of the domino — lay out as many coins as there are dots in total.
- Goal: the child learns to match quantities visually, without counting one by one.
Lalaeva R.I. Dyscalculia in Children, 2005, ch. 4
A number line with dots
Builds: Subitizing, ordinal counting, linking quantity and number
You need: 12 dot cards from 1 to 12 (you can draw them by hand), a strip with 12 spaces
- Spread the dot cards out on the table in random order.
- Pick up the card with one dot and say: “One dot is one. Which card comes next?”
- The child finds the right card and explains the choice.
- Together, lay the cards out in order from left to right.
- When the row is ready, remove one card and ask: “Which one is missing?”
- Harder: the child lays out the row alone, and the adult looks for the “mistake”.
Baryaeva L.B., Kondratyeva S.Yu. Dyscalculia in Children, 2013, pp. 83–84
The number path: counting forwards and backwards
Builds: Counting forwards and backwards within 10, naming a number's neighbors
You need: digit cards 0–10, small objects such as pebbles or buttons
- Lay the digit cards from 0 to 10 in a row on the floor — this is the “path”.
- Ask the child to say all the numbers in order, touching each one with a finger.
- Talk about it: “Where do we see numbers in everyday life?” — house numbers, ages, floors.
- Remove one card: “Which one has gone?”
- Ask the child to say the numbers in reverse order: from 10 down to 0.
- The “Neighbors” game: you say a number, the child says which comes before and after.
- Harder: the cards are shuffled — the child restores the order alone.
Baryaeva L.B., Kondratyeva S.Yu. Dyscalculia in Children, 2013, p. 86
Put the number line back together
Builds: Restoring a sequence of digits, finding the mistake in a row
You need: digit cards 1–10
- Spread the digit cards out on the table in random order.
- Pick up the card with the digit 1: “This is the first. What comes next?”
- The child finds the 2 and places it alongside.
- Continue to 10, saying out loud: “After three comes four, because...”
- When the row is ready, remove one card and swap two others.
- Ask: “What's wrong? Find it and explain.”
- Harder: the child lays out the row and makes one deliberate mistake — you guess which.
Baryaeva L.B., Kondratyeva S.Yu. Dyscalculia in Children, 2013, p. 87
Without help
- Constant counting one by one slows down every calculation — the child can't keep up with the class
- Can't quickly compare two groups: has to count each one
- No image of number as a structure forms — the addition table doesn't stick