← Atlas of Difficulties
S-36
The child counts one by one: gets stuck counting on fingers
Type: operational
What the research says
Getting stuck on counting one by one is the central symptom of difficulties with counting. Children who are good at counting stay stuck at counting one by one not because they are smart, but because they can't do anything else. Counting one by one doesn't let a child build the ordinal-quantitative connections needed to understand the structure of number.
Austrian Federal Ministry of Education. A school-based approach to difficulties with arithmetic., pp. 12–13 (2023)
Finger-counting strategies are a normal stage of development and an important foundation for moving on to structural strategies. The problem is not the fingers; it's when the child doesn't move on from fingers to internal images of number. Banning finger counting is counterproductive.
von Aster, Kaufmann & Lipka, 2015, cited in: Austrian Federal Ministry of Education. A School-Based Approach to Arithmetic Difficulties., p. 9 (2023)
Exercises at home — free
How many? Answer right away, without counting
Builds: Instantly recognizing a quantity by its structure — moving beyond counting one by one
You need: domino tiles or dot cards with the dots in structured arrangements (not in a row), digit cards 1–10
- Show a dot card for 1 second and take it away.
- Ask: “How many were there? Did you count, or did you see it right away?”
- If the child counted, show it again and ask them to find groups: “Here's three and two more — that's five.”
- Gradually increase the number from 2 to 8.
- Use only structured arrangements: two rows, groups of 3.
- Goal: the child names the number right away, relying on the structure.
Austrian Federal Ministry of Education. A School-Based Approach to Arithmetic Difficulties, 2023, p. 14
The twenty frame: I see the number without counting
Builds: Numbers up to 20 as a structure — “part + part = whole” made visible
You need: a sheet of paper with 20 squares (2 rows of 10), 20 identical objects — buttons, coins, counters
- Show the sheet: “This is a twenty frame. Two rows of 10.”
- Put 7 objects in the first row: “How many are here? How did you know?”
- If the child counted, say: “Try to see it: a full five and 2 more.”
- Add 5: “How many now? Don't count — look at the rows.”
- The child names the number, relying on the structure of the frame.
- Harder: cover part of the frame — the child says how many are hidden.
Austrian Federal Ministry of Education. A School-Based Approach to Arithmetic Difficulties, 2023, pp. 14–15
Without help
- Within 100 and beyond, counting one by one is so slow that the child starts avoiding calculations
- The multiplication table doesn't become automatic — there's no foundation of knowing number bonds
- On moving to middle school, the gap with the rest of the class widens sharply
What to work with