Numbers and counting

Counting by age: reciting to ten is not the same as knowing what ten is

Most four-year-olds can count a small pile and say how many. Most three-year-olds can chant to ten and cannot hand you three. Both are normal — here is the order it happens in.

Short answer

Reciting "one, two, three" and knowing what three is are two different skills, and they arrive about a year apart. Most two-year-olds can say a few number words; most four-year-olds can count a small group of things and tell you how many there are; by five, counting to ten is typical, and counting out a given number of objects ("give me seven") is where the real understanding shows.

Every age below is an average with a wide band around it. A child who is a year behind one line and a year ahead of another is normal.

Counting is at least three skills, not one

When parents say "she can count to ten", they usually mean the child can recite the number words in order. That is real and useful, but it is the smallest part. Gelman and Gallistel's classic study of how children learn to count (1978) pulled the skill apart into principles that develop separately:

Later research traced the cardinality piece in surprising detail. Wynn (1990) showed that children learn what the number words mean one at a time: first "one", then "two" several months later, then "three", and only then, usually between three and a half and four and a half, does the whole system click and the child becomes what the literature calls a cardinal-principle knower. Sarnecka and Carey (2008) found the same staircase. So "counts to ten but can't give me three" is not a contradiction. It is the normal order of things.

What to expect, by age

The ages below are drawn from the CDC's milestone guidance, the studies cited at the bottom, and the National Research Council's review of early mathematics. They describe what is typical, not what is required.

AgeTypically canUsually not yetWorth doing
2–3Says a few number words, often "one, two" and then a jumble. Hands you one thing when asked for one. Sees the difference between one, two and three things at a glance, without counting.Counting objects in order; any idea what "four" means.Count out loud in daily life: stairs, buttons, spoons. Ask for "one" and then "two" of something.
3–4Recites to five, often to ten, in a stable order. Knows "two" and usually "three" as amounts. Starts pointing at objects while counting, with slips: skipped objects, double counts, words running ahead of the finger.Answering "how many?" after counting without counting again. Numerals as symbols.Small sets (up to three or four) with a finger on each thing. "Which plate has more?" Matching groups to dots. No numerals yet.
4–5Counts a set of five reliably with one-to-one pointing, and says the last number as the answer to "how many?" (cardinality). Begins to recognise the written numerals 1–5 and to connect a numeral with a quantity.Counting beyond ten; counting a scattered (not lined-up) group; writing numerals neatly.Count and circle the number, count and trace, draw the dots for a numeral. Lining things up before counting helps.
5–6Counts to ten and usually beyond (the CDC lists "counts to 10" at five). Counts out a given number of objects on request. Compares two sets by counting. Writes numerals 1–10, with reversals (a backwards 3 or 7) still common.Counting on from a number other than one; counting by twos or tens; place value.Count and write 1–10, ten frames, "give me seven". Dot-to-dots to twenty and thirty rehearse the sequence while the hand works.
6–7Counts to 100 by rote, counts on ("start at six: seven, eight…"), adds and subtracts small numbers by counting on or back.Mental arithmetic without fingers; multiplication.Board games with dice, counting money, number lines. This is school territory and the school will lead.

One number that catches parents out: the gap between reciting and understanding is about a year. A child who chants to twenty at three has a good memory. It says nothing about whether they know what twenty is, and nothing is wrong when they cannot give you four.

A worksheet to try

For a 3–4-year-old, start with Count to 3: color the circles (PDF): the child counts one to three pictures and colours the same number of circles, with no numerals involved. For 4–5, Count and circle the number 1–5. For 5–6, Count and write the number 1–10 (PDF). All of the counting worksheets are free, A4 or US Letter, no sign-up.

What actually helps

Most of it is talk, not paper:

What to skip

Drilling the sequence to a hundred at four. Apps that reward speed. Correcting every miscount, which teaches a child that counting is a test. And comparing with the neighbour's child, whose "counts to fifty" almost certainly means reciting.

When to ask someone

Talk to your pediatrician or the preschool teacher if you see several of these together and they are not shifting over a few months:

One of these on its own, in a child who is otherwise curious and chatty, is usually just timing.

Sources

  1. CDC, Learn the Signs. Act Early.: Important Milestones: Your Child By Five Years ("Counts to 10"; "Names some numbers between 1 and 5 when you point to them"). cdc.gov
  2. Gelman R., Gallistel C. R. (1978): The Child's Understanding of Number. Harvard University Press. The five counting principles.
  3. Wynn K. (1990): Children's understanding of counting. Cognition 36(2), 155–193. doi.org
  4. Sarnecka B. W., Carey S. (2008): How counting represents number: What children must learn and when they learn it. Cognition 108(3), 662–674. doi.org
  5. National Research Council (2009): Mathematics Learning in Early Childhood: Paths Toward Excellence and Equity. National Academies Press. nap.nationalacademies.org

Written by a parent, from published developmental guidance — the sources are listed above. It is general information, not medical advice. If you are worried about your child's development, speak to your pediatrician.