Early maths
What Counting Really Is: Five Things a Small Child Has to Learn
A child who can say "one, two, three" cannot necessarily count. Five separate ideas sit behind the skill, and each has its own tell-tale mistake.
Most three-year-olds can chant the numbers to ten. Ask the same child to fetch four spoons and you may get two, or seven, or all of them. Saying the numbers and counting are different things.
In the 1970s two researchers, Rochel Gelman and Randy Gallistel, set out what a child actually has to grasp in order to count. They described five principles. Teachers still use them, because each one explains a mistake you will recognise.
1. One number for each thing
Every object gets counted once, and only once. Adults do this without thinking. Small children skip an object, or touch one twice, or say two numbers while pointing at one thing.
What it looks like: the finger and the voice go at different speeds.
What helps: slow down and touch. Move each object as it is counted, from one pile to another. On a screen, point beside each picture.
2. The numbers always go in the same order
One, two, three, four. Not one, two, four, three. The list has to be the same every time or the count means nothing.
What it looks like: a child who counts "one, two, three, five, eight" with great confidence.
What helps: songs, rhymes, counting stairs. This is the part that really is just memorising, and it comes with repetition.
3. The last number is the answer
This is the big one. When you count five apples, "five" is not just the name of the last apple. It is how many there are altogether.
What it looks like: you ask "how many?", your child counts correctly to five, you ask again, and they start counting again from one. They have not yet seen that the count has already answered the question.
What helps: say it back every time. "One, two, three, four, five. Five apples." Then cover them up and ask how many are hiding.
Our game Count It is mostly practice at this idea. A group of pictures appears, your child counts, and then has to choose the number that says how many. Picking the number is the step that matters.
4. Anything can be counted
Apples, claps, jumps, ideas. Counting is not just for things in a row on a table. A mixed group, a spoon, a sock and a toy car, is still three things.
What it looks like: a child who counts toy cars happily but is puzzled when asked to count "things on the table".
What helps: count sounds, steps and days as well as objects.
5. The order you count in does not matter
Start from the left, the right or the middle: the total is the same. Children often believe a group has to be counted in one particular direction.
What it looks like: you ask your child to count again starting from a different object, and they are surprised to get the same number. Or they expect a different one.
What helps: count the same group twice, in two directions, and make a fuss of the fact that it came out the same.
They do not arrive in order
Children pick these up over a couple of years, in fits and starts, and not in the neat order above. A child may be solid on the number list and still shaky on the idea that the last number is the total. That is normal.
It is also why it is worth being patient with a child who "can count to twenty" and still gets small groups wrong. They are not being careless. They are still putting the pieces together.
What to do with this
You do not need to teach the five principles. You only need to count things, often, out loud, with your child watching and joining in. A few habits make it more useful:
- Count real objects more than pictures.
- Touch or move each thing.
- Finish with the total: "Six. Six buttons."
- Count different kinds of things.
- Ask for a number of things: "Can you bring me three?" Giving a set is harder than counting one, and tells you more.
Where the games fit
A screen cannot teach counting. It can give a child a lot of quick practice once the idea has started to form. After Count It, Which Has More asks a child to compare two groups, and Adding Up puts two groups together.
They are HTML5 games, which means they open in the browser on whatever device you have, with nothing to install. Each one is eight questions long, so a round is over in two or three minutes. Then go and count the stairs.