Teaching Addition to Preschoolers: Is Counting on Fingers a Good Idea?

Japan’s national kindergarten curriculum (2017, in Japanese) says that for numbers, kindergartens should value “experiences based on the child’s own sense of need in everyday life” so that interest in and a feel for numbers and letters can grow. It does not expect children to be able to add before school. Adding two one-digit numbers “reliably” is listed in the elementary school guidelines as grade 1 content. The timing differs by country. In the United States, the Common Core standards already ask kindergartners to add and subtract within 10, and they list fingers by name, alongside objects, drawings and claps, as a way to represent addition.

Even so, at four or five, children sometimes ask on their own, “What’s two and three?” How should you answer, and where can you go from there? In this post I write about the order in which to introduce addition to children aged 3 to 6, based on research. I keep to sums up to 10.

What helps before addition

Addition sits on top of counting. Before starting, it is reassuring to check three things.

First, the child can count objects one by one without missing any. Second, they understand that the last number counted tells how many there are altogether. Third, they can see small amounts, up to about three, at a glance without counting. I wrote about these in more detail in Saying Numbers Is Not Understanding Them.

If your child still often starts counting over again, it is better to keep playing counting games for a while before moving on to addition.

Objects and situations before symbols

In a 1994 study by Janellen Huttenlocher, Nancy Jordan and Susan Levine, counters were hidden behind a screen, some were added or taken away, and children were asked to lay out the same number as were now hidden. Children could solve this wordless kind of calculation reliably from a little after age two. Earlier work by the same group had shown that this kind of calculation comes before solving the same problems told in words.

This suggests that addition for young children does not have to start with the “+” sign. Start with real things and situations: “You have two snacks and get three more. How many now?” “Three bears and two rabbits. How many animals altogether?” Showing that “you can also write it like this” can come afterwards.

From counting all to counting on

Children’s ways of adding change gradually. Studies such as a 1984 paper by Thomas Carpenter and James Moser describe stages like these.

Count all. For 3 + 2, count out three, count out two, then count everything from the start: “one, two, three, four, five”
Count on. Keep 3 in mind and count only the rest: “four, five”
Count on from the larger number. For 2 + 5, start at 5 and count “six, seven”

The third is called the min strategy in research, because it needs the fewest counts. In their 1989 book How Children Discover New Strategies, Robert Siegler and Eric Jenkins had 4- and 5-year-olds solve addition problems again and again over a long period, recording each problem one by one. Many of the children found the count-on-from-the-larger-number method for themselves without being taught. And they found it not when they were stuck, but while they were already solving problems well.

One reading of this study is that with young children, it is better to provide plenty of chances to count and then wait, rather than drilling a method in first. If you do teach, it is enough to quietly show the next step: “You already know there are 3, so shall we count on from there?”

Is using fingers a good idea?

For preschool addition, fingers are fine. In fact, fingers are the handiest addition tool there is.

In a 2005 study by Marie-Pascale Noël, children at the start of first grade did a task where, with their hand hidden from view, they had to tell which finger had been touched (finger gnosis). Their scores predicted their number skills 15 months later well, but did not predict their reading. The link between fingers and numbers has been studied many times since.

A 2008 study by Nancy Jordan and colleagues followed 217 children from the start of kindergarten (average age 5.7) to the end of second grade. In kindergarten, children who used their fingers more often were more accurate at addition and subtraction facts, with a correlation of 0.60. The link weakened with each year, and by the end of second grade it was −0.15. The authors conclude that finger use helps most when children are first learning number combinations.

So fingers are on a young child’s side when they add. How long school-age children can keep using them, and how they move away from them, I wrote about separately in Is Counting on Fingers Bad?. Here I only write about fingers in the preschool years.

Tips for using fingers

One hand is five. If a child can look at an open hand and say “five” without counting, then 6 to 10 start to look like “five and one”, “five and two” and so on. To show 7, opening one whole hand and then raising two fingers on the other builds the sense of groups better than raising seven fingers one at a time.

Show a number all at once. When you say “Show me three”, the child puts up three fingers together instead of counting them up one by one. With practice, the shape of the hand becomes the shape of the number.

Two hands are ten. All the fingers of both hands make ten. “Fold down three fingers. How many are still up?” leads straight into making and breaking ten. Adding past ten is grade 1 work in Japan, so before school this kind of game is plenty.

Not teaching too much

Here are some things to keep in mind so that addition does not become something a child dislikes.

Keep it short. A few minutes at a time is enough. I wrote about attention at these ages in How Long Can Preschoolers Focus?
Don’t correct too much. If the child says 3 + 2 is “6”, count the objects again together instead of giving the answer
Ask how, not what. “How did you count?” tells you which stage your child is at
On days the child doesn’t ask, skip it. The “sense of need” in the kindergarten guidelines is something that comes from inside the child

Addition in BrainDojo Kids

BrainDojo Kids is an iPhone and iPad app for children aged 3 to 6 that I make. It has several games for thinking about numbers and addition by looking at fingers.

In Finger Addition, two numbers appear as hand shapes and the child writes the sum by hand. Numbers from 6 to 10 are shown as an open hand of five plus another hand, so the child reads them on top of the five. With the age set to three there is Easy Finger Addition with answers up to 5, and from four the problems go up to 10. From five, Finger Math also appears, which mixes in subtraction. There is also Vegetable Addition, where the child adds up vegetables instead of fingers.

In Sugoroku Together, the family board game, one of the mini games is Finger Addition Battle, where two players sit facing each other, solve finger additions, and whoever writes the right answer first wins. If you want to go step by step, the First Math course under Courses starts with counting to 5 and to 10, then moves on to addition and subtraction. The course opens once First Numbers is cleared.

The three daily games in Today’s Training, the four Recommended games and Sugoroku Together are free, and every other game can be tried once. A Premium subscription (monthly or yearly) opens all courses and games. In the parent settings there is a daily time limit, on by default at 10 minutes. There are no ads and no account to create.

Getting Started with BrainDojo Kids covers the first session. After adding on the screen, try the same sums with real counters or with your child’s own fingers. That helps the numbers on the screen connect with the numbers in their hands.