Is Counting on Fingers Bad? How Long Kids Can Use Them for Math

Japan’s elementary school curriculum guidelines (2017, in Japanese) say that in grade 1, children should be able to add two one-digit numbers, and do the matching subtraction, “reliably”. Sums like 7 + 8 and 13 − 6 are meant to be secure by the end of first grade. In the United States, the Common Core standards set a similar goal a year later: by the end of grade 2, children should know from memory all sums of two one-digit numbers.

Neither says that fingers are not allowed. The Japanese teaching guide for arithmetic (in Japanese) actually recommends “activities using concrete objects such as counters and calculation blocks”. Still, when parents see a child’s fingers moving under the table at every homework problem, many wonder whether this is all right.

In this post I write about what research says on school children counting on their fingers, and how children move away from them. I wrote separately about addition for preschoolers in Teaching Addition to Preschoolers, so here I keep to school-age children.

Two ideas about fingers

Using fingers is not bad. Fingers are a well-made tool that lets a child see the amounts while calculating. At the same time, there is a view that a child needs to grow out of counting every one-digit sum on their fingers, one by one.

These two ideas do not clash. In my developer interview for MathCal, I said, “I think it is good to turn understanding and practice together, like two wheels.” Fingers are a tool for understanding, and moving away from them is the result of practice. Either one alone is not enough.

What research says about fingers

The link between fingers and math has been studied a lot over the past twenty years or so.

In 2016, Jo Boaler and Lang Chen of Stanford University wrote in an article that stopping children from using their fingers is close to halting their mathematical development. Their main evidence is the link between how well children perceive their own fingers and how they do in math.

In a 2015 study by Ilaria Berteletti and James Booth, children aged 8 to 13 solved one-digit subtraction and multiplication problems inside an MRI scanner. Subtraction activated brain areas used for moving the fingers, and larger subtraction problems brought more activity in areas tied to finger sensation. The authors think that even when children are not counting on their fingers, their mental arithmetic draws on a representation of the fingers.

On the other hand, no research says that using fingers forever is best. A 2008 study by Nancy Jordan and colleagues tested 217 children 11 times, from the start of kindergarten (average age 5.7) to the end of second grade. In kindergarten, children who used their fingers more were more accurate, with a correlation of 0.60. The link weakened year by year and was −0.15 by the end of second grade. The authors conclude that fingers help most when children are first learning number facts, and that the benefit shrinks over time.

A 2016 blog post from Cambridge Mathematics at the University of Cambridge agrees that banning fingers seems unwise, but says it is another matter whether the research shows that everyone should use them all the time.

How children move away from fingers

Moving away from fingers does not happen in a day. Ways of adding go through roughly these stages.

1. Count all. For 4 + 3, put up four fingers and three fingers, then count them all from the start
2. Count on. Keep 4 in mind and fold down three fingers: “five, six, seven”
3. Count on from the larger number. For 2 + 7, start at 7 and count “eight, nine”
4. Build from known facts. 6 + 7 is one more than 6 + 6 = 12, so 13. 8 + 5 is 8 and 2 more to make 10, then 3 left, so 13
5. Just know it. Hear 7 + 8 and 15 comes straight away

Stage 3 is called the min strategy in research. In a 1972 study by Guy Groen and John Parkman, the time first graders took to answer an addition problem grew in step with the smaller of the two numbers. That is easy to explain if they start from the larger number and count on by the smaller one.

But these stages are not climbed like a ladder, one rung at a time. In a 1987 study by Robert Siegler, the same child used several methods depending on the problem: recalling the answer, counting on from the larger number, or breaking the numbers apart. A child who answers 2 + 2 instantly may still move their fingers for 8 + 5. That is normal.

Stage 4, building from known facts, is one bridge for leaving fingers behind, especially making and breaking ten. Once a child can think of 8 + 5 as “8 and 2 more makes 10”, there is no need to count five on from 8 on their fingers. I wrote about this in How to Teach the Making Ten Strategy and How to Teach Carrying and Borrowing.

How long is it fine?

There is no fixed age. In Jordan’s study, too, how quickly finger use dropped varied a lot from child to child.

A rough guide is that finger use is fine through first grade. I also wrote this in Getting Ready for School Math. In grade 2, column addition with two-digit numbers and multiplication tables begin. If a child counts on their fingers for every one-digit step in the middle of a column sum, it is easy to lose track of where they were. If partway through second grade your child is still counting up from 7 one by one for 7 + 8, going back to making and breaking ten is one option.

If a child keeps counting one-digit sums on their fingers in later grades, and other things also concern you, talking to the teacher is one option, as I wrote in When Your Child Is Slow at Math Facts.

What to do instead of telling them to stop

Seeing fingers move, it is tempting to say “Don’t use your fingers.” But if you take the fingers away without giving another way to think, the child simply counts one by one in their head instead. Rather than stopping fingers, here are some things to try.

Ask how. “How did you work it out?” tells you whether they count all or count on. If they count all, show them counting on first.

Use fingers in groups, not one at a time. To show 7, open one whole hand and put up two fingers on the other, instead of raising seven fingers one by one. That turns fingers from a counting tool into a tool for seeing fives and tens.

Make ten partners a game. You put up three fingers and the child puts up seven: “three and seven make ten” learned with the body. Once that is easy, play it with words only.

From fingers to pictures, from pictures to numerals. After fingers come amounts you look at, like counters or dots. Last comes thinking with numerals alone. It need not be hurried, and you can wait for the child to move on by themselves.

The same facts, a little every day. Once a child reaches stage 4, the rest is familiarity. Meeting the same facts many times moves them to stage 5, just knowing. If you push for speed while they are still counting on fingers, they only count faster, so speed can wait until after that.

What MathCal offers

MathCal is a math drill app where children write their answers by hand on the screen. I make it.

The settings for the Basic Calculation Drill include Enable Dots on Number. When it is on, dots matching each number appear above the numerals in the problem. The child can check amounts with their eyes instead of their fingers, so it fits the “from fingers to pictures” stage above. Once they are comfortable, turn it off and solve with numerals alone. In the same settings, No Carrying or Borrowing keeps to problems without regrouping, and addition, subtraction, multiplication and division can each be switched on or off.

To explore how addition works with the hands, there is the Addition Beads lesson, where children learn addition by moving beads. In the interview, I said there is an idea in Montessori education “that children deepen their understanding intuitively while playing with their hands”, and that I designed the app so that idea can be put into practice. A child who counted on fingers sees groups of numbers with the beads, then writes with numerals alone in the drill. It can be used in that order.

Today’s Drill, Today’s Challenge and Today’s Lesson on the home screen are free every day. Choosing any drill or lesson from the full lists requires a one-time purchase. There are no ads. How to start is in Getting Started with MathCal.