Counting on fingers to solve simple arithmetic problems is a common strategy among schoolchildren, although some may not always encourage it.
In a 2023 survey conducted in France, 20% of kindergarten teachers and 30% of first-grade teachers considered counting on fingers to indicate that a student is having difficulty understanding numerical concepts, according to two researchers who conducted the study published by the American Psychological Association.
## Concerns and Positives
Catherine Thevenot, professor of developmental psychology at the University of Lausanne and lead researcher in the study, explains to Agence France-Presse that “our fear as parents or teachers is that the child will get stuck in this stage” without being able to perform more complex calculations.
The researcher added: “In fact, thanks to counting on fingers, children become able to grasp” this process.
In their study, Thevenot and her colleague Marie Crinier followed 211 Swiss children between the ages of four and a half and seven and a half years.
They asked them twice a year to solve up to three sets of arithmetic operations of increasing difficulty: adding two numbers between 1 and 5, adding a number between 1 and 5 and another between 6 and 9, and then adding two numbers between 6 and 9. They observed whether the children used their fingers to do so.
The researchers found that the use of finger counting peaked in children between the ages of five and a half and six years. Before the age of five, the number of children who performed additions without using their fingers was greater than the number who used them to solve arithmetic problems.
By the age of six and a half, 92% of children had used their fingers at least once during the tests.
At the age of seven, 43% of them had used their fingers in previous tests but had stopped doing so. 50% of them were still using them, and only 7% had never used their fingers.
## The First Tool
Thevenot, who published a book entitled “Myths in Mathematics” last summer about learning mathematics, confirms that fingers constitute “the first tool” that enables a child to “define quantity”.
When a child is asked to count a set of three things, “he goes through a complete developmental stage in which he believes that the number 3 refers to the third thing and not to the three things in the group,” according to the researcher.
She added: “By counting on fingers, there is no ambiguity; the child feels the issue in his body: each time he raises a new finger, the quantity increases.”
But the child must also understand the principle of “one-to-one correspondence”, that is, that “each thing has its own word,” according to Thevenot, who says: “With fingers, it is very clear: each time he pronounces a word, he raises a finger.”
Also, children who count on their fingers had “already begun to develop these principles,” and with practice, they gradually move to “strategies that rely increasingly on mental abilities.” For example, by imagining 3 fingers in one hand and 4 fingers in the other hand to solve the arithmetic problem 3 + 4, then raising the five fingers of the first hand before continuing to count with the others.
In the study, the best-performing children were those who had counted on their fingers in earlier stages and stopped doing so later. At the age of six, the children in the aforementioned category outperformed all those who had never counted on their fingers and those who continued to do so.
The weakest performing children were those who had never counted on their fingers.
Although counting on fingers is a “fairly normal” behavior, some children do not do it on their own, and “it can be taught to them,” according to the researcher.
If a child is 7 and a half years old and continues to use his fingers, “it is because he still needs this stage for several reasons. And we must let him do so,” according to the researcher’s advice.
