Uni-Tübingen

Gasping numbers

Using our fingers to count and do arithmetic is rooted in all of us. Educational researcher Stephanie Rösch uses these natural abilities to help develop children’s mathematical skills.

Six children are seated around Karin Kullen, an educator at a kindergarten in Metzingen. She is wearing gloves on her hands that are decorated with googly eyes and laughing mouths that the children know as Ed and Ted, the creative duo who regularly play with the five and six-year-old boys and girls in the preschool group. Today they are learning about adding up and determining the difference up to ten. From the games they have already played, the children already know that each number represents a unit. And they have learned that they can represent this number by stretching out their fingers or bending them down. 

The fun starts when Kullen opens a small treasure chest with ten glass stones inside. The kids play against Ed and Ted by rolling some dice for the stones. The aim of the game is to win as many glass stones as they can. Karl, a blond boy sitting at the low table to the left of the teacher, rolls the dice: Four and three. “Seven!” he calls, showing four fingers on his left hand and three on his right. He’s almost right. Ed and Ted’s fingers are positioned slightly differently. Kullen explains: “If you take five fingers on the left hand and two on the right hand, you will see the seven much more clearly.” But that’s a moot point. The children have won the round and receive seven stones from the treasure chest. How many are left? As the children concentrate, they stretch and bend their little fingers. Anastasia is the first to call out the result: “Three!”

Understanding the world of numbers intuitively

Dr. Stephanie Rösch watches the game inconspicuously from a distance. “Here we can see that children naturally use fingers to count. But it’s not just about counting how many fingers are shown. It is important to form finger patterns to understand the world of numbers intuitively.” Rösch is an educational researcher at the Hector Research Institute of Education Sciences and Psychology at the University of Tübingen. In her research project “Fingers and Numbers – Training preschoolers in basic numerical skills with fingers”, she investigates how fine motor skills and finger-based strategies influence the development of mathematical skills in preschool children. The German Research Foundation is funding the project for around five years. Researchers will investigate how children count and calculate using their fingers. The project intends to develop effective play suggestions that can be used to promote mathematical skills in preschool settings. Further, the study provides scientific insights into how motor skills, sensory processes and mathematic ability are related. 

Rösch uses Ed and Ted to teach numeracy in her development program. She tested this in a total of 26 daycare centers for six months. After a preparatory workshop, the educators teach 16 units at their centers independently following her instructions. 

The study is a randomized, controlled intervention study. This type of study is considered the gold standard in research as it involves changing specific variables in a controlled way to determine a precise effect. The participating daycare centers are divided into three groups: The institutions in the first group use the finger-based mathematical training and in the other two control groups the children practice mathematical training without fingers or receive non-mathematical spoken instruction. Rösch and her team of students use special tests to determine for example, how children’s fine motor and mathematical skills in counting and arithmetic change depending on the type of instruction during the project period. 

“This is currently the highest quality survey in this area thanks to its rigorous design. So far, no comparable study has been published with a similar level of detail,” says Rösch.
 


Some children who were indifferent to numbers are now showing great interest. Sitting still for 20 minutes is no longer a problem.


Physical and cognitive processes are related

Rösch’s approach is based on the theory of "Embodied Numerosity". This states that abstract mathematical concepts can also be learned from physical interaction with the environment, for example by counting and calculating using fingers and calling numbers out loud. “Motor and sensory skills, language and other cognitive processes have a reciprocal effect. However, it is still unclear exactly how fingers and numbers interact,” explains Rösch. “That’s why we’re investigating how fine motor skills and finger gnosis, the ability to perceive one’s own fingers without looking, affect early mathematical skills.” 

In terms of promoting mathematical skills, a key point is that children develop an understanding of part-whole relationships. “It is important to understand numbers as sets, which in turn can be broken down into subsets.” The children should grasp with all their senses how the numbers up to ten are composed. This makes it easier for them to develop good arithmetic skills and to move away from mere counting. 

Rösch illustrates this with the scene we have just observed. “Karl rolled a seven. This can be structured into the units four and three; as shown on the dice. However, Karl should not stretch out three fingers on one hand and four on the other but use specific finger sets to represent the quantities: starting with the thumb of one hand until all five fingers are stretched out on it. Then continue on the thumb of the other hand.” In the previous games, the children had first learned to count the finger sets with their palm upwards and then to turn their palm downwards on the table. This makes it easy to perceive the whole number. But now, towards the end of the program, Karl already knows the finger sets well. Therefore, he no longer has to count them but can stretch out the corresponding fingers out at once. 

“This is the decisive step that is not easy to take at the beginning,” says Rösch. “But if the children always form the same set of finger patterns, it will be easier for them in the end to understand part-whole relationships. A glance is enough then to recognize: Seven consists of five and two outstretched fingers, and of the seven, three fingers are still missing until all ten are outstretched.” 

Children can concentrate better 

In practice, the method already has a positive effect. Some children who were indifferent to numbers are now showing great interest, reports Kullen. Their ability to concentrate has also improved. Sitting still for 20 minutes, like now at the exercise table, is no longer a problem. Another interesting observation was also made: “The children also use the finger strategies on other occasions, such as playing in the play area.” 

Kullen and Rösch agree that there is a great need for support in preschool education in general. “In preparing for school, each child brings their own level of development. Support at home also varies,” says Kullen. With the finger method, she can help each child in-dividually wherever they are in their learning. “It is evident that differences in the basic mathematical skills, counting, understanding quantities and basic arithmetic have converged in the group. This has an important inclusive aspect.” Rösch emphasizes: “A finger-based mathematical support concept is also very suitable for children who are less capable of understanding the teaching language.” 

Are fingers really “just for writing”? 

But what do future teachers say about the finger method? Although we often hear that fingers are for writing, not for mathematics, Rösch explains that this is intended to discourage counting to solve arithmetic exercises. Sometimes teachers will stop children counting with their fingers. “But if the child does not yet have any other strategies or 
has not developed an understanding of sets and partwhole relationships, they will just count with something else like pens.”

People count using their fingers all over the world 

“Our approach is not to count with fingers. Instead, we want to understand number structures with our fingers,” she emphasizes. At the same time, she wants to use the children’s intuitive abilities: “Finger counting is a natural ability. Children – and adults – count with fingers in most cultures. In Germany, we start with our thumbs. English 
schoolchildren start with the index finger. In some other regions of the world, people start with the little finger." The aim is not to continue the tradition of counting with 
fingers but to promote a visual understanding of partwhole relationships. 

Rösch is convinced that fingers are an effective tool. “The big advantage from a scientific point of view is that the motor and sensory process coincides when people calculate with their fingers. When Karl represents the number four, he stretches out four fingers in a natural movement. If he taps the four fingers on the table, looks at the fingers and pronounces the number four, this is a multisensory unit.” On the other hand, moving beads on an abacus requires a swiping movement which is distracting. Finally, Rösch’s method has a very practical argument on its side: “You always have your fingers with you!"

About “fingers and numbers – training preschoolers in basic numerical skills with fingers” 

The project is led by Dr. Stephanie Rösch at the Hector Research Institute of Education Sciences and Psychology at the University of Tübingen. It runs from June 2020 to February 2025 and explores the development of basic mathematical skills in preschool children using the “Embodied Numerosity” approach which suggests that physical and sensory experience and the development of mathematical skills are related. A total of 26 daycare centers are participating in the study. The first results of the study are expected to be published by the end of 2024.

Text: Christoph Karcher


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