Korbinian Moeller is Professor of Mathematical Cognition at Loughborough University in the United Kingdom. Korbinian investigates mathematical learning from different angles using different technologies to examine behaviour, cognition, and the brain. He develops learning resources to determine whether his theories about how mathematical skills develop hold when applied to real children. Korbinian tells Eva Amsen about how children acquire mathematical skills, why using fingers helps, and why picking up math at an early age is important.

Eva Amsen: How do young children first learn math concepts?

Korbinian Moeller: Children pick up quantity information from the world they live in. I see this with my own children. For instance, when siblings play together, they care about who has more toy cars. To establish this, they need to have a grasp of what “more” means before they count the cars.

However, “more” goes beyond numerical information. “More” of something is typically associated with it being bigger and/or heavier. This means that the concept of numbers is naturally connected to our perception of the surrounding world. Interestingly, we seem to process the concept of numbers in a similar way to density and other perceptual features in the brain, and this is partly how children start learning about numbers.

While we share an ability to process approximate quantity information with great apes, horses, birds, and other animals, specific math requires symbols like language (i.e., number words) and digits.

Many children begin learning the number words that describe how old they are, but gradually learn more as they start counting and understanding the quantities these number words represent. However, language influences are not limited to number words. Instead, children who better understand spatial terms, like “above” or “below”, also tend to perform better in math. So learning about numbers and math is not isolated – it happens in the context of language and perceptual features, but also bodily experiences like using your fingers.

“By using their fingers, children further develop their understanding of counting, but also basic calculations.”

EA: How do finger counting and calculating help children learn math?

KM: From an evolutionary point of view, numbers are a relatively recent invention as they have only been around for about 3000 years. This is too recent for our brains to have developed a dedicated number area. Instead, we most likely process numbers using parts of the brain that process visual information including perceptual features like density. We also use the brain area that supports finger movements, which seems predisposed to do this because fingers and numbers share some attributes. For example, we distinguish fingers in the same way we distinguish between individual numbers.

By using their fingers, children further develop their understanding of counting, but also basic calculations. For example, children typically count on their fingers in the same order, which helps them reinforce their understanding of number sequences. It teaches them in a playful way that number words and numbers always come in the same order. Stretching out additional fingers and folding them in again also naturally reflect the concepts of addition and subtraction, respectively.

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EA: What is the role of play in learning math?

KM: Children naturally learn through play without formal instruction. My colleagues and I take advantage of this when designing educational math games because they motivate children. The games include math in a narrative and/or award points when children get the math right.

The better we integrate math content into the game’s mechanics, the better it is for learning. For example, in a number line estimation game, players move an avatar along a number line showing only the start and end points. They have to estimate where ¾ is on a number line ranging from 0 to 1, for example. The closer the avatar is to the correct position, the more gold coins it digs up, earning the player more points. Such estimation tasks are valuable for learning math as children who do well in these tasks also do better in other math tasks.

Integrating numbers and math within the gameplay is crucial for maintaining motivation. When the math content is unrelated to the gameplay, children lose interest faster, which colleagues of mine call “chocolate-covered broccoli”.

“Integrating numbers and math within the gameplay is crucial for maintaining motivation.”

EA: Is there a difference in how children learn from a physical game compared to a digital game?

KM: It is hard to give a definite answer to this. In some studies, we incorporated full-body movement into math learning. To stick with the number line estimation example, we taped a three-meter-long number line from 0 to 100 on the floor and asked children to walk to the position of target numbers, like 65. Children learned more in terms of counting, magnitude understanding, and basic arithmetic from physical versions of such games than from digital versions. This does not mean that physical games are always better, but they can provide additional support for the math learning – in particular, when physical activities are meaningfully connected to the learning content, such as walking longer distances for larger numbers on the number line.

EA: Why is it important that children learn math at an early age?

KM: Math is hierarchically organised. More complex topics typically build on earlier ones, so a strong foundation is essential. Basic mathematical skills early in primary school predict later math achievement in fractions, for example, and more advanced topics like algebra. Math is also crucial for everyday life. People with poorer math skills are more likely to encounter financial issues.

“Basic mathematical skills early in primary school predict later math achievement.”

Opinions vary about which basic mathematical skills are most important for early learners. Some argue that children need to understand magnitude to understand numbers. For example, comparing the prices of two chocolate bars requires a basic understanding of magnitude. However, I think focusing only on magnitude is not enough. Math is also about procedures, like understanding the principles of basic arithmetic operations like addition and subtraction. It also requires conceptual understanding, like the fact that anything multiplied by 0 equals 0.

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EA: Have you learnt anything from watching your own children learn math?

KM: Yes, I find it fascinating that my children show more interest in math when it feels useful to them. For instance, math enables them to count their toy cars to find out who has more. And like with many  other skills, I think children need to “use it or lose it” with math, too. For example, we taught finger-based math strategies to first graders and kindergarteners. First graders were able to apply the learned strategies immediately in their regular math lessons and improved in math compared to children who attended regular math lessons only. However, in Germany, where we conducted the study, there is no kindergarten math curriculum, so kindergarteners didn’t benefit from using the finger-based strategies in their everyday lives in a similar way. So, making math useful and relevant helps children learn.

“Making math useful and relevant helps children learn.”

Footnotes

This interview has been edited for clarity.

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