Introduction
For many years, mathematics was viewed as a subject that children learn only through formal instruction in school. However, over the past four decades, research in developmental psychology, cognitive science, and neuroscience has challenged this long-held assumption.
A growing body of scientific evidence suggests that human infants can distinguish between small quantities within the first few months of life, even before they learn to count or understand number words such as one, two, and three. This remarkable early ability is known as Number Sense or Numerosity.
This article reviews some of the landmark studies that have shaped our understanding of early mathematical cognition and demonstrates that the foundations of mathematics begin developing long before children enter school.
What Is Number Sense?
Number sense is the innate ability to perceive and distinguish small quantities without counting.
For example:
- Imagine two balls placed on a table.
- If a third ball is added without asking anyone to count, even a young infant is likely to notice that something has changed.
- Although the infant does not know the word three, they can detect that the quantity is different.
It is important to understand that this is not counting. Rather, it is the brain’s natural ability to perceive and compare quantities—a foundational cognitive skill that supports later mathematical learning.
Early Research on Number Sense in Infants
1. Starkey and Cooper (1980)
One of the earliest and most influential studies on infant number perception was conducted by Prentice Starkey and Richard G. Cooper in 1980.
The researchers studied infants between 16 and 30 weeks of age using a technique known as the Looking Time Method, a widely accepted method in developmental psychology for investigating infant cognition.
During the experiment, infants were shown a series of visual slides.
- The first slide displayed two dots.
- The following slide displayed three dots.
Rather than asking infants to respond verbally—which is impossible at this age—the researchers measured how long the infants looked at each image.
The findings were striking. When the display changed from two dots to three dots, infants looked at the new image significantly longer.
Longer looking times indicate that infants detected something novel or unexpected. In this case, the increased attention suggested that they noticed the change in quantity.
Although the infants were far too young to count, they were able to distinguish between two and three objects.
2. Strauss and Curtis (1981)
A year later, Strauss and Curtis (1981) extended this research using photographs of everyday objects instead of simple dot patterns.
To ensure that infants were responding specifically to number, the researchers systematically varied other visual characteristics:
- the size of the objects,
- their colour,
- and their spatial arrangement.
The only feature that remained constant was the number of objects.
This careful experimental design ruled out the possibility that infants were simply reacting to changes in colour, size, or position.
The results closely mirrored those of the earlier study.
Whenever the number of objects changed from two to three, infants looked significantly longer at the new display.
These findings provided further evidence that infants were sensitive to changes in quantity rather than to other visual properties.
What Do These Studies Tell Us?
Together with many subsequent studies, these experiments support an important conclusion:
Infants can discriminate between small quantities even before they learn to count.
In other words, young infants:
- do not know number words such as one, two, or three;
- cannot count verbally;
- yet can detect changes in small numerical quantities.
Researchers refer to this early ability as Numerosity or Early Number Sense.
Is Number Sense Innate?
Whether number sense is entirely innate remains an active area of research. Nevertheless, a substantial body of evidence suggests that humans are born with a biological predisposition to perceive quantity.
When infants only a few weeks or months old consistently distinguish between small quantities without formal teaching or extensive experience, it is difficult to argue that this ability has been learned solely from the environment.
For this reason, many cognitive scientists propose that the human brain is equipped with an evolutionarily developed system for processing quantity, often referred to as the Approximate Number System (ANS). This early system provides the foundation upon which later mathematical knowledge is built.
However, it is equally important to clarify what this does not mean.
Being born with number sense does not mean that children are born knowing mathematics.
Skills such as counting, arithmetic, fractions, algebra, and mathematical reasoning require years of instruction, meaningful experiences, and deliberate practice. Number sense simply provides the cognitive foundation that makes this learning possible.
Evidence from Neuroscience
Neuroscience also provides compelling evidence for the biological basis of number processing.
Mathematical cognition researcher Brian Butterworth has documented patients who experienced damage to specific brain regions responsible for numerical processing.
In several cases:
- language abilities remained largely intact;
- general reasoning skills were preserved;
yet the individuals:
- struggled to understand numerical quantities,
- were unable to perform even simple calculations,
- and found it difficult to recognise or compare numbers.
These neurological cases suggest that numerical processing relies on specialised brain systems rather than being merely a by-product of language or general intelligence.
Tobias Dantzig’s Perspective
In his influential book Number: The Language of Science, mathematician and historian Tobias Dantzig argued that humans possess a primitive ability to detect changes in small collections of objects.
According to Dantzig, people can often recognise when an object has been added to or removed from a small group without consciously counting.
Although modern cognitive science explains this phenomenon in much greater detail, Dantzig’s observations anticipated many of the ideas later confirmed by empirical research on number sense.
What Does This Mean for Teachers and Parents?
If children are born with an early sense of quantity, then early mathematics education should build upon this natural foundation rather than focusing exclusively on memorising counting sequences.
Young children benefit from experiences that encourage them to:
- compare small quantities;
- recognise quantities without counting (subitising);
- observe what happens when objects are added or removed;
- understand relationships such as more, less, and equal;
- explore numbers through play, conversation, and hands-on activities.
These experiences strengthen children’s intuitive understanding of quantity and prepare them for formal learning of counting, arithmetic, and higher-level mathematics.
Conclusion
Research from developmental psychology, cognitive science, and neuroscience consistently suggests that number sense is one of the earliest cognitive abilities to emerge in human development. Even within the first few months of life, infants can distinguish between small quantities despite having no knowledge of counting or number words.
This early ability forms the foundation of later mathematical learning. However, innate number sense alone is not sufficient. High-quality teaching, rich mathematical experiences, meaningful interactions, and sustained practice are essential for transforming this early intuition into strong mathematical understanding and competence.
Recognising that children come to school with an emerging sense of quantity can help educators design learning experiences that build on children’s natural abilities rather than beginning from the assumption that they know nothing about numbers.
Key References
- Butterworth, B. (1999). The Mathematical Brain. Macmillan.
- Dantzig, T. (1954). Number: The Language of Science. Macmillan.
- Dehaene, S. (1997). The Number Sense: How the Mind Creates Mathematics. Oxford University Press.
- Starkey, P., & Cooper, R. G. (1980). Perception of Numbers by Human Infants. Science, 210(4473), 1033–1035. https://doi.org/10.1126/science.7434014
- Starkey, P., Spelke, E. S., & Gelman, R. (1990). Numerical Abstraction by Human Infants. Cognition, 36(2), 97–127. https://doi.org/10.1016/0010-0277(90)90001-Z
- Strauss, M. S., & Curtis, L. E. (1981). Infants’ Perception of Numerosity. Child Development, 52(4), 1146–1152. https://doi.org/10.2307/1129500