At The Conversation, psychology professor Silke Goebel offers some perspective on the differences between the way animals and small children process numbers and the way adults do.

As a researcher in numerical cognition, she tries to focus on how brains process numbers. Her research shows that

Humans and animals actually share some remarkable numerical abilities – helping them make smart decisions about where to feed and where to take shelter. But as soon as language enters the picture, humans begin outperforming animals, revealing how words and digits underpin our advanced mathematical world.

Silke Goebel, “Why animals recognise numbers but only humans can do maths” at The Conversation (July 28, 2021)

Essentially, she says, there are two different types of counting systems. Infants, fish, and bees can recognize changes in number between 1 and 3 but don’t get beyond that. A second, “approximate,” counting ability enables many life forms to detect differences between more and less in much larger numbers.

Children grasp numbers in stages:

When children acquire the meaning of numerical digits, they already know number words. Indeed, the words for small numbers are typically within the first few hundred words that children produce, reciting sequences like “one-two-three-four-five” with ease.

Silke Goebel, “Why animals recognise numbers but only humans can do maths” at The Conversation (July 28, 2021)

Indeed, many nursery rhymes are counting rhymes:

…
Eight, nine, ten
Come again

Eleven, twelve
Dig and delve
…

The rhymes teach children the names of the numbers, which they will need in order to begin working with them.

What’s interesting here is that it takes young children some time to grasp the fact that the last word in the counting sequence doesn’t only describe the order of the object in the count list (the fifth object), but also the number of all objects counted so far (five objects). While this is obvious to the numerate adult, the so-called “cardinality principle” is a conceptually difficult and important step for children, and takes months to learn.

Silke Goebel, “Why animals recognise numbers but only humans can do maths” at The Conversation (July 28, 2021)

Numerical symbols, as opposed to names, make it easier to understand cardinality. 10, 11, 12 — for example — forms a visual pattern of increase in number that is not apparent in “ten, eleven, twelve” But recognition of such a visual pattern is easier when the child can read.

Both the names and the symbols for numbers are unique to human language because, of course, they are abstractions — which is what animals and small children don’t do.

Very early instances of what may be the beginning of counting as a symbol system include incisions made on a shell (80,000 years ago) and a deer horn (51,000 years ago). Early on, it may have been difficult to distinguish counting from record-keeping as such.

It was the development of symbol systems such as the decimal system that enabled the development of complex mathematical theories but they were thousands of years in the making. And they have led us into some remarkable abstract worlds.

There is a current conflict among researchers as to whether our number sense is biological or cultural (nature or nurture). But the conflict appears to miss the point: Elaborate number sense depends on the ability to abstract. If that ability is biological, where exactly is it? If it is cultural, it is an iteration of the ability to abstract.

When comparing the way animals and small children handle numbers, we should keep in mind that animals do not have the ability to abstract. Children do have the ability to abstract but it is latent. Language skills (and the attendant math skills) take years to acquire from nothing. The remarkable thing is that almost all children do it and no animals do.

You may also wish to read: Is our “number sense” biology, culture — or something else? It’s a surprisingly controversial question with a — perhaps unsettling — answer. Mathematics supports a dualist view of the universe. Both concrete and abstract, depending. Both the Chimp Chocolate Stakes and Chaitin’s Unknowable Number. (Denyse O’Leary)

and

The mystery of numeracy: How DID we learn to count? Some animals can do rough figuring but only humans count. It goes beyond counting. Numbers lead to a world of wonders, only apprehended by abstraction.