First author

Most children at primary school spend years mastering single-digit addition and multiplication. These precise numerical operations require instruction and can be difficult. But Camilla Gilmore, an experimental psychologist at the Learning Sciences Research Institute at the University of Nottingham, UK, and her colleagues show on page 589 that even preschool children can perform symbolic addition and subtraction problems — if only in approximate terms.

What has been the biggest surprise recently regarding children's aptitude for maths?

It was shown some years ago that infants understand basic numerical concepts. We now know that before they are ever taught maths or the ability to manipulate numerical symbols, children can approximate addition and subtraction. As soon as they learn verbal counting, they can do symbolic addition and subtraction, which is surprising given the struggles often evident in learning exact addition and subtraction.

Why does arithmetic take so long to master if children can solve approximations?

The key is the difference between approximate and exact. Children found our symbolic problems easy to solve. We used visual displays and problems with large differences, and asked them to add, subtract and compare numbers. But the type of maths done at school is exact and has to be learned.

Did you find any surprising gender or socioeconomic differences?

We found no gender differences at all. And children from a broad range of backgrounds could do our symbolic problems.

Were teachers surprised by their students' mathematical abilities?

They were not only surprised that children could solve the problems, but by how much they enjoyed doing them. I think it's because maths is defined by exact maths. We don't think about approximate addition and subtraction. Teachers aren't aware that students have these abilities. We were surprised they could do it without any maths instruction at all.

How might these findings help teachers teach maths?

This is a first, and very simple, study. It's exciting that such remarkable abilities can be shown without a complex study. But it's just a first step. To understand how this could benefit maths education, the next stage is to learn more about how children build on these intuitive competencies in learning formal maths in school.