Preschool children can multiply and divide intuitively

What do babies and pre-school children know about maths? You probably think it's very little, if anything at all. After all, just the basics of maths require years of hard work, the memorisation of many rules and principles and constant practice. But recent research in developmental psychology is challenging this traditional view. It shows that preschoolers, toddlers and even newborns have some truly amazing numerical skills.

Preschoolers, toddlers and even newborns have some truly amazing number skills.

For example, when newborns hear a sequence of sounds, they look at a picture with circles whose number corresponds to the number of sounds they hear. Six-month-old babies are surprised when 16 objects are hidden in a box and - when the box is opened - there are only eight objects inside. These behaviours point to the existence of an intuitive «number sense» - a quick and imprecise ability to see, hear or feel numbers without counting. Many developmental psychologists theorise that number sense is a fundamental core of mathematical knowledge that humans and animals alike possess. According to this theory, further mathematical skills can be learnt from this core.

Recent research has shown that intuitive number sense can expand to include more complex mathematical operations and problems such as multiplication and division. In one study, for example, pre-school children watched a video of a bee collecting pollen from flower petals. The children were told that each petal contained the same number of pollen (for example, five) and that the bee always collected all the pollen from all the petals. They were then shown a flower with a visible petal containing five pollen. However, the pollen on the other three petals was hidden. When the children were then asked to point to the honey pot with the pollen collected by the bee, they chose the pot with 20 pollen and not the ones with ten or 40. These children had not previously had any formal lessons in multiplication and, by chance, gave the correct answer to the question of how much 5 x 4 makes. Although they lacked formal knowledge, they seemed to have intuitively multiplied the number of pollen on the visible petal by the number of petals to arrive at the approximately correct answer.

In my own laboratory, we showed five-year-old children a picture with three dots. We told them that these dots together were called «toma». Then we showed them different pictures with between 15 and 63 dots. We then asked them how many tomas they could see. Surprisingly - and although not all the children in our study were familiar with the labelling of large numbers such as «sixty-three» - they all answered that they could see approximately «five tomas» when we showed them the picture with 15 dots, approximately «twenty-one tomas» for the picture with 63 dots, and so on. In short, the children intuitively divided 63 dots by 3 (the «toma») to arrive at the correct answer - without any formal lesson in dividing numbers.

My lab tests the hypothesis that the main problem with many curricula is that they distract children from their intuitive number sense.

So why is it such a struggle for children to learn multiplication and division in formal lessons? We don't know the answer to this question, but many researchers have plausible theories that we are currently investigating. My lab is testing the hypothesis that the main problem with many curricula is that they take children away from their intuitive number sense. Maths is often taught as a subject in which there is only ever one exactly correct answer. Children are usually only taught to use certain procedures, such as written division, which - with enough discipline and attention - guarantee the right result every time.

Many developmental psychologists hope that intuitive number sense may be the core that allows formal maths to blossom in the minds of all children.

The approach is not wrong and children should learn how to arrive at the exact result of a maths problem (I wouldn't recommend relying solely on your intuitive number sense when completing your tax return!) But it ignores a great treasure trove of children's intuition - as well as their desire to explore maths through play rather than following strict rules and discipline. Ongoing studies in various laboratories are trying to combine these two approaches and offer children interactive activities that allow them to play with their intuitive number sense. Only then do they learn to extend this with more systematic calculation methods to solve problems. Many everyday experiences, such as asking children to estimate the number of their toys (or pairs of toys), could help them to sharpen their intuition about how to categorise a set of objects into groups. This is an important realisation for more formal division.

We know that the best way to teach children to read is through an environment of joyful exploration, where mistakes are celebrated and children are encouraged to try things out on their own. Many developmental psychologists hope that intuitive number sense can be the core that allows formal maths to blossom in the minds of all children.