Preschoolers have an intuitive sense of multiplication and division
What do babies and preschoolers know about math? You might assume they know very little, if anything at all. After all, even elementary math requires years of hard work, the memorization of many rules and principles, and constant practice. Emerging research in developmental psychology challenges this traditional view, revealing that preschoolers, infants, and even newborns have some truly astonishing number abilities.
“Preschoolers, infants, and even newborns have some truly astonishing number abilities.”
When newborns hear a sequence of sounds, for example, they will look towards a picture with the number of circles that matches the number of tones they hear. Six-month-olds are surprised when a collection of, say, 16 objects is hidden in a box – and then the same box is revealed to contain only eight. These behaviours point to the existence of an intuitive “number sense” – a quick and approximate way of seeing, hearing, or feeling number without counting. Many developmental psychologists theorize that the number sense is a foundational kernel of mathematical knowledge that is shared across humans and non-human animals alike, from which more advanced mathematical skills may be formed.
Recent research shows that the intuitive number sense can expand to include even more complex mathematical operations and problems, including multiplication and division. For example, in one study, preschoolers watched a video of a bee collecting pollen from flower petals. They were told that each petal holds the same number of pollen pieces (say, five) and that the bee always collects all of the pollen from all of the petals. They were then shown a flower with one visible petal – displaying five pieces of pollen – but the pollen on the other three petals was hidden. Asked to point to the honey pot containing the number of pollen pieces the bee had collected, the preschoolers chose the one with 20 pieces rather than those with 10 or 40. These children had no formal education in multiplication, and performed entirely at chance when asked what 5 x 4 is. Despite lacking this formal knowledge, they appeared to intuitively multiply the pollen on the visible petal by the number of petals to arrive at the approximately correct answer.
“My lab is looking at the possibility that a major problem is in most curricula pushing children away from their intuitive number representations.”
In my own lab, 5-year-old children were shown a collection of three dots and told that they are together called a “toma”. They were then shown collections of between 15 and 63 dots and asked how many tomas they saw. Incredibly – and despite the fact that not all of the children in our sample were even familiar with high number words like “sixty-three” – they responded that they could see about “five tomas” when they were shown 15 dots, about “twenty-one tomas” for 63, and so on. In other words, the children intuitively divided 63 dots by 3 (the “toma”) to arrive at the correct answer, despite having no formal education in division.
Why, then, do children struggle so much to learn multiplication and division in formal school settings? While we don’t yet know the answer to this question, many researchers have reasonable guesses that we are currently exploring. My lab is looking at the possibility that a major problem is in most curricula pushing children away from their intuitive number representations. Math is frequently taught as a domain in which there is always one exactly right answer. Children are trained almost exclusively in procedural skills, such as long division, that will – with sufficient discipline and attention – guarantee the right answer each time.
“Many developmental psychologists hope that the intuitive number sense can be the kernel that makes formal mathematics pop in the mind of every child.”
There’s nothing wrong with this approach, and children should learn how to arrive at exactly the right answer to math problems (I wouldn’t recommend filing your taxes based solely on your intuitive number sense!). But this approach misses a rich set of intuitions that children are equipped with, and their desire to treat mathematics as a domain of exploration and play, rather than strict procedure and discipline. Ongoing research in multiple labs is trying to wed these two approaches, providing children with interactive activities that allow them to flex their intuitive number sense, and then teaching them how to extend this to more systematic, procedural approaches to solving problems. Many everyday experiences, like asking children to estimate the number of toys (or pairs of toys) might help sharpen their intuition about how a set of items might be divided into groups, a key insight for more formal division.
Just as we know that teaching children to read is best done in a setting of fun exploration, celebrating mistakes, and encouraging them to try things their own way, many developmental psychologists hope that the intuitive number sense can be the kernel that makes formal mathematics pop in the mind of every child.