# Crying, Cooing, and Calculating?

We all know babies are hardwired to eat, sleep, and be cute. But do they also know how to count?

This is just one of the questions Kelly Mix investigates in her laboratory in the Indiana University Bloomington Department of Psychology. An assistant professor of psychology, Mix carries out a variety of research projects related to mathematical development in infancy and early childhood, including the question of number concepts in babies and how children learn fractions.

A former elementary teacher who specialized in math education and a mother of two, Mix came naturally to the study of mathematical concepts in children.

“I like to think of ways to test abstract concepts in children who can’t say very much or complete a paper test,” says Mix. “I like to observe children and learn from them. It’s so interesting to see how they go about solving everyday tasks. Kids are fascinating to watch—I spend a lot of time watching my own.”

By studying what pre-schoolers understand about math and how these understandings develop, Mix hopes to inform teachers and parents about what kids bring to school and how teachers can build on children’s informal knowledge.

But how do preverbal babies exhibit numerical thinking? According to Mix, a major source of evidence is research showing that babies react when set sizes change. One experimental design involves showing babies a series of displays with the same number of items until they lose interest. For example, they may see a series of displays with two squares. Pretty soon, they become bored. At this point, two additional test displays are shown: one is a set of two new squares, and the other features a new number, say three.

“Infants’ looking times usually go way up when they see the new number, but not when they see the new display of the familiar number,” says Mix. “This suggested that infants know the difference between two and three.”

Mix’s research, however, proves that it’s not that simple.

She points out that several things change when you go from two objects to three objects: the number increases, but so does the surface area and contour length of the objects. The ratio of foreground to background also changes, as does the brightness of the display. Mix wondered, “Are babies reacting to these cues and not quantity?”

To find out, Mix and graduate student Melissa Clearfield designed a study to focus on contour length (all the edges of the items added up). First, she habituated babies to identical squares with a total content length of 16 cm. Then she showed two different test displays: one featuring two bigger squares (a contour length of 24 cm), and one with the original contour length but a new number (three squares with a total contour length of 16 cm).

Just as she thought, the babies showed more interest in the new contour length.

“This suggested that in the previous experiments, infants were really noticing the change in contour length when the set size changed, not the change in number per se,” says Mix.

Since discovering that babies are not innately prepared to notice number in these displays, Mix has been investigating what does get them to notice number. Previous research has shown that infants use movement cues to tell objects apart. For example,if a baby sees a ball roll across the floor, she can tell that the floor and the ball are separate. Similarly, banging two blocks together tells the baby that the blocks are not connected. Using a similar contour-length experiment, Mix is now comparing infants’ responses to moving squares with their responses to static squares. “Maybe,” she says, “babies will attend to number for the moving displays even though they don’t for static displays.”

Such research has earned Mix honors: she recently received the American Psychological Association’s Boyd McCandless Award for significant and distinguished contributions to developmental science within seven years of completion of the doctoral degree.

In this age of cutthroat assessment and aptitude exams, Mix warns parents not to press the math issue. “There’s a danger in forcing things, and I think that children guide their own learning to a large extent,” she says. “Just mentioning number when it comes up is an easy thing to do. When you’re giving your child some crackers, ask if he’d like two or three. The set you produce will be feedback about the word’s meaning.”

To bring your child in for an experiment in the Mix lab, contact Char Wozniak, chwoznia@indiana.edu.