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What Babies Can Teach Us About Math

A visit with Kristy vanMarle, Assistant Professor of Psychological Sciences

By Spencer Melgren
Published: - Topics: children research lab psychology mathematics

Dr. Kristy vanMarle studies the mathematical abilities of infants and toddlers, seeking new insights into how the human brain develops, formats, and represents concepts of quantity. Basic cognitive quantifying abilities progress into ideas of number, time, and space, and are crucial to the everyday tasks that our adult brains perform. “Babies,” Dr. vanMarle tells SyndicateMizzou, “give you a window into what kind of initial, foundational core [mathematical] capacities are there, how they get elaborated, and what kinds of experiences are necessary for different capacities to come online.”

Dr. vanMarle became interested in developmental psychology as an undergraduate at the University of Arizona. She joined a research lab where she discovered, to her surprise, that babies have intuitive math abilities. “Babies can count. It’s not the kind of counting you think of when people sit there going one, two, three, four, five, or using the count list. But babies have a mechanism in their brain that lets them keep track of numbers of things that they see." Dr. vanMarle’s interest in this mechanism lead her to Yale University for a PhD in Developmental Psychology, and a three-year Postdoctoral Fellowship at Rutgers University’s Center for Cognitive Science. In 2007 Dr. vanMarle joined the MU Department of Psychological Sciences as an assistant professor, and began directing the Developmental Cognition Lab. She now conducts new research into the nature and development of our brains’ quantifying abilities.

Studying infants’ quantifying abilities involves multiple challenges. These abilities are, by their very nature, abstract. A pair of elephants and a pair of apples look completely different, yet the notion of “two” applies to both. This abstraction makes it difficult to design studies that expose the mental processes of subjects, and the problem is compounded by working with infants. “You can’t talk to babies,” Dr. vanMarle points out, “you can’t ask them what they’re thinking , you can’t tell them what you’re investigating or even tell them what part of the task to pay attention to.”

To overcome these obstacles, researchers examine babies’ “looking time,” a measure of their visual attention. Like adults, babies pay more attention to things that they have not encountered before, but over time will lose interest in the same stimuli. Measuring “looking time” involves showing a subject a simple visual stimulus, such as an array of dots, until the subject loses interest. The stimulus is then changed slightly—the number of dots is increased, for example—and the researchers measure whether or not the subject regains interest. “If they can discriminate the new from the old, they’ll look longer at, and recover interest, towards the new item,” Dr. vanMarle notes. This change in interest, inferred from looking time, provides evidence of the subject’s ability to recognize and understand quantity. Studying this ability to discriminate between quantities and other stimuli forms the cornerstone of the Developmental Cognition Lab’s three main projects, the “ratio cross-modal study,” the “rate learning study,” and a study of expectations with physical constraints on substances.

The experiments that Dr. vanMarle and her team perform in developmental cognition have roots in animal cognition literature, and understandings in the two areas frequently overlap. The ability to perceive quantity is not unique to humans. Animals’ representations of quantity are necessarily imprecise (because they don’t have language and a count list), especially for larger quantities, but they still derive an evolutionary advantage from this capacity. Some birds “count” their eggs to prevent other birds from surreptitiously placing additional eggs in the nest. Mammals often count their offspring. Foraging animals must be able to tell which locations offer the most food. Seeing these “similar performance signatures” across species provides strong evidence that these abilities arose from a common “underlying mechanism” deep in our shared evolutionary history.

Examining our innate quantifying capacity casts new light on the process of learning and teaching mathematics. Success at more complex math seems to be contingent on certain basic understandings, Dr. vanMarle tells us, such as “understanding that each number represents a specific quantity,” "knowing that larger numbers are built out of smaller sets,” or being able to simply “judge which of two quantities is greater.” In addition to her work with infants, Dr. vanMarle also studies preschoolers to analyze the relationship between the formal abilities learned in school, like counting verbally or identifying numerals, and how these “new representations map onto ancient, built-in representations.” Dr. vanMarle anticipates that this research will help us understand and address core deficiencies in math before they become problematic for students. Dr. vanMarle is optimistic about the field; “The research has given us a much better understanding of which component skills are necessary for moving on to the next level.”

Dr. vanMarle teaches in both the Developmental Cognition Lab, and in the classroom. In her lab, she works with 8-12 undergraduate students per semester and, currently, two graduate students. To operate the lab experiments requires many people, and Dr. vanMarle works closely with her undergraduates during both design and execution. Her students contribute important insights into the work, identifying “things we take for granted doing these kinds of [studies] all the time.” Her students also keep her “excited about the research.” Outside of the lab, Dr. vanMarle teaches the large developmental psychology class. "It always reminds me of why I fell in love with psychology in the first place,” she says, “why kids are so amazing, why parents are so important, [and] why schools are so important.” Dr. vanMarle appreciates students who question, disagree, and politely challenge her in class; “it gives me a chance to go into the details,” she says. "Cognitive development is not an exact science. We understand human development to the best of what our data tell us so far. It’s always changing, it’s always being modified, and we should be critical in accepting the conclusions.”