Numerical Acquisition in Children

Clinton Early Learning Center students Dalton Eisenhut and Isidor Marcus with Celia Yu '12 and Masaaki Kamiya.
Clinton Early Learning Center students Dalton Eisenhut and Isidor Marcus with Celia Yu '12 and Masaaki Kamiya.
If you told your 10-year-old nephew to eat three pieces of broccoli before he could eat dessert, he could probably figure out that eating four or five pieces would still get him that sundae. But at what age do children learn to distinguish ‘at least n,’ ‘at most n’ and ‘exactly n’ and apply them? Celia Yu ’12 received an Emerson grant to study the numerical acquisition of children with regard to their interpretation of such expressions.

Although the implications of the expressions ‘at most n,’ ‘at least n’ and “exactly n” are very clear to adults, they had to learn the meanings and differences as children. Children’s linguistic development is a subject often covered by psychologists, but studying the semantics and acquisition of these expressions bridges the gap between the study of linguistics and psychology. Yu’s advisor, Associate Professor of East Asian Languages and Literatures Masaaki Kamiya, has experience in linguistics, which blends well with Yu’s major in psychology and minor in Japanese. Together, Kamiya and Yu designed an experiment to determine the age at which children understand these expressions as well as the various factors that affect the children’s interpretations.

In 2003, a researcher named Julien Musolino conducted an experiment similar to the one Yu and Kamiya designed. Although he determined that the children had an understanding but don’t understand the exact meaning of “at least” or “at most,” “[Musolino’s] method and age group are a little suspicious,” Yu said. “We’re going to redo the experiment and change a few factors so we can figure out the age at which children can understand ‘at least’ and ‘at most’.” Although Musolino's results are interesting, it seems that children in Yu’s study understand the literal meaning of 'at least' and 'at most' earlier than in Musolino’s.

To get the best results, Yu and Kamiya created conversation-based scenarios that can be repeated without directly affecting the children’s behavior. Pictures on a PowerPoint accompany the words: “Barbie tells Batman to move at least three cars so he can get ice cream. Does Batman get the ice cream?” Depending on how the five- and six-year-old subjects respond, Yu can determine whether or not they understand the concept of the expressions.

Yu and Kamiya are also testing for the influence of individual versus set presentation of the images. The way the images are presented, whether individually or grouped together, may influence the way children see and interpret the scenario. So far there does not seem to be any significant influence, but Yu will have to further analyze the statistics in order to determine whether the presentation makes a difference in the results.

After their first round of testing, Yu saw a possible correlation between a child’s education and understanding of the concepts, even at age five; the two five-year-olds from the Clinton Elementary School had a better understanding than did their peers of the same age at the Clinton Early Learning Center.

“You never really get taught how to interpret things like this. It’s significant that we understand how children figure it out so we can see how we figure it out,” Yu said.

Yu is a graduate of the Manhattan Center for Science and Mathematics and is an Opportunities Program student.
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