# Children's Understanding of Number Value Starts Early, Study Finds

Children begin to understand number place value by age 3—much earlier than previously believed, according to a new study in Child Development— and they may be ready for more substantive math lessons in preschool.

"Contrary to the view that young children do not understand place value and multidigit numbers, we found that they actually know quite a lot about it," says Kelly S. Mix, a Michigan State University professor of educational psychology and a co-author on the study, in a statement on it. "They are more ready than we think when they enter kindergarten."

Mix and researchers at Indiana University tested 200 children ages 3-7 on their ability to identify which of a pair two- or three-digit numbers, or of arrays of dots or blocks represented the larger amount. While the researchers found older students performed better on the tasks than did younger ones, children as young as age 3 showed some understanding of place value, particularly when identifying or comparing numbers as opposed to arrays.

Mix found this "remarkable" because, in both this study and previous ones, preschoolers typically don't show much understanding or improvement on place value as shown in manipulatives, such as the base-10 blocks typically used to teach numerical value in elementary school.

"This is not to say children have mastered place value at this age, but rather that they know
more than previous research might lead one to believe," the authors conclude. "Even kindergarten students who are unlikely to have received direct instruction in place value can
accurately identify and compare written numerals—better, in fact, than they can identify and compare pictorial representations of the same quantities. This indicates that children are actively making sense of multidigit numerals they encounter in everyday life."

Mix and her colleagues suggested that young children may become familiar with the symbols for multidigit numbers through normal conversations with their parents and other adults— looking  for an address, for example, or pressing an upper-level elevator button. In particular, Mix found young children were significantly better at identifying the larger of two numbers (such as 614 vs. 461), than the larger of two arrays of dots or blocks.

Moreover, while training kindergarteners in using block manipulatives did not significantly improve their understanding of place values, training using the numerals did significantly improve their understanding, suggesting that teachers can build on students' math vocabulary to help them grapple with early math concepts.

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