The amount of time parents spend talking about numbers has a much bigger impact on how young children learn mathematics than was previously¹ known, researchers at the University of Chicago have found. For example, children whose parents talked more about numbers were much more likely to understand the cardinal² number（基数） principle--which states that the size of a set of objects is determined³ by the last number reached when counting the set (e.g., a set of 10 items is larger than a set of seven items).

"By the time children enter preschool, there are marked individual differences in their mathematical knowledge, as shown by their performance on standardized⁴ tests," said University of Chicago psychologist Susan Levine, the Stella M. Rowley Professor in Psychology⁵ and the leader of the study. Other studies have shown that the level of mathematics knowledge entering school predicts future success.

The results of the study were published in the article, "What Counts in the Development of Young Children's Number Knowledge?" in the current issue of Developmental Psychology. Joining lead author Levine in the study were four other scholars.

"The findings underscore the important role that caregivers can play in children's early mathematical learning," said Soo-Siang Lim, program director for the National Science Foundation's Science of Learning Centers Program. NSF partially⁶ funded the research.

"The frequency with which parents' talk with their toddlers（初学走路的孩子） about numbers, such as counting the number of objects in spatial⁷（空间的） arrays and labeling these set sizes, predicts their children's understanding of numbers," said Lim.

"These findings suggest that encouraging parents to talk about numbers with their children, and providing them with effective ways to do so, may positively⁸ impact children's school achievement," said Levine.

Although other researchers have examined early mathematics learning, the University of Chicago team is the first to record parent-child interactions in the home and to analyze⁹ the connections between parents' number talk and subsequent performance.

Parents often point to objects and say there are three blocks on the floor, for instance. Children can repeat a string of numbers from an early age, but saying "one, two, three" is not the same as actually knowing that the words relate to set size, which is an abstraction.

Frequent use of number words is important, even if the child doesn't seem to pick up on the meanings of the number words right away, Levine said. Children who hear number words in everyday conversation have a clear advantage in understanding how the count words refer to set size. To perform the study, team members made five home visits and videotaped interactions between 44 youngsters and their parents. The taping sessions lasted for 90 minutes and were made at four-month intervals¹⁰, when the youngsters were between the ages of 14 and 30 months.

The variation in number words was startling for researchers as they reviewed tapes of the 44 youngsters interacting with their parents in everyday activities. Some parents produced as few as four number words during the entire period they were studied, while others produced as many as 257.

"This amount of variation would amount to a range of approximately 28 to 1,799 number-related words in a week," said Levine.

Those differences were shown to have a big impact at the end of the study, when the children were asked to connect the words for numbers with sets of squares presented on sheets of paper. For example, those children who heard a lot of number talk were more likely to respond correctly when shown a set of five squares and four squares and asked to "point to five."