# Study reveals children see number lines in different ways

Phone numbers, credit card numbers, passwords, and mailing addresses: These are all numbers that we deal with on a daily basis. As we grow from children to adults, how do we actually learn to remember these numbers? A recent study published in *Psychological Science* suggests that it’s more complex than simple memorization.

Robert Siegler, a professor of cognitive psychology at Carnegie Mellon, recently co-authored a study that describes how young children think about numbers. A better understanding of how numbers are represented in children’s minds will improve methods for teaching mathematics to young children and helping children with math-related learning disabilities.

“We found in previous experiments that the sense of magnitudes that children and adults have is strongly correlated with many aspects of their ability to work with numbers,” Siegler said, commenting on his motivation to conduct the study. Essentially, he wanted to know how children “see” and process numbers in their heads.

The study was conducted by asking preschoolers and second graders from Pittsburgh-area schools to perform certain tasks involving numbers. For instance, some children were given a sheet of paper with a line drawn on it; the left end of the line was labeled “0” and the right end of the line was labeled “20.” The children were then presented with the numbers one through 19 in random order and asked to guess the position of each number on the number line. Next, the children listened to several short audio scenes involving numbers and were tested on their ability to recall certain numbers from the scenes. Lastly, the children were tested on their ability to count and identify numbers.

The results showed that children generally visualized the number line in two different ways: one in which smaller numbers were more spaced out and larger numbers were closer together, and one in which the numbers were equally spaced apart. Researchers labeled these “logarithmic” and “linear,” respectively.

Interestingly, the children whose number lines were linear were able to better recall the numbers from the audio scenes than the children whose number lines were logarithmic. Large numbers were most accurately recalled by the children with a linear number line, but small numbers were recalled equally well by children with both kinds of number lines.

It was also found that the children’s ability to count and identify numbers did not affect their ability to recall numbers.

Overall, children who have a linear representation of numbers are able to remember numbers better than children who have a logarithmic representation. This is most likely because large numbers, when represented logarithmically, are less discernible, while a linear representation has all numbers equally spaced apart regardless of how large or small they are.

The authors noted that their findings needed closer examination; despite the fact children might remember small numbers more easily because they’ve been exposed to them more, it does not explain the relationship between the children’s number lines and their ability to recall small or large numbers.

“The kids who used the linear representation are only a little bit better at remembering the small numbers than kids who use the logarithmic representation, but they are much better at remembering the large numbers,” Siegler explained.

The results of this research can be used to help children with numbers and mathematics at an early age by emphasizing the importance of the size of numbers, helping to develop a more accurate number line.

Siegler suggests various ways of communicating this information to benefit children. “We’ve done experiments that provide quite strong evidence that teaching kids through playing a numerical board game how to think about numerical magnitudes helps them in a lot of different ways — it improves their ability to compare the sizes of the numbers, helps them recognize which number they’re dealing with, and it helps them learn novel arithmetic problems,” he said.