Multiple Representations in Number Line Estimation: A Developmental Shift or Classes of Representations?

Abstract

Children's estimation patterns on a number line estimation task may provide information about the mental representation of the magnitude of numbers. Siegler and his colleagues concluded that children's mental representations shift from a logarithmic-ruler representation to a linear-ruler representation. However, there are important methodological issues with respect to their number-line studies that threaten the validity of the conclusions. We discuss these methodological issues and propose an alternative method to analyze estimation data. One hundred nineteen children from kindergarten, first, and second grade performed a number-line estimation task in which they had to estimate the position of 30 numbers on a 0-to-100 number line. The results supported the hypothesis that children show various kinds of estimation patterns. Five classes of children were distinguished, which were characterized by different estimation patterns. A remarkable result was that the logarithmic-ruler representation was not found. Although young children were more likely to show overestimation of small numbers than older children, this developmental trend was small and not significant.