Elida V. Laski, Carnegie Mellon University
Abstract: Previous studies using estimation tasks have found a developmental shift from logarithmic to linear representations of numerical magnitude between kindergarten and second grade for numbers between 0 and 100. The present experiment examined whether this trend also applied children's qualitative categorizations of numbers and whether, with age and experience, children's numerical categorizations become increasingly flexible across numerical contexts.
Kindergartners, first graders, and second graders were asked to categorize a set of numbers as low, medium, or high in three numerical contexts (0-20, 0-50, and 0-100). The logarithmic to linear shift was found in children's numerical categorizations. In addition, first and second graders' categorizations of numbers were sensitive to context -- for example, they classified 18 as a big number in the 0-20 context but as a small number in the 0-100 context -- whereas kindergartners tended to have more rigid categories -- they viewed 18 as a big number regardless of the numerical context. These and previous results suggest that a common representation of numerical magnitude shapes performance on many numerical tasks. The current results also suggest that kindergartners' logarithmic representations may, in part, reflect an inappropriate emphasis on the magnitude of individual numbers and a disregard for the magnitude of that number in relation to the numerical context.