Abstract

We examined children’s and adults ’ numerical estimation and the representations that gave rise to their estimates. The results were inconsistent with two prominent models of numerical representa-tion: the logarithmic-ruler model, which proposes that people of all ages possess a single, logarithmically spaced representation of num-bers, and the accumulator model, which proposes that people of all ages represent numbers as linearly increasing magnitudes with scalar variability. Instead, the data indicated that individual children possess multiple numerical representations; that with increasing age and nu-merical experience, they rely on appropriate representations increas-ingly often; and that the numerical context influences their choice of representation. The results, obtained with second graders, fourth graders, sixth graders, and adults who performed two estimation tasks in two numerical contexts, strongly suggest that one cause of chil-dren’s difficulties with estimation is reliance on logarithmic represen-tations of numerical magnitudes in situations in which accurate estimation requires reliance on linear representations. Estimation is a pervasive process in both school and everyday life. It is also a process that many children find difficult. This difficulty has been ascribed to inadequate central conceptual structures, mindless symbol manipulation, lack of number sense, and misunderstanding of