Varieties of quantity estimation in children

In the number-to-position task, with increasing age and numerical expertise, children's pattern of estimates shifts from a biased (nonlinear) to a formal (linear) mapping. This widely replicated finding concerns symbolic numbers, whereas less is known about other types of quantity estimation. In Experiment 1, Preschool, Grade 1, and Grade 3 children were asked to map continuous quantities, discrete nonsymbolic quantities (numerosities), and symbolic (Arabic) numbers onto a visual line. Numerical quantity was matched for the symbolic and discrete nonsymbolic conditions, whereas cumulative surface area was matched for the continuous and discrete quantity conditions. Crucially, in the discrete condition children's estimation could rely either on the cumulative area or numerosity. All children showed a linear mapping for continuous quantities, whereas a developmental shift from a logarithmic to a linear mapping was observed for both nonsymbolic and symbolic numerical quantities. Analyses on individual estimates suggested the presence of two distinct strategies in estimating discrete nonsymbolic quantities: one based on numerosity and the other based on spatial extent. In Experiment 2, a non-spatial continuous quantity (shades of gray) and new discrete nonsymbolic conditions were added to the set used in Experiment 1. Results confirmed the linear patterns for the continuous tasks, as well as the presence of a subset of children relying on numerosity for the discrete nonsymbolic numerosity conditions despite the availability of continuous visual cues. Overall, our findings demonstrate that estimation of numerical and non-numerical quantities is based on different processing strategies and follow different developmental trajectories.