Spontaneous partitioning and proportion estimation in children's numerical judgments.

What do numerical estimates tell us about developing an understanding of number? One theory is that bounded number line estimation (NLE) tasks reveal a "representational shift" from logarithmically to linearly organized mental representations of number over development. According to a different theoretical framework, developmental change in estimation reflects changes in children's numerical knowledge and their ability to make appropriate relative judgments. Empirical support for this "proportion estimation" framework includes the fact that quantitative models of proportion estimation describe signature patterns of estimation bias. A recent study argued against this latter theory by suggesting that patterns of curvature in number line placements are simply artifacts of a task procedure in which participants receive explicit information about the location of the numerical midpoint. We tested this claim in two experiments with children aged 6-8 years (Experiment 1: N = 47; Experiment 2: N = 104). Results demonstrated that the proportion estimation framework provides a good explanation of children's number line placement in the absence of explicit midpoint cues, that explicit cues to the midpoint are associated with more frequent use of middle reference points in young children, and that children can use a middle reference point spontaneously in the absence of explicit cues (with this tendency increasing with age). These findings provide novel support for the idea that psychophysical models of proportion estimation successfully account for numerical estimates across development regardless of whether spatial and numerical midpoint cues are provided as part of the NLE task.