The impact of set size on cumulative area judgments.

The ability to track number has long been considered more difficult than tracking continuous quantities. Evidence for this claim comes from work revealing that continuous properties (specifically cumulative area) influence numerical judgments, such that adults perform worse on numerical tasks when cumulative area is incongruent with number. If true, then continuous extent tracking abilities should be unimpeded by number. The aim of the present study was to determine the precision with which adults track cumulative area and to uncover the process by which they do so. Across two experiments, we presented adults with arrays of dots and asked them to judge the relative cumulative area of the displays. Participants performed worse and were slower on incongruent trials, in which the more numerous array had the smaller cumulative area. These findings suggest that number interferes with continuous quantity judgments, and that number is at least as salient as continuous variables, undermining claims in the literature that continuous properties are easier to represent, and more salient to adults. Our primary research question, however, pertained to how cumulative area representations were impacted by set size. Results revealed that the area of a single item was tracked much faster and with greater precision than the area of multiple items. However, for sets with more than one item, results revealed less accurate, yet faster responses, as set size increased, suggesting a speed-accuracy trade-off in judgments of cumulative area. Results are discussed in the context of two distinct theories regarding the process of tracking cumulative area.

Preschoolers' number knowledge relates to spontaneous focusing on number for small, but not large, sets.

Much research has examined the reciprocal relations between a child's spontaneous focus on number (SFON) in the preschool years and later mathematical achievement. However, this literature relies on several different tasks to assess SFON with distinct task demands, making it unclear to what extent these tasks measure the same underlying construct. Moreover, prior studies have investigated SFON in the context of small sets exclusively, but no work has explored whether children demonstrate SFON for large sets and how this relates to children's math ability. In the current study, preschoolers were presented four distinct SFON tasks assessing their spontaneous attention to number for small (Experiment 1) and large (Experiment 2) sets of numbers. Results revealed performance across the four distinct SFON tasks was unrelated. Moreover, preschooler's SFON for small sets (1-4 items) was significantly stronger than that for large sets (10-40 items), and analyses revealed that number knowledge was only associated with SFON for small sets and not large. Together, findings suggest that SFON may not be a set-size-independent construct and instead may hinge upon a child's number knowledge, at least in the preschool years. The role of number language and how it relates to children's SFON are discussed. (PsycInfo Database Record (c) 2020 APA, all rights reserved).

Numerical intuitions in infancy: Give credit where credit is due.

Leibovich et al. overlook numerous human infant studies pointing to an early emerging number sense. These studies have carefully manipulated continuous magnitudes in the context of a numerical task revealing that infants can discriminate number when extent is controlled, that infants fail to track extent cues with precision, and that infants find changes in extent less salient than numerical changes.