Developmental change in the acuity of approximate number and area representations.

Abstract

From very early in life, humans can approximate the number and surface area of objects in a scene. The ability to discriminate between 2 approximate quantities, whether number or area, critically depends on the ratio between the quantities, with the most difficult ratio that a participant can reliably discriminate known as the Weber fraction. While developmental improvements in the Weber fraction have been demonstrated for number, the developmental trajectory of improvement in area discrimination remains unknown. Here we investigated whether the development of area discrimination parallels that of number discrimination. We tested forty 3- to 6-year-old children and adults in both a number and an area discrimination task in which participants selected the greater of 2 quantities across a range of ratios. We used formal psychophysical models to derive, for each participant and each age group, the Weber fraction for both number and area discrimination. We found that, like number acuity, area acuity steadily improves during childhood. However, we also found area acuity to be consistently higher than number acuity, suggesting a potential difference in the underlying mechanisms that encode and/or represent approximate area and approximate number. We discuss these findings in the context of quantity processing and its development.

Developmental Continuity in the Link Between Sensitivity to Numerosity and Physical Size

“…Recent studies probing this question, however, have provided conflicting answers. Some studies with adults have found correlations between acuity for number and line length or between number and the cumulative area of dot arrays (DeWind & Brannon, 2012;Lourenco, Bonny, Fernandez, & Rao, 2012), whereas other studies have failed to find correlations in comparison performance between magnitude dimensions (Agrillo, Piffer, & Adriano, 2013;Cappelletti et al, 2014;Odic, Libertus, Feigenson, & Halberda, 2013). Although it can be difficult to interpret a null finding, differences in study design and sample size may have contributed to these conflicting results.…”

Numerical and area comparison abilities in Down syndrome

“…One would expect that this relative visuospatial ability would predict relative ability in comparing both area and numerosity. As a consequence, if the ability of individuals with DS to compare both area and large numerosities are preserved, we should find a pattern similar to that reported in typically developing children, that is, better performance at comparing area than number (Odic et al, 2012). Current theories of number development have stressed the importance of continuous quantity discrimination in early number processing (Cantrell & Smith, 2013;Leibovich & Henik, 2013), and testing this prediction could provide important information about the ability of individuals with DS to improve their numerical processing.…”

“…Critically, although the complexity of the stimuli were different (e.g., in Xu and Spelke, stimuli changed not only in numerosity, but also in other continuous features), infants dishabituated to two-fold changes, that is, to a new numerosity that was either double or half, or to an Elmo face that was twice the size of the original. In childhood as well as in adulthood, better performance has been reported for area comparison than for number comparison tasks (Odic, Libertus, Feigenson, & Halberda, 2012). To the best of our knowledge, there has been no investigation of the ability of individuals with DS to compare quantities other than number.…”

Core mathematical abilities in infants

“…Still, although the acuity seems to be equivalent across these dimensions, which would support the view of a single magnitude system (Walsh, 2003), it is still possible that subtle differences in processing these quantitative dimensions remained undetected in previous studies (de Hevia et al, in preparation) and that representations of these dimensions of magnitude are clearly differentiated from one another (Deroy and Spence, 2013). In fact, there is evidence that the developmental trajectory of the acuity of 3-to 6-year-old children's representations of number and size differs, such that size representations have higher acuity than number representations and improvements in acuity occur more quickly for size than for number (Odic et al, 2013). Overall, these studies have provided evidence for infants' sensitivity to number and other quantitative dimensions such as area and temporal duration, which has opened the further question of how are these representations related to each other.…”