Poster #29 - Context Dependent Numerosity Representations in Children

• In Event: 1-005 - Poster Session 01
  In Poster Session: PS 01 Section - Cognitive Processes

Integrative Statement

Researchers hypothesize that there are two core systems for representing numerical magnitudes: one enumerates and tracks small quantities, and the other approximately represents large quantities. This Approximate Number System (ANS) represents a numerosity by a distribution of possible values centered around the true value. Two competing ANS models represent numerosity on either a linear scale with increasing variability around the central value, or on a logarithmic scale with equal variability around this value, where distributions of higher numerosities are greatly compressed (Dehaene, 2003, Gallistel & Gelman, 2000).
Children have been theorized to transition from a logarithmic to a linear mental representation as their numeracy skills develop, (Siegler, Thompson, & Opfer, 2009), but recent research with adults has shown that either representation could be used depending on the numerical comparison context (Ratcliff & McKoon, 2018). That is, sometimes the perceptual features of stimuli, such as total pixels occupied by dots on the computer screen, impacted comparisons, and sometimes not. These perceptual features naturally covary with changes in number, and research (e.g., Leibovich et al., 2017) has suggested numerosity and perceptual information are both utilized in numerosity comparisons.
In the present study, 57 children from 2nd-5th grade completed two non-symbolic numerosity comparison tasks: (1) judging the total numerosity of dots as more/less than 25 and (2) comparing numerosities of intermingled blue and yellow dots. In half of the trials, the total area of dots was held equal regardless of numerosity to limit cues drawn from perceptual features. In the other trials, total dot area was proportional to numerosity. Data from children’s performance were fit using the Diffusion Decision Model, (DDM) which captures the underlying process of simple two-choice decisions. In this model, evidence is noisily accumulated towards one of two boundaries until a boundary is crossed, at which point a decision is made (e.g., more vs. less than 25 dots). Formulae were integrated into the evidence accumulation parameter of the model to approximate either the linear or logarithmic ANS.
When children judged whether there were more/less than 25 dots, the logarithmic model fit was superior. When children compared blue and yellow dots, however, only the linear model captured the pattern of results. These results were consistent with those of adults who completed comparable tasks (Ratcliff & McKoon, 2018), though the children’s lower accuracy and longer response times reflect a still-developing number system. Despite weaker numeracy skills, children did not rely more heavily on perceptual features relative to adults. Furthermore, removing the perceptual feature of area as a cue impacted performance when comparing blue and yellow dots, but not when judging whether the numerosity was more/less than 25.
Overall, these findings provide information on the form and development of the underlying representations used when making everyday numerical judgements, which often involve larger quantities and the need to estimate. The ANS is hypothesized to be a building block upon which all math abilities are based, so an understanding of the contexts in which the different representations are used can inform instructional practices.

Authors

• Michael Sales, The Ohio State University
  Presenting Author

• Roger Ratcliff, The Ohio State University
  Non-Presenting Author

• Clarissa A Thompson, Kent State University
  Non-Presenting Author