Perceived numerosity as a function of array number, speed of array development, and density of array items

Abstract

College-student subjects engaged in judgments of numerosity received stimulus arrays on a computer screen that varied in their number level (low, medium, and high), the speed with which the array developed (slow, medium, or fast), and the density of the items in the array (low or high density). The subjects overestimated number when the array was small (75-125 items) but significantly underestimated number when it was at a medium (150-250) or high level (550-650). Density of array items was a significant variable, since subjects showed more underestimation under the high-density condition. Additionally, there was a speed x density interaction. The results are discussed with respect to which class of variable, sensory or cognitive, most influences perceived numerosity. Although they deal with the animal literature, Davis and Perusse (1988), in their excellent review, distinguish among a number of approaches to the measurement of numerical competence. One of the approaches, estimation, is different from subititing because the subject is re

Dissociation between small and large numerosities in newborn infants

“…First, infants may have encoded all numerosities in terms of the Approximate Number System (ANS), but this system may not be operational or may be unreliable for very small numerosities. Indeed, if the computations underlying extraction of numerosity in the ANS rely on some summary statistics on stimuli (for example if the perception of numerosity is based on estimates of density and area; Dakin, Tibber, Greenwood, Kingdom & Morgan, ; Gebius & Reynvoet, ; Hollingsworth, Simmons, Coates & Cross, ; Hurewitz, Gelman & Schnitzer, ), these estimates may not be reliable for small numerosities, as it is hard to define summary statistics such as density for very small arrays. If that hypothesis is correct, because numerosity perception presents the same characteristic signatures throughout lifetime, the drop in precision between large and small numbers should be visible into adulthood as well.…”

Calibrating the mental number line

“…The amount of underestimation increases in the course of the experiments, but is also present from the very first trial (Krueger, 1982). Estimates are modulated by the non-numerical parameters of the stimuli, as more dense dot arrays tend to be more underestimated (Hollingsworth, Simmons, Coates, & Cross, 1991), and arrays are judged to contain more dots when dots are regularly spaced (Ginsburg, 1978). Furthermore, the estimation pattern seems to be influenced by the range of stimuli tested.…”

Ontogenetic Origins of Human Integer Representations

“…Compatible with this hypothesis, adults exhibit mappings between verbal numerals and approximate numerical magnitudes (19)(20)(21)(22)(23)(24)(25)(26). These mappings begin to emerge early in development (27)(28)(29)(30)(31) and play a role in numerical computations (1).…”