Grouping Mechanisms in Numerosity Perception

Enumeration of a dot array is faster and easier if the items form recognizable subgroups. This phenomenon, which has been termed “groupitizing,” appears in children after one year of formal education and correlates with arithmetic abilities. We formulated and tested the hypothesis that groupitizing reflects an ability to sidestep counting by using arithmetic shortcuts, for instance, using the grouping structure to add or multiply rather than just count. Three groups of students with different levels of familiarity with mathematics were asked to name the numerosity of sets of 1–15 dots in various arrangements, for instance, 9 represented as a single group of 9 items, three distinct groups of 2, 3, and 4 items (affording addition 2 + 3 + 4), or three identical groups of 3 items (affording multiplication 3 × 3). Grouping systematically improved enumeration performance, regardless of whether the items were grouped spatially or by color alone, but only when an array was divided into subgroups with the same number of items. Response times and error patterns supported the hypothesis of a multiplication process. Our results demonstrate that even a simple enumeration task involves mental arithmetic.

Grouping mechanisms in numerosity perception

Enumeration of a dot array is faster and easier if the items form recognizable subgroups. This phenomenon, which has been termed groupitizing, appears in children after one year of formal education and correlates with arithmetic abilities. We formulated and tested the hypothesis that groupitizing reflects an ability to sidestep counting by using arithmetic shortcuts, for instance using the grouping structure to add or multiply rather than just count. Three groups of students with different levels of familiarity with mathematics were asked to name the numerosity of sets of 1-15 dots in various arrangements, for instance 9 represented as a single group of 9 items, three distinct groups of 2, 3, and 4 items (affording addition 2+3+4), or three identical groups of 3 items (affording multiplication 3x3). Grouping systematically improved enumeration performance, regardless of whether the items were grouped spatially or by color alone, but only when an array was divided into subgroups with the same number of items. Response times and error patterns supported the hypothesis of a multiplication process. Our results demonstrate that even a simple enumeration task implicitly involves mental arithmetic.

Possible Associations between Subitizing, Estimation and Visuospatial Working Memory (VSWM) in Children

Researchers have focused on identifying the mechanisms involved in subitizing and its differences with estimation. Some suggest that subitizing relies on a visual indexing system in charge of the simultaneous individuation of objects that is also used by visuospatial working memory (VSWM). In adults, studies found associations between subitizing and VSWM, in the absence of correlation between VSWM and estimation. The present study analyzed the performance of 120 4 and 6-year-old children in three tasks: dot enumeration to measure subitizing capacity, quantity discrimination for estimation, and Corsi Block-tapping task for VSWM. In the enumeration task RTs (F(9, 1062)=720.59, MSE=734394, p<.001, η2=.86) and errors (F(9, 1062)=42.15, MSE=.194, p<.001, η2=.26.) increased with the array, but this growth was statistically significant only from 4 dots onward. Each subject’s subitizing range was estimated by fitting RTs with a sigmoid function of number of dots and obtaining the bend point of the curve. Data fit (age 4: R2 = .88; SD = .08; age 6: R2 = .91, SD = .08) showed a mean subitizing range of 2.79 (SD = .66) for 4 year-olds and of 3.11 (SD = .64) for 6 year-olds. Subitizing ranges and average RTs showed low association with storage (r = .274; p < .05; r = –.398; p < .001) and average RTs with concurrent processing (r = –.412; p < .001) in VSWM. Subitizing range and speed showed no association with estimation speed and a poor association with accuracy (r = .234, p < .01; r = –.398, p < .001), which suggests independent systems for small and large quantities. Subitizing and estimation measures correlated with VSWM (p < .01), which suggests that both processes may require VSWM resources.

Multiple Object Individuation and Exact Enumeration

Exact computation of numerosity requires the selective individuation of the elements to be enumerated so that each element is counted once and only once. Such a mechanism should operate not only when the elements to be enumerated are presented in isolation but also when they are presented in cluttered scenes. To uncover the electrophysiological correlates of the level of object representation necessary for exact enumeration, we examined ERP measures during the execution of a target enumeration task. A variable number (1–4) of lateralized targets were presented with or without distracters on the target side. An early nonlateralized response (N1, 120–180 msec) was modulated by target numerosity only when presented without distracters. By contrast, the amplitudes of a lateralized and later response (N2pc, 180–300 msec) increased as a function of target numerosity both with and without distracters, reaching a plateau at three targets. We propose that the stage of processing reflected in the N2pc corresponds to the component of individuation that binds specific indexes to properties and locations and that this provides the representation type necessary for exact enumeration.