The emergence of "groupitizing" in children's numerical cognition

Improvements in enumeration abilities that emerge over late childhood are primarily thought to reflect perceptual developments such as increases in subitizing limits for small sets and faster shifting of attention associated with serially counting larger sets. Contributions of conceptual knowledge development, such as the growing appreciation of how whole numbers are composed of subsets of whole numbers, are not as well understood. This study examined the emergence of a process referred to as "groupitizing," which captures how children may capitalize on grouping information to facilitate enumeration processes. We examined enumeration speed in a cross-sectional sample of children (N=378), spanning kindergarten through third grade, using arrays of dots. Arrays were either unstructured or grouped by proximity into subsets in the subitizing range (i.e., three subgroups of 1-3 items). Kindergarten children showed no evidence of grouping structure on enumeration. First-grade children enumerated grouped arrays faster than unstructured arrays. This structure effect grew progressively stronger in subsequent grades. Enumeration speed for unstructured arrays increased with set size, yet for grouped arrays the impact of set size was dependent on grade level. For kindergartners, the grouping manipulation had no impact on the effect of set size. For older children, the grouping manipulation reduced the effect of set size on enumeration. Furthermore, individual differences in how set size affected enumeration of grouped arrays showed unique patterns of association with performance on standardized symbolic arithmetic fluency tests, suggesting a unique role for the construct of groupitizing in the development of enumeration fluency and symbolic math skills.