Enumeration of small and large numerosities: The effect of element visibility

Abstract

Precise enumeration is associated with small numerosities within the subitizing range (<4 items), while approximate enumeration is associated with large numerosities (>4 items). To date, there is still debate on whether a single continuous process or dual mutually exclusive processes mediate enumeration of small and large numerosities. Here, we evaluated a compromise between these two notions: that the precise representation of number is limited to small numerosities, but that the approximate representation of numerosity spans across both small and large numerosities. We assessed the independence of precise and approximate enumeration by looking at how luminance contrast affected enumeration of elements that differ by ones (1–8) or by tens (10–80). We found that enumeration functions of ones and tens have different characteristics, which is consistent with the presence of two number systems. Subitizing was preserved for small numerosities. However, simply decreasing element visibility changed the variability signatures of small numerosities to match those of large numerosities. Together, our results suggest that small numerosities are mediated by both precise and approximate representations of numerosity.

Keywords:

• Subitization
• Visual enumeration
• Detection
• Counting
• Estimation
• Numerosity
• Approximation

Acknowledgments

We thank Breana Carter for help in collecting data and Doug Wedell for helpful discussion. This study was supported, in part, by the University of South Carolina Promising Investigator Research Award and the Research Consortium for Children and Families. A poster based on preliminary data was presented at the 2011 Psychonomics Society Meeting in Seattle, WA.