Behavioral evidence for format-dependent processes in approximate numerosity representation

Abstract

A genuinely abstract number representation is thought to be capable of representing the numerosity of any set of discrete elements, whether they are sequentially or simultaneously presented. Recent neuroimaging studies, however, have demonstrated that different areas of intraparietal sulcus play a role in extracting numerosity across simultaneous or sequential presentation during a quantification process, suggesting the existence of a format-dependent numerical system. To test whether behavioral evidence exists for format-dependent numerical processing in adult humans, we measured the Weber fractions of numerosity discrimination for sequential stimuli, simultaneous stimuli, and cross-format stimuli with a carefully controlled experimental procedure. The results showed distinct differences between the performance in the simultaneous and sequential conditions, supporting the existence of format-dependent processes for numerosity representation. Moreover, the performance on cross-format trials differed among participants, with the exception that performance was always worse than in the simultaneous condition. Taken together, our findings suggest that numerical representation may involve a complex set of multiple stages.

The association between higher education and approximate number system acuity

“…The initial estimate was based on the median w for a large number of participants (≈200) tested in our lab 3 . This estimate is also consistent with estimates documented in previous research (Pica et al, 2004; Halberda and Feigenson, 2008; Halberda et al, 2008; Tokita and Ishiguchi, 2012). We used both a simultaneous and a sequential version.…”

“…ANS acuity is typically measured using paradigms where the participant is asked to identify which of two sets of objects is the more numerous, with too brief exposure for the two sets to be serially counted. Although the ANS is considered a primitive system that everyone can utilize, recent studies have documented substantial individual variability in ANS acuity ( w :s for adults are often in the range 0.1–0.45, see; e.g., Pica et al, 2004; Halberda and Feigenson, 2008; Halberda et al, 2008; Tokita and Ishiguchi, 2012). The acuity improves with age from childhood to adulthood (Halberda and Feigenson, 2008; Halberda et al, 2012) but seems to peak at about age 30 followed by a decrease into old age.…”

The role of ANS acuity and numeracy for the calibration and the coherence of subjective probability judgments

“…The acuity of the ANS is often conceptualized as the smallest change in numerosity, as quantified by a Weber fraction ( w ) (Pica et al, 2004; Halberda and Feigenson, 2008; Halberda et al, 2008, 2012; Tokita and Ishiguchi, 2010), which can be detected. Several studies document considerable individual variation in ANS acuity (Pica et al, 2004; Halberda and Feigenson, 2008; Halberda et al, 2008; Tokita and Ishiguchi, 2012; Lindskog et al, 2013). A first numerical ability thus involves a nonlinear, ordinal appreciation for magnitudes.…”

Effects of perceptual variables on numerosity comparison in 5–6-year-olds and adults

“…Several studies show that the development of symbolic numerical knowledge relies on the representation of approximate numerosities, and that the ability of approximate numerosity increases with age and throughout the school years (Halberda et al, 2008; Piazza et al, 2013). However, certain researchers have also challenged the idea of the abstract numerical representation by presenting various empirical data that demonstrate methodological and theoretical limitations (e.g., Kadosh et al, 2008; Kadosh and Walsh, 2009; Tokita and Ishiguchi, 2012). For example, Kadosh and Walsh (2009) prompted extensive investigation of number representation processes in the behavioral and neurophysiological fields, suggesting the existence of a general magnitude system serving all sorts of quantity.…”