Abstract
The Approximate Number System (ANS) allows individuals to assess nonsymbolic numerical magnitudes (e.g., the number of apples on a tree) without counting. Several prominent theories posit that human understanding of symbolic numbers is based – at least in part – on mapping number symbols (e.g., 14) to their ANS-processed nonsymbolic analogs. Number-line estimation – where participants place numerical values on a bounded number-line – has become a key task used in research on this mapping. However, some research suggests that such number-line estimation tasks are actually proportion judgment tasks, as number-line estimation requires people to estimate the magnitude of the to-be-placed value, relative to set upper and lower endpoints, and thus do not so directly reflect magnitude representations. Here, we extend this work, assessing performance on nonsymbolic tasks that should more directly interface with the ANS. We compared adults’ (n = 31) performance when placing nonsymbolic numerosities (dot arrays) on number-lines to their performance with the same stimuli on two other tasks: Free estimation tasks where participants simply estimate the cardinality of dot arrays, and ratio estimation tasks where participants estimate the ratio instantiated by a pair of arrays. We found that performance on these tasks was quite different, with number-line and ratio estimation tasks failing to the show classic psychophysical error patterns of scalar variability seen in the free estimation task. We conclude the constraints of tasks using stimuli that access the ANS lead to considerably different mapping performance and that these differences must be accounted for when evaluating theories of numerical cognition. Additionally, participants showed typical underestimation patterns in the free estimation task, but were quite accurate on the ratio task. We discuss potential implications of these findings for theories regarding the mapping between ANS magnitudes and symbolic numbers.
Highlights
Humans and many nonhuman animals are equipped with a phylogenetically ancient approximate number system (ANS) that allows them to rapidly enumerate the items in a set without counting (Kaufman et al, 1949; Mechner, 1958; Meck and Church, 1983; Feigenson et al, 2004; Izard and Dehaene, 2008)
Number-line estimation – in which participants place numerical values on a bounded number-line – has become a key task used in research on the link between symbolic numbers and numerical magnitudes (Siegler and Opfer, 2003; Whyte and Bull, 2008; Schley and Peters, 2014)
We investigated how three separate tasks that employ the same sorts of ANS stimuli lead to differences in mapping performance: free estimation, number-line estimation, and ratio estimation
Summary
Humans and many nonhuman animals are equipped with a phylogenetically ancient approximate number system (ANS) that allows them to rapidly enumerate the items in a set without counting (Kaufman et al, 1949; Mechner, 1958; Meck and Church, 1983; Feigenson et al, 2004; Izard and Dehaene, 2008) These findings have led many to conclude that the meanings of symbolic numbers. Some consider the spacing and precision of number-line placements to directly reflect the spacing and precision of the magnitudes mapped to symbolic numbers (Siegler and Opfer, 2003; Whyte and Bull, 2008). This interpretation of number-line performance remains contested.
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