Abstract
Currently, there is a controversial debate on whether there is an abstract representation of number magnitude, multiple different ones, or multiple different ones that project onto a unitary representation. The current study aimed at evaluating this issue by means of a magnitude comparison task involving Arabic numbers and structured as well as unstructured non-symbolic patterns of squares. In particular, we were interested whether a specific numerical effect, the unit-decade compatibility effect reflecting decomposed processing of tens and units complying with the place-value structure of the Arabic number system, is affected by input notation. Indeed, a reliable unit-decade compatibility effect was observed in the symbolic-digital notation condition but was absent for unstructured non-symbolic notation. However, for structured non-symbolic notation a – albeit negative – compatibility effect was observed as well. Theses results are hard to reconcile with the notion of an abstract representation of number magnitude. Instead, our data support the existence of multiple representations of numerical magnitude. In addition, the current data indicate that it may not be a question of symbolic vs. non-symbolic notation only but also an issue of the structuring of the input notation. While unstructured non-symbolic quantities seemed to be processed holistically we found evidence suggesting at least partially decomposed processing not only for symbolic Arabic numbers but also for structured non-symbolic quantities.
Highlights
The most evident and important semantic information conveyed by a number is its magnitude (e.g., Miller and Gelman, 1983)
As there were even conditions in which participants did not commit a single error, we focused our analyses on response latencies
Comparable to the results of Experiment 1 this interaction indicated that a difference in decade distance effects between symbolic-digital and non-symbolic notation was observed for incompatible number pairs with a small unit distance in particular
Summary
The most evident and important semantic information conveyed by a number is its magnitude (e.g., Miller and Gelman, 1983). All theoretical models, which have been proposed for the cognitive mechanisms underlying numerical cognition, include a representation for number magnitude as a central aspect (e.g., McCloskey, 1992). This is the case for the currently most influential model in numerical cognition, the so-called TripleCode Model by Dehaene and colleagues (Dehaene et al, 2003; Dehaene and Cohen, 1995, 1997). As regards the representation of number magnitude, the dominant view claims that “robust evidence demonstrates that with or without language, number is represented abstractly – independently of perceptual features, dimensions, modality, and notation
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