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Julie Castronovo, Virginie Crollen, Xavier Seron; Visual enumeration: A bi-directional mapping process between symbolic and non-symbolic representations of number?. Journal of Vision 2010;10(7):1327. doi: 10.1167/10.7.1327.
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© ARVO (1962-2015); The Authors (2016-present)
Over the last 30 years, numerical estimation has been largely studied. Recently, Castronovo and Seron (2007) pointed out that, according to the type of numerical estimation task (perception vs. production of numerosities), reverse patterns of performance are found (i.e., under- and over-estimation respectively). They postulated the bi-directional mapping hypothesis to account for that particular phenomenon. This hypothesis relies on classical assumptions, assuming the existence of several numerical mental representations, having transcoding routes between them (Dehaene, 1992) and presenting difference in precision (Piazza et al., 2007). Based on these assumptions, the bi-directional mapping hypothesis suggests that the opposite patterns of performance found in perception and production numerical estimation tasks result from the opposite direction of their transcoding activities between the non-symbolic magnitude representation (i.e., the mental number line) and its corresponding symbolic representation. Here, we further investigated the bi-directional mapping hypothesis by submitting participants to 3 visual numerical estimation tasks, involving three different mapping processes: 1) a perception task, involving a non-symbolic (sets of dots) to symbolic (Arabic numeral) mapping; 2) a production task, involving a symbolic (Arabic numeral) to non-symbolic mapping (set of dots); 3) a reproduction task, involving a non-symbolic (set of dots) to non-symbolic (set of dots) mapping. Our results confirmed that different patterns of performance are found according to the type of numerical estimation task: 1) under-estimation in the perception task; 2) over-estimation in the production task; 3) accurate estimation in the reproduction task. Moreover, correlation analyses revealed that the more a participant under-estimated in the perception task, the more he/she over-estimated in the production task. These results gave further support to the bi-directional mapping hypothesis, by directly showing for the first time how different numerical estimation tasks, involving different mapping routes have an impact on the patterns of performance that can be found.
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