Are small additions solved by direct retrieval from memory or automated counting procedures? A rejoinder to Chen and Cam
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Are small additions solved by direct retrieval from memory or automated counting procedures? A rejoinder to Chen and Campbell (2018) Catherine Thevenot 1 & Pierre Barrouillet 2 Accepted: 16 September 2020 # The Author(s) 2020
Abstract Contrary to the longstanding and consensual hypothesis that adults mainly solve small single-digit additions by directly retrieving their answer from long-term memory, it has been recently argued that adults could solve small additions through fast automated counting procedures. In a recent article, Chen and Campbell (Psychonomic Bulletin & Review, 25, 739–753, 2018) reviewed the main empirical evidence on which this alternative hypothesis is based, and concluded that there is no reason to jettison the retrieval hypothesis. In the present paper, we pinpoint the fact that Chen and Campbell reached some of their conclusions by excluding some of the problems that need to be considered for a proper argumentation against the automated counting procedure theory. We also explain why, contrary to Chen and Campbell’s assumption, the network interference model proposed by Campbell (Mathematical Cognition, 1, 121–164, 1995) cannot account for our data. Finally, we clarify a theoretical point of our model. Keywords Numerical cognition . Mental arithmetic . Strategies . Retrieval network . Automatization
Scholars of numerical cognition generally agree that adults typically solve small single-digit additions (i.e., with a sum ≤ 10) by directly retrieving their answer from long-term memory (e.g., Ashcraft, 1982, 1992; Ashcraft & Guillaume, 2009; Campbell, 1995). It is assumed that the recurrent solving of these additions during childhood leads to the creation and strengthening of problem–answer associations in long-term memory to the point that the presentation of the problem would trigger the activation and retrieval of the associated answer (e.g., Siegler & Shrager, 1984). However, this consensus has recently been challenged by the alternative view that adults could solve small additions through fast and unconscious automated counting procedures involving the mental scanning of a portion of an ordered spatial or verbal representation such as a number line or a verbal number sequence (Barrouillet & Thevenot, 2013; Fayol & Thevenot, 2012; Mathieu, Gourjon, Couderc, Thevenot, & Prado, 2016;
* Catherine Thevenot [email protected] 1
SSP, Institute of Psychology, University of Lausanne, Géopolis Building, Room 4536, CH-1015 Lausanne, Switzerland
2
University of Geneva, Geneva, Switzerland
Mathieu et al., 2018; Thevenot, Barrouillet, Castel, & Uittenhove, 2016; Thevenot et al., 2020; Uittenhove, Thevenot, & Barrouillet, 2016). These procedures could be limited to very small addition problems involving operands from 1 to 4 because rapid mental scanning of a numerical sequence could be impossible beyond the size of the focus of attention estimated at about 4 items by Cowan (2001). In a recent article, Chen and Campbell (2018) reviewed empirical findings and arguments on which the hypothesis
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