Are small additions solved by direct retrieval from memory or automated counting procedures? A rejoinder to Chen and Campbell (2018).

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.