Scrutinizing patterns of solution times in alphabet-arithmetic tasks favors counting over retrieval models

According to associationist models, initial sequential processing of algorithmic steps is replaced through learning by single-step access to a memory instance. In an alphabet-arithmetic task where equations such as C + 3 = F have to be verified, the shift from algorithmic procedures to retrieval would manifest in a transition from steep slopes relating solution times to addends at the beginning of learning to a flat function at the end (e.g., Logan & Klapp, 1991). Nevertheless, we argue that computation of the slopes at the end of training is biased by a systematic drop in solution times for the largest addend in the study set. In this paper, this drop is observed even when the longest training period in alphabet-arithmetic literature is doubled (Experiment 1) and even when the size of the largest addend is increased (Experiment 2). We demonstrate that this drop is partly due to end-term effects but remains observable even when end-term problems are not considered in the analyses. As Logan and Klapp suggested, we conclude that the drop is partly due to deliberate memorization of the problems with the largest addend. In contrast, departing from Logan and Klapp, we demonstrate that, when problems with the largest addend are excluded from the analyses, the possibility that counting is still used after learning cannot be discarded. This conclusion is reached because after this exclusion, the slopes were still significant. To conclude, our results advocate that practicing an algorithm leads to its acceleration and not to a shift from algorithmic procedures to retrieval.