In this study, 17 adult participants were trained to solve alphabet-arithmetic problems using a production task (e.g., C + 3 = ?). The evolution of their performance across 12 practice sessions was compared to the results obtained in past studies using verification tasks (e.g., is C + 3 = F correct?). We show that, irrespective of the experimental paradigm used, there is no evidence for a shift from counting to retrieval during training. However and again regardless of the paradigm, problems with the largest addend constitute an exception to the general pattern of results obtained. Contrary to other problems, their answers seem to be deliberately memorized by participants relatively early during training. All in all, we conclude that verification and production tasks lead to similar patterns of results, which can therefore both confidently be used to discuss current theories of learning. Still, deliberate memorization of problems with the largest addend appears earlier and more often in a production than a verification task. This last result is discussed in light of retrieval models.
We would like to thank Jacques Dubochet for helping us with the recruitment of participants in the group of older adults. We declare no conflict of interest. We have complied with APA ethical standards in the treatment of our human samples.
As a theory of skill acquisition, the instance theory of automatization posits that, after a period of training, algorithm‐based performance is replaced by retrieval‐based performance. This theory has been tested using alphabet‐arithmetic verification tasks (e.g., is A + 4 = E?), in which the equations are necessarily solved by counting at the beginning of practice but can be solved by memory retrieval after practice. A way to infer individuals’ strategies in this task was supposedly provided by the opportunistic‐stopping phenomenon, according to which, if individuals use counting, they can take the opportunity to stop counting when a false equation associated with a letter preceding the true answer has to be verified (e.g., A + 4 = D). In this case, such within‐count equations would be rejected faster than false equations associated with letters following the true answers (e.g., A + 4 = F, i.e., outside‐of‐count equations). Conversely, the absence of opportunistic stopping would be the sign of retrieval. However, through a training experiment involving 19 adults, we show that opportunistic stopping is not a phenomenon that can be observed in the context of an alphabet‐arithmetic verification task. Moreover, we provide an explanation of how and why it was wrongly inferred in the past. These results and conclusions have important implications for learning theories because they demonstrate that a shift from counting to retrieval over training cannot be deduced from verification time differences between outside and within‐count equations in an alphabet‐arithmetic task.
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