Problem-size effect in 6 and 12-year-old children: from counting to memory retrieval

Currently, there is a heated debate regarding the cognitive processes involved in solving single-digit addition problems and their inherent problem-size effect. The problem-size effect corresponds to an increase in the solution times as the size of the operands increases, and two theoretical accounts (memory retrieval and automatized counting) have been proposed to explain this effect. In the present study, we investigated the developmental changes behind the problem-size effect to pit these accounts against each other. To do so, 61 first-grade and sixth-grade children solved single-digit addition problems (with operands ranging from 0 to 9), and we scrutinized the problem-size effect within both tie and non-tie problems. We observed that tie problems presented a problem-size effect in first-grade children and this effect disappeared by the sixth grade. This is consistent with recent observations showing a developmental shift from counting to direct memory retrieval for small tie problems (Bagnoud et al., 2021), and we extend these findings by showing that this shift occurs at different speed for large ties. In contrast, non-tie problems always presented a problem-size effect in the first-grade children and critically in the sixth-grade children. This is inconsistent with the automatized counting theory (Uittenhove et al., 2016), which proposes different cognitive mechanisms for very-small and medium-small non-tie problems. Conversely, our data are better accommodated by the memory retrieval accounts (e.g., Campbell, 1995), which posit that small non-tie additions are initially solved by algorithmic procedures, but later transition to be solved by direct memory retrieval.