Patterns of solution times for simple addition problems in 12-year-old children are not compatible with retrieval models: A rebuttal to Andras and Macizo (2025)

The cognitive mechanisms supporting arithmetic learning, in simple addition in particular, have long been debated. Whereas traditional models propose that counting strategies are gradually replaced by direct retrieval over development, the automatized counting theory suggests that expert performance on very small additions rather relies on rapid, unconscious one-by-one counting procedures. A central point of disagreement between these accounts concerns the interpretation of the problem-size effect, namely the increase in solution times for larger addition problems. Retrieval models attribute this effect to increased interference among arithmetic facts in memory, whereas the automatized counting theory posits that the effect reflects the larger number of counting steps required for larger problems. Nevertheless, recent findings showing that the size effect disappears for sums beyond 7 challenge the interference account, which would predict a monotonic increase in solution times with increasing problem size. Rather, these findings are consistent with the automatized counting theory, according to which problems involving operands greater than 4 fall outside the range of automatization. However, Andras and Macizo (2025) recently reported a failure to replicate this breakpoint at sum 7 in 6th graders and concluded that the monotonic increase of solution times they observe support retrieval-based accounts. Nonetheless, an examination of their data indicates that this conclusion is not empirically supported. In reality, Andras and Macizo (2025)'s results reveal a non-monotonic pattern, with a lack of problem size effect for problems with sums beyond 7, which is inconsistent with retrieval-based interference models and aligns with the automatized counting theory.