The model ties the speed of each strategy to experience. Repeated practice speeds up counting along a mental sequence, while repeated exposure strengthens direct memory links between a problem and its answer. When practice follows certain orders, such as skipping items or repeating blocks, those patterns change which strategy becomes more reliable. The work reproduces surprising experimental findings, like larger problems sometimes being memorized earlier, by connecting the microdynamics of practice to performance shifts.
For educators and anyone thinking about how learning unfolds, this approach reframes automaticity as an emergent balance rather than a final state. The details point toward practical questions: how should practice be arranged to support flexible fluency, who benefits from patterned sequences, and how does this interact with individual differences in memory? Follow the full article to see how a computational lens links simple exercises to broader ideas about human growth and inclusive learning design.
Abstract
This article presents a computational learning model in which procedural execution and memory retrieval codevelop, using simple arithmetic, which provides a particularly well-controlled domain for investigating this issue. In single-digit addition learning, strategies employed initially rely on counting due to the lack of stored answers in memory. Over time, associations between problems and their solutions are strengthened. The model accounts for this learning process by dynamically selecting between counting and memory retrieval, based on their expected duration. It also introduces a mechanism for accelerating counting throuSUPPLEMgh repeated practice along the mental sequence. The model was first tested on data collected from adults learning to solve alphabet arithmetic problems over a 3-week experiment. It successfully replicated the empirical finding that larger problems are memorized earlier than smaller ones. A second simulation was conducted using data from an experiment manipulating problem structure: participants were trained on either contiguous (A+…, B+…, C+…) or noncontiguous (A+…, C+…, E+…) sequences. This variation affected the transition between strategies: participants in the noncontiguous condition showed a greater tendency to rely on retrieval, as the practice of moving from one letter to the next differed. The model also reproduced this pattern. Overall, the results suggest that no single strategy dominates at the end of learning; rather, counting and retrieval coexist, depending on problem size and structure. This model is, to our knowledge, the only one to incorporate a counting acceleration mechanism in line with the automated counting theory and memory retrieval.
