Pathways for learning arithmetic: Distinct dynamics for associative and procedural acquisition

Learning is a multifaceted process that continues across the lifespan, with variation in how different types of knowledge are acquired and retained. One distinction exists between the cognitive skills learned through memory-based associations and those learned through rule-based (strategy) execution. While both forms are central to arithmetic acquisition, little is known about their dynamics in adulthood and their cognitive underpinnings. Addressing this gap is essential for developing effective re-education programs, especially in arithmetic, where learning difficulties can impact personal, academic, and socio-economic outcomes. Here, healthy adults with varying ages and cognitive profiles learned to solve a limited set of novel arithmetic problems using either associative (memory-based) or procedural (strategy-based) methods. Group-level analyses revealed that both learning conditions reached comparable performance. Individual learning trajectories, modeled using a composite efficiency index (inverse efficiency score), revealed similar efficiency gain but distinct dynamics: associative learning showed a steep, abrupt gain, whereas procedural learning progressed gradually along a smoother trajectory. Regression analyses indicated that verbal long-term memory predicted associative learning, while arithmetic abilities specifically predicted procedural learning. Notably, efficiency gains in one condition did not predict gains in the other, further supporting that, notwithstanding their similarities, the two learning trajectories are different in nature. Error analysis further revealed that performance in the procedural condition shifted from calculation-based to retrieval-based processes with practice. These findings demonstrate that associative and procedural arithmetic learning are initially supported by distinct cognitive mechanisms but converge over time, underscoring the importance of considering individual cognitive profiles when designing tailored educational/rehabilitation interventions.