Counting on automatization: The automatized counting theory of mental arithmetic

• Counting procedures may automatize with development rather than being replaced. • Arithmetic fluency may emerge through quantitative not qualitative change. • Same neural mechanisms support problem-size effects from childhood to adulthood. • Developmental changes reflect increasing procedural efficiency, not strategy shift. • Dyscalculia may involve impaired procedural automatization across development. Counting—enumerating sets by establishing one-to-one correspondence with an internal counter—is fundamental to the invention and development of mathematics. Yet, dominant models assume that counting is abandoned over the course of learning as children achieve proficiency with basic arithmetic calculations (e.g., 2 + 3), being replaced by the retrieval of associations between operands (e.g., 2 + 3) and answers (e.g., 5) from long-term memory. Here we challenge this assumption, arguing that counting remains at the very heart of arithmetic fluency even in adults alongside associative retrieval. Using mental addition as our test case, we present evidence that associative models fail to account for key behavioral and neuroimaging findings. We then put forward the automatized counting hypothesis , a novel framework proposing that counting procedures initially used by children become progressively accelerated through practice until they operate unconsciously and effortlessly. Automatized counting may become so efficient that it may generate answers to simple addition problems as fast as (or faster than) retrieval of associations from memory, particularly for problems with small operands. Recognizing the role of counting in arithmetic development explains a range of problematic data for purely associative accounts. We present behavioral and neuroimaging evidence supporting our model and discuss its theoretical, educational, and clinical implications. Overall, counting should not be seen as a steppingstone to be abandoned, but as an enduring foundation of arithmetic skills. This view challenges the assumption that automaticity necessarily relies on associative retrieval, suggesting that procedural automatization might be fundamental to skilled performance across domains of symbolic knowledge.