Neural evidence for procedural automatization during cognitive development: Intraparietal response to changes in very-small addition problem-size increases with age

Cognitive development is often thought to depend on qualitative changes in problem-solving strategies, with early developing algorithmic procedures (e.g., counting when adding numbers) considered being replaced by retrieval of associations (e.g., between operands and answers of addition problems) in adults. However, algorithmic procedures might also become automatized with practice. In a large cross-sectional fMRI study from age 8 to adulthood (n = 128), we evaluate this hypothesis by measuring neural changes associated with age-related reductions in a behavioral hallmark of mental addition, the problem-size effect (an increase in solving time as problem sum increases). We found that age-related decreases in problem-size effect were paralleled by age-related increases of activity in a region of the intraparietal sulcus that already supported the problem-size effect in 8- to 9-year-olds, at an age the effect is at least partly due to explicit counting. This developmental effect, which was also observed in the basal ganglia and prefrontal cortex, was restricted to problems with operands ≤ 4. These findings are consistent with a model positing that very-small arithmetic problems-and not larger problems-might rely on an automatization of counting procedures rather than a shift towards retrieval, and suggest a neural automatization of procedural knowledge during cognitive development.

The development of simple addition problem solving in children: Reliance on automatized counting or memory retrieval depends on both expertise and problem size

In an experiment, 98 children aged 8 to 9, 10 to 12, and 13 to 15 years solved addition problems with a sum up to 10. In another experiment, the same children solved the same calculations within a sign priming paradigm where half the additions were displayed with the "+" sign 150 ms before the addends. Therefore, size effects and priming effects could be considered conjointly within the same populations. Our analyses revealed that small problems, constructed with addends from 1 to 4, presented a linear increase of solution times as a function of problem sums (i.e., size effect) in all age groups. However, an operator priming effect (i.e., facilitation of the solving process with the anticipated presentation of the "+" sign) was observed only in the group of oldest children. These results support the idea that children use a counting procedure that becomes automatized (as revealed by the priming effect) around 13 years of age. For larger problems and whatever the age group, no size or priming effects were observed, suggesting that the answers to these problems were already retrieved from memory at 8 to 9 years of age. For this specific category of large problems, negative slopes in solution times demonstrate that retrieval starts from the largest problems during development. These results are discussed in light of a horse race model in which procedures can win over retrieval.