Individual differences and developmental change in the associative relations among numbers

Children in grades 3 through 5 and adults performed a number-matching task in which they were required to verify the presence of a target digit (i.g., 7) in a previously presented pair (e.g., 2 + 7). For adults, targets that were the sum of the initial pair (e.g., 9) and targets that were close to the initial pair (e.g., 6) were rejected more slowly than unrelated digits. Activation of sums is consistent with models of arithmetic knowledge in which addition facts are stored in a network representation. Activation of close targets (the distance effect) may reflect the counting-based origins of number representations. Consistent with these hypotheses, 8- to 10-year-old children showed minimal effects of sum activation, but large effects of distance. Even at this age, however, distance effects were smaller for subjects with higher levels of arithmetic skill. Thus, changes in the strength of arithmetic connections occurred with development and accounted for individual differences among adults. For children, however, individual differences were related to changes in the strength of number-line connections.