Children's early accuracy on place value (PV) tasks longitudinally predicts their later multidigit calculation skills. However, another window into children's emerging base-ten concepts is the pattern of errors -- "smart errors" -- they exhibit on these measures. Past research has speculated that these smart errors -- similar to invented…

In simple rule-switching tests, 3- and 4-year-olds can follow each of two sorting rules but sometimes make perseverative errors when switching. Older children make few errors but respond slowly when switching. These age-related changes might reflect the maturation of executive functions (e.g., inhibition). However, they might also reflect…