Smart Errors in Learning Multidigit Number Meanings

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 spelling - might reflect children's initial PV understanding that might be important for later learning of multidigit numbers and calculation. The current study examines the development of smart errors on Base-Ten Counting (invented counting errors) and Transcoding (expanded errors) in 279 U.S. kindergartners (Mage = 5.76 years) and investigated whether the presence of smart errors is associated with 1) higher concurrent levels of PV task accuracy, 2) greater growth in PV understanding over one year, 3) higher levels of multidigit calculation in second grade. Results indicate that the two errors emerged in an overlapping waves pattern, with expanded errors appearing first and waning earlier than invented counting errors. Kindergartners who made invented counting errors but not expanded errors demonstrated the highest overall concurrent PV understanding. Second, kindergartners who made Transcoding expanded errors showed the greatest growth in PV understanding compared to those who exhibited only invented-counting errors. Third, kindergartners who made invented counting errors alone showed stronger multidigit calculation skills in second grade compared to those who made neither error. Thus, these smart errors reflect partial structural knowledge of place value that is a potentially important developmental contributor to learning multidigit number meanings.