Smart Errors in Learning Multidigit Number Meanings

ABSTRACT

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 (M_age = 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.

Acknowledgments

We thank the teachers and families of Wyoming, Michigan, Howard County, Maryland, Prince Georges County, Maryland, and Bloomington, Indiana, for their generous participation. This research was supported by the National Science Foundation (DRK-12 1664781 to K. S. Mix and DRK-12 1621093 to L. B. Smith).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

Deidentified data are available via the Digital Repository at the University of Maryland, http://hdl.handle.net/1903/31583.

Open scholarship

This article has earned the Center for Open Science badge for Open Data. The data are openly accessible at https://doi.org/10.1080/15248372.2024.2338722

Notes

¹ The pairwise comparison results are the same when using Tukey’s Honestly Significant Difference test.

Additional information

Funding

The work was supported by the National Science Foundation [DRK-12 1664781 to K. S. Mix; DRK-12 1621093 to L. B. Smith].