Use these descriptions of diagnostic and instructional tools to help young learners move beyond reliance on physical materials to negotiate arithmetic tasks.

Contributor Notes

Jonathan N. Thomas,, is an assistant professor of mathematics education at Northern Kentucky University and a Kentucky Center for Mathematics faculty associate.

Pamela D. Tabor,, is a school-based elementary math specialist in Harford County, Maryland.

(Corresponding author is Thomas
(Corresponding author is Tabor
Teaching Children Mathematics
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