Abstract
The principle of inversion—that a + b − b must equal a—requires a sensitivity to the relation between addition and subtraction that is critical for understanding arithmetic. Use of inversion, albeit inconsistent, has been observed in school-age children, but when use of a computational shortcut based on inversion emerges and how awareness of the inversion principle relates to other mathematical or numerical skills remain unclear. Two possibilities were explored in 3-year-olds by adapting a method used previously with older children involving the addition and subtraction of blocks differing in length. These children were significantly more accurate on inversion than standard problems, this difference was observed even in children who did not count well, and performance did not differ between formats that afforded qualitative or quantitative solutions. Thus, 3-year-olds appear to develop an early sensitivity to quantitative inversion.
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