ON THE ADDITION AND SUBTRACTION OF INTEGERS: WE CAN'T REMOVE WHAT WE DON'T HAVE.

The article focuses on the mathematical processes involved in the addition and subtraction of integers, critically examining the common heuristic "flip the sign." It argues that this heuristic oversimplifies and obscures key concepts such as the inverse relationship between addition and subtraction, the non-commutative nature of subtraction, and the central role of the additive identity (zero) and zero pairs in understanding integer operations. Using visual models like tiles and number lines, the article demonstrates how introducing zero pairs clarifies why subtracting a negative number results in addition, emphasizing that one cannot remove more than is present without conceptual adjustments. The discussion highlights the importance of moving beyond simplistic shortcuts to foster deeper mathematical understanding in students.