Toward A Coherent Treatment of Negative Numbers

The transition from whole numbers to integers involves challenges for both students and teachers. Leadership in mathematics education calls for an ability to translate depth of understanding into effective teaching methods, and this landscape includes alternative treatments of familiar topics. Noting the multiple meanings associated with the horizontal bar that is often referred to as “minus sign,” the authors introduce a novel notation intended to address this ambiguity. In this system, the symbol “−” is reserved exclusively for subtraction. The four arithmetic operations and the concept of a number's opposite are then illustrated in light of such a notational shift. A valuable aspect of this excursion is that it encourages teachers to reflect on the relationship between some important mathematics and the pedagogical approaches they now use.