RUME 27
2025
Alexandria, Virginia
Undergraduate Students’ Models of Subtraction and its Significance for Calculus
Page: 750
The operation of subtraction, though emphasized at the elementary level, has a central role in expressing key ideas in Calculus. In graphical representations of Calculus concepts, a magnitude interpretation of a difference, that b–a gives the distance between a and b, often supports students in making sense of the representation. A magnitude interpretation uses a determine the difference model of subtraction, in which subtraction find how much a differs from b. Using exploratory teaching interviews, we investigated the models of subtraction that nine undergraduate students used on tasks designed to support them in using a magnitude interpretation. We found four distinct models of subtraction that students employed in these tasks. We describe these models and associated observable behavior. We discuss implications of these findings for the teaching and learning of Calculus and future research directions.