RUME 28
2026
Alexandria, Virginia
Investigating the Role of Various Conceptions of Subtraction in Calculus: A Textbook Analysis
Page: 1175
The concept of difference, and its representation as distance within a graphical representation pervades Calculus. Indeed, difference expressions represent change, the very foundation of the subject. Yet, students may often default to a takeaway conception of subtraction, which may be incompatible with viewing subtraction as finding change. Other ways of conceiving of subtraction may support additional ideas in Calculus, related to translating functions, finding areas and volumes, or indexing terms of a sequence. In this preliminary report, we investigate the prevalence of various conceptions of subtraction in the study of Calculus through a textbook analysis of Stewart’s Calculus: Early Transcendentals. We report our findings from our analysis and future directions for research.