RUME 28
2026
Alexandria, Virginia
Defining a “Differentials-within-limits” Framework for First-year Calculus
Page: 875
Work in first-year calculus has clearly shown the power that “differentials” afford for first-year calculus learning, but it also speaks of the need to build ideas of limits. While some researchers have loosely described informal differentials and limits within the same paradigm, their actual conceptual definitions and relationships have not always been explicitly constructed. Continued progress in this area could benefit from theoretical consideration of: (a) providing clearer intuitive definitions for differentials inside a limits-based approach to calculus, and (b) defining more exactly the relationships between differentials and limits. We provide here a theoretical framework for building a simultaneous differentials-and-limits approach to first-year calculus.