Abstract

Work in first-year calculus has clearly shown the power that treating differentials (such as dx) as tiny quantities affords for first-year calculus learning, yet a traditional limits-based approach leaves no room for them. While some researchers have loosely described informal differentials and limits within the same paradigm, their actual conceptual definitions and relationships have not 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. In this study, I propose a theoretical framework for a differentials-within-limits approach to first-year calculus centered around the idea of a model. I also present the results of a teaching experiment in which two pairs of students worked through a series of quantities-based tasks intended to develop differentials within limits. I examine their emerging understandings of limits, differentials, and derivatives under my framework.

Degree

MS

College and Department

Computational, Mathematical, and Physical Sciences; Mathematics Education

Rights

https://lib.byu.edu/about/copyright/

Date Submitted

2026-04-10

Document Type

Thesis

Keywords

calculus, differentials, limits, derivatives

Language

english

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