First-Year Engineering Students’ Interpretations of Differentials and Definite Integrals

Abstract

In this paper we focus on Norwegian first-year engineering students’ interpretations of differentials and definite integrals. Through interviews with 15 engineering students, we investigated how the students interpreted the different symbols involved in the Fundamental Theorem of Calculus (FTC), as displayed in the textbook used in their calculus course. Through the students’ reflections, we aimed to gain insight into the students’ interpretations of differentials, infinitesimals, and limits, and how these concepts were used to interpret the definite integral. Despite a rather rigorous limit-based approach to definite integrals, provided in teaching and in the students’ textbook, we observed that most students offered conceptual interpretations closer linked with an infinitesimal approach, in terms of integrals being regarded as sums of narrow bars, in line with Leibniz.