RUME 28
2026
Alexandria, Virginia
The Alignment of Student Conceptions With Course Learning Outcomes: A Case Study on the Definite Integral
Page: 1233
Students pursuing science, technology, engineering, and mathematics (STEM) degrees require some proficiency in Calculus. The Fundamental Theorem of Calculus is arguably the most important theorem taught in a Calculus I course, yet it is not covered until the last weeks of the semester in a traditional three-part Calculus sequence. As a result, students tend not to hold deep conceptual understandings around integration, and the conceptions that they do hold are procedurally based. This paper illustrates the disconnection between student conceptions around integration (primarily area-based) and the general emphasis (from mathematics education literature) on accumulation. In addition, our work highlights how course learning objectives may drive a primarily area-based interpretation of integration. Our preliminary findings from interview data with Calculus III students confirm prior research, suggesting that students hold strong procedural and area-based conceptions, rather than accumulation conceptions.