RUME 27
2025
Alexandria, Virginia
The Complexity Coordinating the “Product Layer” and Definite Integrals in Introductory Physics
Page: 55
Research on students’ construction and interpretation of integrals has grown significantly over the past decade. The present paper contributes to recent research on challenges which students experience while coordinating the “product layer”, 𝑓(𝑥) ∙ 𝑑𝑥, and the definite integral in applied contexts. In particular, we demonstrate a case study which examines how an undergraduate student, Matthew, linked the “product layer” and definite integral in an introductory physics task by blending mathematics, physics, and visualization knowledge resources. We analyzed Matthew’s moment-to-moment reasoning by utilizing a modified dynamic conceptual blending diagram (MDCBD), coming from the dynamic conceptual blending perspective, and an expanded Visualization/Analysis/Physics (VAP)-model, as detailed in (Sus & Izsák, 2024). Our findings indicate that students’ understanding of multiplication with quantities in applied integration contexts is highly complex and that neglecting the dynamic interactions of knowledge resources represents a significant gap in integration research