Student thinking about the divergence and curl in mathematics and physics contexts

TL;DR

This study investigates undergraduate students' understanding of divergence and curl in mathematics and physics, revealing common misconceptions and the impact of instruction on conceptual improvement.

Contribution

It provides comparative analysis of student conceptions before and after instruction, highlighting areas needing better teaching strategies for divergence and curl.

Findings

Students' understanding improved post-instruction

Physics students had more misconceptions related to graphical representations

Instruction significantly enhanced conceptual understanding

Abstract

Undergraduate physics students are known to have difficulties with understanding mathematical tools, and with applying their knowledge of mathematics to physical contexts. Using survey statements based on student interviews and written responses to open-ended questions, we investigated the prevalence of correct and incorrect conceptions regarding the divergence and curl of vector fields, among both mathematics and physics students. We compare and contrast pre-instruction responses from intermediate-level E&M students at KU Leuven and the University of St Andrews, with post-instruction responses from St Andrews students enrolled in a vector calculus course. The differences between these student populations were primarily in areas having to do with physics-related concepts and graphical representations of vector fields. Our comparison of pre- and post-instruction responses from E&M students shows that their understanding of the divergence and curl improved significantly in most areas, though not as much as would be desired.