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

PERC Proceedings 2015, AIP Press (submitted)

Charles Baily, Laurens Bollen, Andrew Pattie, Paul van Kampen and Mieke De Cock

**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. In comparing pre- and post-instruction responses from E&M students we see that, although their understanding of the divergence and curl improved, relatively few of them were able to provide completely correct survey responses at mid-semester.

**Keywords:** physics education research, electromagnetism, divergence, mathematics, conceptual understanding.

**PACS:** 01.40.Fk