This study explored students' conceptual understanding of and learning difficulties with the gradient in an upper-level electromagnetism course. The participants were 25 pre-service teachers in the Physics Education Department of a university in Korea. For the data collection, reflective journal writing, paper and pencil tests, and interviews were done after lectures. The results showed some lack of coherence between physical meanings of and mathematical expressions for the gradient, and some lack of congruence between symbolic and geometric representations. The participants had a tendency to draw the gradient as a tangential line. Additionally, some of them confused the gradient with the divergence or the curl on a test that involved drawing the direction of the gradient, writing mathematical expressions for the gradient, and calculating the gradient. From the analysis of the reflective journals, we found that the sudents generally had more than a medium level of a difficulty in learning about the gradient.

Keywords: Gradient, Vector derivatives, Electromagnetism, Upper-level physics, Pre-service physics teacher, Representation