• Accepted Paper

Learning vector field concepts with multiple representations in introductory physics - Robustness of effects across instructional contexts

Larissa Hahn, Alexander Voigt, and Pascal Klein

Phys. Rev. Phys. Educ. Res. - Accepted 14 October, 2026

DOI: https://doi.org/10.1103/hsd4-qy8s

Abstract

Students in introductory electromagnetism often struggle with the conceptual interpretation of vector differential operators such as divergence and curl, particularly when reasoning from graphical representations of vector fields. To address these difficulties, we developed research-based multi-representational learning tasks that combine sketching activities with an interactive simulation to support conceptual understanding of vector calculus concepts. Building on a previous field study demonstrating the effectiveness of these tasks in a homework implementation setting, the present study investigates whether these learning effects generalize across instructional contexts. To this end, we evaluated an independent in-class implementation at RWTH Aachen University and compared the results with a reanalysis of data from the previously investigated homework implementation at the University of Göttingen using the same performance measure. Students participated in an in-class intervention group (IG1), a homework intervention group (IG2), or a control group (CG) working on traditional calculation-based tasks (N=131). Students in both intervention groups showed significant improvements in response accuracy (IG1: p<.001, ηG2=.20; IG2: p<.001, ηG2=.11) and response confidence (IG1: p<.001, ηG2=.17; IG2: p=.003, ηG2=.03), whereas no significant improvement was observed in the control group. The comparable learning gains observed in the independently implemented in-class intervention and the reanalyzed homework intervention (normalized Hake gain gH,IG1=.44, gH,IG2=.38) indicate that the effectiveness of the multi-/representational learning tasks is robust across instructional and institutional contexts. Exploratory analyses further revealed no evidence for a dose-response relationship between the number of completed learning tasks and the learning gains, highlighting the need for future research on the role of intervention intensity in multi-representational learning about differential operators.

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