Undergraduate students’ conceptual understanding of electromagnetic waves

Understanding electromagnetic (EM) waves remains challenging for undergraduates, and research on their conceptual grasp of EM waves is comparatively scarce. This pilot study reports the development and validation of a hybrid two-tier multiple-choice diagnostic test on EM waves, administered to 35 second-year engineering students enrolled in an Electromagnetism course at Politecnico di Milano. The instrument comprises six items targeting three domains: sources of EM waves, propagation relationships, and reception mechanisms. Each item combines a multiple-choice tier with an open-ended justification, enabling concurrent quantitative analysis within the framework of Classical Test Theory and qualitative phenomenographic analysis of students’ reasoning. Item statistics show moderate difficulty (mean p = 0.58) and strong discrimination (mean D = 0.67; Ferguson’s Δ = 0.95), indicating satisfactory psychometric functioning for a pilot instrument. Phenomenographic analysis reveals predominantly fragmented, hybrid models in which students correctly recall isolated facts (e.g., field orthogonality, propagation speed in vacuum) but struggle to construct coherent causal explanations, particularly for wave generation and reception. The strong consistency between answer correctness and quality of justifications supports the interpretive validity of the test. The pilot study illustrates the potential of hybrid two-tier diagnostics to inform instructional design on EM waves.