The impact of multiple representations on students' understanding of vector field concepts: Implementation of simulations and sketching activities into lecture-based recitations in undergraduate physics

Multiple external representations (e. g. diagrams, equations) and their interpretations play a central role in science and science learning as research has shown that they can substantially facilitate the learning and understanding of science concepts. Therefore, multiple and particularly visual representations are a core element of university physics. In electrodynamics, which students encounter already at the beginning of their studies, vector fields are a central representation typically used in two forms: the algebraic representation as a formula and the visual representation depicted by a vector field diagram. While the former is valuable for quantitative calculations, vector field diagrams are beneficial for showing many properties of a field at a glance. However, benefiting from the mutual complementarity of both representations requires representational competencies aiming at referring different representations to each other. Yet, previous study results revealed several student problems particularly regarding the conceptual understanding of vector calculus concepts. Against this background, we have developed research-based, multi-representational learning tasks that focus on the visual interpretation of vector field diagrams aiming at enhancing a broad, mathematical as well as conceptual, understanding of vector calculus concepts. Following current trends in education research and considering cognitive psychology, the tasks incorporate sketching activities and interactive (computer-based) simulations to enhance multi-representational learning. In this article, we assess the impact of the learning tasks in a field study by implementing them into lecture-based recitations in a first-year electrodynamics course at the University of Goettingen. For this, a within- and between-subjects design is used comparing a multi-representational intervention group (IG) and a control group (CG) working on traditional calculation-based tasks (<i>N</i> = 81). Group comparisons revealed that students in the intervention group scored significantly higher on a vector field performance test after the intervention (<i>p</i> = 0.04, <i>d</i> = 0.40) while perceiving higher cognitive load during task processing (extraneous <i>p</i> < 0.001, <i>d</i> = 0.75; intrinsic <i>p</i> = 0.02, <i>d</i> = 0.47; germane <i>p</i> = 0.02, <i>d</i> = 0.48). Moreover, students who worked with multi-representational learning tasks achieved higher normalized learning gains in tasks addressing conceptual understanding and representational competencies related to vector field diagrams and vector calculus concepts (<i>g</i> _{<i>H, IG</i>} = 0.35, <i>g</i> _{<i>H, CG</i>} = 0.13). These results provide guidance for the design of multi-representational learning tasks in field-related physics topics and beyond.