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

Abstract

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 Göttingen. For this, a within- and between-subjects design is used comparing a multi-representational intervention group and a control group working on traditional calculation-based tasks. To analyze the impact of multiple representations, students' performance in a vector calculus test as well as their perceived cognitive load during task processing is compared between the groups. Moreover, analyses offer guidance for further design of multi-representational learning tasks in field-related physics topics.

Keywords: conceptual understanding; lecture-based recitations; multiple representations; physics; simulation; sketching; task-based learning; vector fields.

Figure 1

Study design with timeline from left (t₀) to right (t₂; intervention group IG, control group CG, multiple representations MRs). The designations “IG-CG group” and “CG-IG group” refer to the chronological order of the groups in the rotational design (first intervention group, then control group, or vice versa).