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.

A research-informed graphical tool to visually approach Gauss’ and Stokes’ theorems in vector calculus

“…However, providing an appropriate educational embedding with explicit tasks, that call for user actions, help to avoid misinterpretations and difficulties as well as support scientific working with the tool [44]. For this purpose, we developed research-informed learning tasks, which are based on the visual interpretation of the vector field concepts proposed in sections 2 and 3, integrate drawing activities, and involve the graphical tool in a structured manner (see [45,46] for conceptualisation of the learning tasks). The materials cover four units on divergence, Gauss' theorem, curl, and Stokes' theorem.…”

“…In summer semester 2022 and 2023, we implemented the aforementioned multi-representational learning tasks in recitations of a weekly second-semester course on electromagnetism at the University of Goettingen and examined their impact on different outcome variables, for example, conceptual understanding, cognitive load, and representational competencies [46]. Using a rotational design, students were first working with the multi-representational tasks and the tool and completed traditional, calculation-based tasks afterwards or vice versa (see [46] for a detailed description of the study design and the methods). However, learning efficiency is not supposed to be the topic of this article, but we reveal first insights into students' usability and perceived educational impact of the tool.…”

How Multiple Representations Using Cyber–Physical System to Teach Rectilinear Motion Improves Learning and Creativity

“…Multiple representations refer to an instructional approach based on cognitive engagement. Here, students make connections between different representations, addressing the gap between mathematical and conceptual reasoning [3]. It is supported by the constructivist learning theory, where learners construct knowledge through active engagement with the material, creating their own understanding [4], and the cognitive load theory, which emphasizes the importance of managing the amount of information processed at one time to maximize learning [5].…”

Objective Analysis of Orbital Rim Fracture CT Images Using Curve and Area Measurement

“…Numerous studies have focused on simplifying and standardizing spaces or structures and their relationships, employing methods such as Hamilton's Ricci ow, geometrization, and vector calculus [2][3][4][5] . These theoretical approaches offer satisfactory solutions to complex structures and shapes that are di cult to grasp intuitively.…”