Larissa Hahn

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 (N = 81). Group comparisons revealed that students in the intervention group scored significantly higher on a vector field performance test after the intervention (p = 0.04, d = 0.40) while perceiving higher cognitive load during task processing (extraneous p < 0.001, d = 0.75; intrinsic p = 0.02, d = 0.47; germane p = 0.02, d = 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 (g_{H, IG} = 0.35, g_{H, CG} = 0.13). These results provide guidance for the design of multi-representational learning tasks in field-related physics topics and beyond.

Teachers commonly use examples that omit friction to teach Newton’s first and second law. Beyond the motion of planets, the flow of horizontal high-altitude winds along the isobars presents a real-world motion scenario with negligible friction. This natural phenomenon serves as an applicable context for the exploration of Newton’s first and second axioms and the vector addition of forces. This paper explores wind dynamics as a context that addresses force concepts, a relevant topic in high school physics. Here, we focus on forces affecting air parcels at high altitudes. For comparison, we also explain the wind at ground level (called surface wind), where friction plays an important role. We aim to elucidate the complexities of wind forces, offering a comprehensive understanding of how these forces interplay in real-world scenarios. Furthermore, we provide detailed examples of tasks for high school students to acquire an understanding of wind and aligning forces.

The current dropout rate in physics studies in Germany is about 60%, with the majority of dropouts occurring in the first year. Consequently, the physics study entry phase poses a significant challenge for many students. Students’ stress perceptions can provide more profound insights into the processes and challenges during that period. In a panel study featuring 67 measuring points involving up to 128 participants at each point, we investigated students’ stress perceptions with the perceived stress questionnaire (PSQ), identified underlying sources of stress, and assessed self-estimated workloads across two different cohorts. This examination occurred almost every week during the first semester, and for one cohort also in the second semester, yielding a total of 3241 PSQ data points and 5823 stressors. The PSQ data indicate a consistent stress trajectory across all three groups studied that is characterized by significant dynamics between measuring points, spanning from M = 20.1 , S D = 15.9 to M = 63.6 , S D = 13.4 on a scale from 0 to 100. Stress levels rise in the first weeks of the lecture, followed by stable, elevated stress levels until the exams and a relaxation phase afterward during the lecture-free time and Christmas vacation. In the first half of the lecture period, students primarily indicated the weekly exercise sheets, the physics lab course, and math courses as stressors; later on, preparation for exams and the exams themselves emerged as the most important stressors. Together with the students’ self-estimated workloads that correlate with the PSQ scores, we can create a coherent picture of stress perceptions among first-year physics students, which builds the basis for supportive measures and interventions. Published by the American Physical Society 2024

Gauss’ and Stokes’ theorems are fundamental results in vector calculus and important tools in physics and engineering. When students are asked to describe the meaning of Gauss’ divergence theorem, they often use statements like this: ‘The sum of all sources of a vector field in a region gives the net flux out of the region’. In order to raise this description to a mathematically sound level of understanding, we present an educational approach based on the visual interpretation of the vector differential operators, i.e. divergence and curl. As a starting point, we use simple vector field diagrams for a qualitative approach to connect both sides of the integral theorems, and present an interactive graphical tool to support this connection. The tool allows to visualise two-dimensional vector fields, to specify vector decomposition, to evaluate divergence and curl point wise, and to draw rectangles to determine surface and line integrals. From a meta-perspective, we situate this educational approach into learning with (multiple) representations. Based on prior research, the graphical tool addresses various learning difficulties of vector fields that are connected to divergence and curl. The tool was incorporated into the weekly lecture-based recitations of Physics II (electromagnetism) in 2022 and 2023, and we assessed various educational outcome measures. The students overall reported the tool to be intuitive and user-friendly (level of agreement 76%, N = 125 ), considered it helpful for understanding and recommended its use for introductory physics courses (level of agreement 65%, N = 65 ).

In mathematics education, students are repeatedly confronted with the tasks of interpreting and relating different representations. In particular, switching between equations and diagrams plays a major role in learning mathematical procedures and solving mathematical problems. In this article, we investigate a rather unexplored topic with precisely such requirements—that is, vector fields. In our study, we first presented a series of multiple-choice tasks to 147 introductory university students at the beginning of their studies and recorded students’ eye movements while they matched vector field diagrams and equations. Thereafter, students had to solve a similar coordination task on paper and justify their reasoning. Two cluster analyses were performed including (i) transition and fixation data on diagrams and options (Model 1), and (ii) additionally the number of horizontal and vertical saccades on the diagram (Model 2). In both models, two clusters emerge—with Model 1 distinguishing behaviors related to representational mapping and Model 2 additionally differentiating students according to representation-specific demands. Model 2 leads to a better distinction between the groups in terms of different performance indicators (test score, response confidence, and spatial ability) which also transfers to another task format. We conclude that vertical and horizontal saccades reflect executive actions of perception when approaching vector field coordination tasks. Thus, we recommend targeted interventions for mathematics lessons; these lessons must focus on a visual handling of the vector field diagram. Further, we infer that students’ difficulties can be attributed to covariational reasoning, thereby indicating the need for further investigations. From a methodological perspective, we reflect on the triangulation of eye-tracking and verbal data in (multiple-choice) assessment scenarios.

Eye tracking is becoming increasingly popular in physics education research (PER). As technology has advanced considerably in recent years and has become more user friendly, it is anticipated that eye tracking will play an increasingly significant role in assessing student learning at the process level in future studies. The main objective of this systematic review is to summarize the current status quo regarding eye tracking in PER and reviewing (a) the dissemination, (b) the methodological implementation, and (c) the insights provided by eye tracking in PER. We identified 33 journal articles, published between March 2005 and April 2021, that used eye tracking for original empirical research in the area of physics education. The results reveal that although eye tracking has been used in many different areas of physics, a clear focus on mechanics is evident, particularly for measuring visual attention in assessment scenarios like problem solving. While a high methodological rigor in the selection and analysis of the visual stimuli was apparent, only a few studies have provided a complete documentation of the technological implementation (e.g., movement restrictions, accuracy, and calibration information) and a theoretical embedding for interpreting eye-tracking data. To synthesize the results of the different studies, we created an inductive category system in accordance with the considered independent variables of the studies. Accordingly, visual attention was most frequently compared between levels of performance (correct vs incorrect or high vs low achievers), thereby leading to performance-discriminating factors of eye movement across studies. Furthermore, learners’ eye movements were compared across different stimuli, different time points, or between student groups to inform multimedia design and shed light on students’ learning progression. In summary, eye tracking is particularly useful for studying processes in different domains that are relevant to PER. Specific gaps in the literature, methodological limitations, and implications of existing findings were also identified to recommend future research and practices.