The understanding of graphs and extraction of relevant information from graphs plays a major role in physics education and is also important in several related fields. Recently, Susac et al. [Phys. Rev. Phys. Educ. Res. 14, 020109 (2018)] compared physics and psychology students' understanding of graphs in the contexts of physics and finance. They showed that physicists scored significantly higher in both domains and that all students solved the slope problems better than the area problems. Moreover, eye-tracking data revealed that physics students spent more time on problems associated with the area under the graph and focused longer on the axis labels of finance graphs, indicating higher cognitive demands. In this eyetracking study, we aim for a generalization of the results obtained by Susac et al. by comparing physics students to another nonphysics sample, viz., economics students. The findings broadly confirm the results of Susac et al.; that is, physics students perform better than nonphysics students. While economics students likely have better prior knowledge on finance context than psychology students, the physics students still outperform them on the finance questions. In contrast to the work by Susac et al., both groups of students had the same visit duration on the graphs, consequently proving total dwell time to be an inadequate predictor of performance. Instead, we identify that attention on concept-specific areas of interest within the graphs discriminates the correct from the incorrect performers. Furthermore, we analyzed the confidence level of the two student groups and found that physics students have a higher ability to correctly judge their own performance compared to economics students. Overall, our results highlight the importance of an instructional adjustment towards a more mathematical-and graphical-based education.

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The coordination of multiple external representations is important for learning, but yet a difficult task for students, requiring instructional support. The subject in this study covers a typical relation in physics between abstract mathematical equations (definitions of divergence and curl) and a visual representation (vector field plot). To support the connection across both representations, two instructions with written explanations, equations, and visual representations (differing only in the presence of visual cues) were designed and their impact on students' performance was tested. We captured students' eye movements while they processed the written instruction and solved subsequent coordination tasks. The results show that students instructed with visual cues (VC students) performed better, responded with higher confidence, experienced less mental effort, and rated the instructional quality better than students instructed without cues. Advanced eye-tracking data analysis methods reveal that cognitive integration processes appear in both groups at the same point in time but they are significantly more pronounced for VC students, reflecting a greater attempt to construct a coherent mental representation during the learning process. Furthermore, visual cues increase the fixation count and total fixation duration on relevant information. During problem solving, the saccadic eye movement pattern of VC students is similar to experts in this domain. The outcomes imply that visual cues can be beneficial in coordination tasks, even for students with high domain knowledge. The study strongly confirms an important multimedia design principle in instruction, that is, that highlighting conceptually relevant information shifts attention to relevant information and thus promotes learning and problem solving. Even more, visual cues can positively influence students' perception of course materials.

Relating mathematical concepts to graphical representations is a challenging task for students. In this paper, we introduce two visual strategies to qualitatively interpret the divergence of graphical vector field representations. One strategy is based on the graphical interpretation of partial derivatives, while the other is based on the flux concept. We test the effectiveness of both strategies in an instruction-based eye-tracking study with N ¼ 41 physics majors. We found that students' performance improved when both strategies were introduced (74% correct) instead of only one strategy (64% correct), and students performed best when they were free to choose between the two strategies (88% correct). This finding supports the idea of introducing multiple representations of a physical concept to foster student understanding. Relevant eye-tracking measures demonstrate that both strategies imply different visual processing of the vector field plots, therefore reflecting conceptual differences between the strategies. Advanced analysis methods further reveal significant differences in eye movements between the best and worst performing students. For instance, the best students performed predominantly horizontal and vertical saccades, indicating correct interpretation of partial derivatives. They also focused on smaller regions when they balanced positive and negative flux. This mixedmethod research leads to new insights into student visual processing of vector field representations, highlights the advantages and limitations of eye-tracking methodologies in this context, and discusses implications for teaching and for future research. The introduction of saccadic direction analysis expands traditional methods, and shows the potential to discover new insights into student understanding and learning difficulties.

Smartphones and Tablets are used as experimental tools and for quantitative measurements in two traditional laboratory experiments for undergraduate physics courses: The Doppler effect is analyzed and the speed of sound is determined with an accuracy of about 5 % using ultrasonic frequency and two smartphones, which serve as rotating sound emitter and stationary sound detector. Emphasis is put on the investigation of measurement errors in order to judge experimentally derived results and to sensitize undergraduate students to the methods of error estimates. The distance dependency of the illuminance of a light bulb is investigated using an ambient light sensor of a mobile device. Satisfactory results indicate that the spectrum of possible smartphone experiments goes well beyond those already published for mechanics.