Visual cues improve students’ understanding of divergence and curl: Evidence from eye movements during reading and problem solving

Pascal Klein,Jouni Viiri,Jochen Kuhn

doi:10.1103/physrevphyseducres.15.010126

Pascal Klein, Jouni Viiri + Show 1 more

Open Access

https://doi.org/10.1103/physrevphyseducres.15.010126

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Abstract

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.

Highlights

Visual representations have the potential to substantially promote the learning of abstract concepts [1]
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
They are important in many branches of physics, and oftentimes, they are expressed as vector field plots

Summary

Introduction

Visual representations have the potential to substantially promote the learning of abstract concepts [1]. Students must learn about the representations before they can be used for learning or problem solving. This interdependence is known as the representational dilemma [2]. One example which has recently been studied in this context consists of the visual interpretation of twodimensional vector field plots with respect to divergence or curl [3,4,5,6]. Vector fields are mathematical structures that assign a vector to every point in space. They are important in many branches of physics, and oftentimes, they are expressed as vector field plots (see Fig. 1). Learning how divergence or curl relate to this representation contributes

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