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Understanding Maxwell's equations in differential form is a prerequisite to study the electrodynamic phenomena that are discussed in advanced electromagnetism courses. It is therefore necessary that students master the use of vector calculus in physical situations. In this light we investigated the difficulties second year students at KU Leuven encounter with the divergence and curl of a vector field in mathematical and physical contexts. We have found they are quite skilled at doing calculations, but struggle with interpreting graphical representations of vector fields and applying vector calculus to physical situations. We have found strong indications that traditional instruction is not sufficient for our students to fully understand the meaning and power of Maxwell's equations in electrodynamics.
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... To determine divergence and curl, students have to compare arrows in terms of their length and direction. In contrast, research showed that students had less problems determining these aspects mathematically via equations [2,10]. Bollen et al. [10] investigated students' difficulties in understanding divergence and curl using vector fields in the context of electrodynamics and electromagnetism (see also [9]). ...
... In contrast, research showed that students had less problems determining these aspects mathematically via equations [2,10]. Bollen et al. [10] investigated students' difficulties in understanding divergence and curl using vector fields in the context of electrodynamics and electromagnetism (see also [9]). They found that students struggled with interpreting graphical representations of vector fields, indicating a lack of conceptual understanding [9,10]. ...
... Bollen et al. [10] investigated students' difficulties in understanding divergence and curl using vector fields in the context of electrodynamics and electromagnetism (see also [9]). They found that students struggled with interpreting graphical representations of vector fields, indicating a lack of conceptual understanding [9,10]. ...
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Visual–graphical representations are used to visualise information and are therefore key components of learning materials. An important type of convention-based representation in everyday contexts as well as in science, technology, engineering, and math (STEM) disciplines are vector field plots. Based on the cognitive theory of multimedia learning, we aim to optimize an instruction with symbolical-mathematical and visual-graphical representations in undergraduate physics education through spoken instruction combined with dynamic visual cues. For this purpose, we conduct a pre-post study with 38 natural science students who are divided into two groups and instructed via different modalities and with visual cues on the graphical interpretation of vector field plots. Afterward, the students rate their cognitive load. During the computer-based experiment, we record the participants’ eye movements. Our results indicate that students with spoken instruction perform better than students with written instruction. This suggests that the modality effect is also applicable to mathematical-symbolical and convention-based visual-graphical representations. The differences in visual strategies imply that spoken instruction might lead to increased effort in organising and integrating information. The finding of the modality effect with higher performance during spoken instruction could be explained by deeper cognitive processing of the material.
... To determine divergence and curl, students have to compare arrows in terms of their length and direction. In contrast, research showed that students had less problems determining these aspects mathematically via equations (Bollen, van Kampen, & De Cock, 2015;Singh & Maries, 2013). Bollen et al. (2015) investigated students' difficulties in understanding divergence and curl using vector fields in the context of electrodynamics and electromagnetism (see also Bollen et al., 2016). ...
... In contrast, research showed that students had less problems determining these aspects mathematically via equations (Bollen, van Kampen, & De Cock, 2015;Singh & Maries, 2013). Bollen et al. (2015) investigated students' difficulties in understanding divergence and curl using vector fields in the context of electrodynamics and electromagnetism (see also Bollen et al., 2016). They found that students struggled with interpreting graphical representations of vector fields, indicating a lack of conceptual understanding (Bollen et al., 2015(Bollen et al., , 2016. ...
... Bollen et al. (2015) investigated students' difficulties in understanding divergence and curl using vector fields in the context of electrodynamics and electromagnetism (see also Bollen et al., 2016). They found that students struggled with interpreting graphical representations of vector fields, indicating a lack of conceptual understanding (Bollen et al., 2015(Bollen et al., , 2016. Based on previous findings, Klein et al. (2018) developed materials with multiple representations, including an equation, a graphical vector field representation, and a written instruction, to promote a step-by-step procedure for visually assessing the divergence of a field. ...
... While temporary magnetism is a pervasive topic in K-12 education, it is also one that is not well studied. Many studies that focus on how older students reason about magnetism in general [1][2][3][4][5][6] do not include reasoning about temporary magnetism. Here we examine how students reason about temporary magnetism. ...
... Importantly, how a student reasons about temporary magnetism may influence their understanding of both permanent magnetism and electromagnetism, but yet temporary magnetism is traditionally unexplored in PER. Research has focused on other important aspects such as electromagnetic induction [1] and vector fields [2,3]. However, as temporary magnetism is commonly encountered during inquiry-based lessons on magnetism, the students' experience with temporary magnetism may be a confounding factor in how the students understand magnetism. ...
... Other research has approached magnetism from a more qualitative viewpoint in order to examine student reasoning about magnetism [1]. However, much of this research [1][2][3][4][5][6] is focused on undergraduate and high school students. Whereas less research is focused on younger grades, despite students in those lower grades commonly encountering temporary magnetism in their instruction. ...
... For the analysis of the interviews, we explore students' knowledge of the expectation value from a concept image perspective [14]. This perspective originated in undergraduate mathematics education research but has more recently been used in physics education research to categorize student thinking about vector calculus concepts in electrodynamics [18][19][20][21]. A concept image is a multifaceted and dynamic construct. ...
... A set of categories appearing in multiple situations is considered stable for that student [22]. Previous research in electricity and magnetism has used phenomenography to categorize student ideas related to vector operators [20] and magnetic fields [23]. ...
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... These representation formats are very essential in studying physics, including verbal representations, pictures, graphs and mathematics [5]. Graphical representation can help students to conceptualise abstract mathematical structures in vector calculus when understanding Maxwell's [6]. It is necessary to introduce learning models and teaching materials with multiple representations to students in order to gain a better understanding. ...
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... Certain types of questions we used to ask are no longer suitable for the open book, open internet environment, such as ones heavily reliant on computation or on drawing a diagram, in essence any question easily outsourced to an advanced calculator (see also Bailey et al., 2020). Proficiency at vector calculus is not demonstrated by computation, however (Bollen et al., 2015). We argue that it is demonstrated by information interpretation, recognizing available options and effective decision-making. ...
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