Phenomenographic analysis and comparison of students’ conceptual understanding of electric and magnetic fields and the principle of superposition

There are studies of students’ understanding of the concept of the electric field, the magnetic field, and the use of the superposition principle that have contributed to the creation of both educational strategies and assessment tools. However, the difficulties of these two concepts have not been compared comprehensively. Therefore, this study aims to compare students’ conceptual understanding of electric and magnetic fields in questions regarding the field created by one source and the field produced by a system of two sources. We focus our study on students’ explanations about the magnitude and direction of the field and their application of the superposition principle in both contexts (electric and magnetic). We conducted this study with 322 engineering students in a Mexican university. We designed two versions of an open-ended questionnaire, one with the context of electricity and the other with magnetism. We created the questions using the parallelism between electricity and magnetism and used schematic representations with similar surface features to represent this parallelism. Analyzing the data through a phenomenographic approach, the students’ drawings and explanations gave insight into their understanding of the concept of field and the superposition principle application in the context of electricity and magnetism. We found that students have similar categories of understanding the concept of the electric and the magnetic field. In both contexts, there is an evident relationship between applying the principle of superposition and understanding the concept of field. We found that there is a greater tendency that a student correctly applies the superposition principle if that student has a robust representation of the field. We found evidence that students consistently merge two different representations (vector plots and field lines) in electricity and magnetism. We named this category of representation “hybrid vectors and field lines.” We also found that some students who draw hybrid representations of the field can still apply the superposition principle correctly. However, some conceptual understanding difficulties are dependent on the context: the known difficulty of confusion between forces and fields is more attached to the electricity context. The confusion between electricity and magnetism concepts is more relevant in the magnetism context. As in other literature, we found more evidence that the correct answer in multiple-choice questions may lead students who have mild difficulties (such as memorization and creating a hybrid representation) to choose a correct answer. We recommend that teachers and researchers of electricity and magnetism acknowledge the relationship between the conceptual understanding of the field and applying the superposition principle. We suggest that instructors be attentive to how they approach using representations of electric and magnetic fields.

Figure 1

The four questions analyzed in this study. On the left are the two items of the electricity version, and on the right, the same items of the magnetism version. The first question focuses on conceptual understanding of the electric and magnetics field’s magnitude and direction, through their drawings and explanations. The second question focuses on applying the superposition principle in the context of electric and magnetic fields, respectively.

Figure 2

The expected drawings for the questions of the field and the principle of superposition. On the left are those in the context of electricity. On the right, those in the context of magnetism. (a) The expected drawing for the electric field in question 1. (b) The expected drawing for the magnetic field in item 1. (c) The expected drawing for the electric field in question 2. (d) The expected drawing for the magnetic field in item 2.

Figure 3

We present examples of the drawings that students made in the first question of the electricity version. (a) An example of the drawing category vector diagram. (b) An example of the drawing category, hybrid vectors, and field lines. (c) An example of the drawing category, confusion between electric and magnetic fields.

Figure 4

Examples of the drawings that students made in the first question of the magnetism version. (a) An example of the drawing category vector diagram. (b) An example of the drawing category hybrid of vectors and field lines. (c) An example of the drawing category confusion between electric and magnetic fields.

Figure 5

Examples of the drawings that students made in the second question of the electricity version. (a) An example of the category superposition. (b) An example of the category contribution by each source. (c) An example of the category confusion force and field. (d) An example of the category E&M interference. (e) An example of the category difficulties with graphic addition. (f) An example of the category other.

Figure 6

Examples of the drawings that students made in the second question of the magnetism version. (a) An example of the category superposition. (b) An example of the category contribution by each source. (c) An example of the category confusion force and field. (d) An example of the category E&M interference. (e) An example of the category vectors cancel. (f) An example of the category other.