Huang, H., Wang, J., Chen, C. & Zhang, X. (2013). Teaching divergence and curl in an Electromagnetic Field course. International Journal of Electrical Engineering Education, 50(4), 351-357.
 
The authors teach an electromagnetic field course and recognise that physical interpretation of divergence and curl are a difficulty for students, even though the actual calculations are not. They suggest a teaching method which begins with capturing the students’ interest through fictional and theoretical invisibility cloaks. The maths behind the theory involves Maxwell’s equations and hence divergence and curl. The authors suggest ways of teaching divergence and curl through flux and circulation, beginning with the macro and moving to the micro in logical ways.
 
Do not treat this blog entry as a replacement for reading the paper. This blog post represents the understanding and opinions of Torquetum only and could contain errors, misunderstandings or subjective views.
 Pepper, R.E., Chasteen, S.V., Pollock, S.J. & Perkins, K.K. (2012) Observations on student difficulties with mathematics in upper-division electricity and magnetism. Physical Review Special Topics – Physics Education Research, 8(010111), 1-15.
 
The authors focus in this paper on the mathematical difficulties experienced by physics and engineering students in an “upper division” electricity and magnetism course. They categorise the difficulties as (p. 2):
  • “Students have difficulty combining mathematical calculations and physics ideas. This can be seen in student difficulty setting up an appropriate calculation and also in interpreting the results of the calculation in the context of a physics problem. (However, students can generally perform the required calculation.)
  • Students do not account for the underlying spatial situation when doing a mathematical calculation.
  • Students do not access an appropriate mathematical tool. Students may instead choose a mathematical tool that will not solve the relevant problem, or may choose a tool that makes the problem too complex for the student to solve.”
Using the troublesome concepts of Gauss’s Law, various vector calculus techniques, and electrical potential, the authors demonstrate these three categories of difficulty with many examples of specific problems and student responses. Of specific interest to me were the vector calculus issues. They find that students struggle with the “vector nature” of a vector field, struggling to think of magnitude and direction simultaneously. Additionally, students can calculate gradient, divergence and curl easily, but struggle with the physical interpretation of these quantities. The authors hypothesise that the way vector calculus is taught in mathematics class, the students fail to see integrals as “sums of little bits of stuff”, which I would like to think is not true in my maths classes, where the sum nature of integrals is repeatedly emphasised. Another vector integration difficulty is found in students struggling to express dA and dV in suitable coordinate systems.
 
They discuss methods they have used in classroom pedagogy, out of classroom assistance and transformed resources to address these difficulties. Even with all their changes, they find that certain problems remain challenging for the students. They argue that these concepts are hard to understand and that the instructors are not keeping this well enough in mind. They discuss ways of moving forward. I thoroughly enjoyed this paper, found it pertinent to current and future work of mine, and benefited from the thorough literature review.
 
Do not treat this blog entry as a replacement for reading the paper. This blog post represents the understanding and opinions of Torquetum only and could contain errors, misunderstandings or subjective views.
 Leppävirta, J. (2011). The impact of mathematics anxiety on the performance of students of electromagnetics. Journal of Engineering Education, 100(3), 424-443.
 
The author investigated the relationship between mathematical anxiety and performance in an electromagnetics course. There is a literature review of studies on mathematics anxiety showing, in general, that there is a correlation between high anxiety and poor performance. The causal relationship tends to be less clear, however, although there is some evidence to show that poor prior performance leads to higher anxiety which in turns impacts negatively on performance in procedural tasks. Two maths anxiety scales are discusses, the Fennema-Sherman scale and the MARS scale. Those scales and others were adapted to make the Electromagnetics Mathematics Anxiety Rating Scale (EMARS) which was used in this study. The scale had several subscales which measured perceived usefulness of the course, confidence, interpretation anxiety, fear of asking for help, and persistency. The data and results are discussed in some detail. Conclusions include that high anxiety students perform less well in procedural work than low anxiety students, but that conceptual performance is less clearly aligned with anxiety. In addition, high anxiety students felt less confident about their maths ability and also self-describe as being less persistent in solving mathematical problems. The authors close with the suggestion that assessment should be more aligned with conceptual understanding rather than procedural processes.
 
Do not treat this blog entry as a replacement for reading the paper. This blog post represents the understanding and opinions of Torquetum only and could contain errors, misunderstandings or subjective views.

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