Analytic Framework for Students' Cognitive Mistakes in Studying Electromagnetic Fields

Abstract

Students at various levels often experience cognitive difficulties when learning electromagnetic (EM) fields and waves. This can be attributed to the intensive mathematical reasoning and invisibility of physical EM phenomena. Students’ common misconceptions and alternative conceptual frameworks of EM concepts have been extensively studied. Students’ difficulties with mathematical thinking and manipulation in the contexts of EM have also been reported. However, most of the previous research studies were conducted using either multiple-choice surveys, or in-depth interviews conducted outside of class. There have been few efforts, however, to address students’ performance on the topic of EM fields and waves through examination of the artifacts that students create as part of their course i.e. homework. To get a broader and systematic understanding on students’ learning difficulties and knowledge development in EM, we conducted a comprehensive study in a junior-level EM fields class in the department of electrical engineering, with 53 students. An analytical framework for written response analysis was proposed based on knowledge associated with structured problem solving include situation, conceptual and procedural. The framework was used to inform the development of a coding scheme to analyze students’ weekly homework. Our results indicate students make two main types of mistakes on their homework: conceptual and procedural mistakes. Each of these categories contain a range of specific examples of common mistakes students demonstrate in their problem solving of course homework. Because of the unfamiliarity with EM learning context, students may have conceptual difficulty in activating the declarative knowledge needed to solve the problems. Also, consistent with other research, we find that students face significant procedural challenges in combining their physics knowledge with mathematical strategies at their early stage of learning. Common homework mistakes for learning topics Coulomb’s law, Gauss’s law, electric potential and energy, current flow and density, polarization in dielectrics, boundary conditions, capacitance, Ampere’s law and etc. are also reported. Finally, we discuss the implications of this study for increasing instructor’s awareness of students’ difficulties, and also providing in-time feedback for instructors to design new learning activities or adjusting instructional strategies to improve teaching efficiency. Introduction Electromagnetic (EM) fields are an important foundation of modern society. A course introducing EM fields is a common core course for electrical engineering and physics students. In the study of EM fields, as with any topic that requires intensive mathematical reasoning of invisible physical phenomena, students at various levels often experience cognitive difficulties when first facing problems that use abstract notions and operators varying with time or/and space. We provide a brief background of research on student difficulties with EM phenomena. We first discuss the conceptual difficulties and later the difficulties in mathematical problem solving. Students’ Conceptual Difficulties with EM