Duality as a Central Organizing Theme in Linear Circuit Analysis Instruction

(Full paper, Innovative Practice.) Linear circuit analysis is a complex topic in which students must use many principles to complete problems successfully, which may overload working memory and thereby impede learning. Introducing organizing principles may help students develop schemas that help reduce this burden and develop deeper conceptual understanding. The use of duality as such an organizing concept is explored in this work. To be effective, however, all the topics should be presented in a dual manner. Historically, definitions of series and parallel elements have been used that are not dual to each other, and mesh analysis has been performed in a way that is not fully dual to nodal analysis. This paper examines the research question of whether these key topics can be presented in a novel, fully dual fashion and whether students will accept and appreciate such a treatment. The revised approaches were implemented using lectures, online interactive tutorials, and step-based tutoring software exercises. Surveys using both quantitative and qualitative analysis were conducted over three semesters and showed positive reactions from 72-83% of students. These results can lead to development of a full set of instructional materials centered around duality to enable improved learning of circuit analysis.