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Contribution: A new operational definition of series connections is given based on elements belonging to the same two meshes, which is properly dual to the usual definition of parallel elements being connected to the same two nodes. Furthermore, computer-based exercises have been developed and tested to teach students about such connections in gateway linear circuits courses, using color coding of nodes and meshes as a pedagogical device. Background: Series and parallel connections are a crucial but difficult concept. Existing textbooks give them limited attention, resulting in later difficulties learning circuit analysis. Research Questions: RQ1: Can an improved definition of series elements aid student understanding and student satisfaction? RQ2: Can a computer-based ``game'' lead to effective mastery and student satisfaction at a wide range of institutions, including minority-serving ones? Methodology: Standard and new definitions were elaborated in a multiple-choice tutorial. A game was developed focusing on identifying series and parallel connections, with color coding of both nodes and meshes. Student learning was assessed over eight years using pretest and posttest in 14 varied institutions. Student opinions were assessed using several types of surveys. Findings: Strong learning gains were observed every semester from built-in pretest and posttest, with average scores of 28%more »
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.
Elementary linear circuit analysis is a core competency for electrical and many other engineers. Two of the standard approaches to systematic analysis of linear circuits are nodal and mesh analysis, the latter being limited to planar circuits. Nodal and mesh analysis are related by duality and should therefore be fully symmetrical with each other. Here, the usual textbook approach to mesh analysis is argued to be deficient in that it obscures this fundamental duality and symmetry, and may thereby impede the development of intuition and the understanding of the nature of “mesh currents.” In particular, the usual distinction between “inner” and “outer” meshes (if the latter is even recognized) is argued to be meaningless, as can be seen when drawing a planar circuit on the surface of a sphere. A generalized definition of a mesh is proposed that includes both inner and outer meshes on the same footing. Selection of a reference node in nodal analysis should be paralleled by the selection of any mesh to be the reference mesh in mesh analysis, which is always selected to be the outer mesh by default in the usual approach. All branch currents are shown to the difference of two mesh currents,more »
Step-based tutoring systems are known to be more effective than traditional answer-based systems. They however require that each step in a student’s work be accepted and evaluated automatically to provide effective feedback. In the domain of linear circuit analysis, it is frequently necessary to allow students to draw or edit circuits on their screen to simplify or otherwise transform them. Here, the interface developed to accept such input and provide immediate feedback in the Circuit Tutor system is described, along with systematic assessment data. Advanced simplification methods such as removing circuit sections that are removably hinged, voltage-splittable, or current-splittable are taught to students in an interactive tutorial and then supported in the circuit editor itself. To address the learning curve associated with such an interface, ~70 video tutorials were created to demonstrate exactly how to work the randomly generated problems at each level of each of the tutorials in the system. A complete written record or “transcript” of student’s work in the system is being made available, showing both incorrect and correct steps. Introductory interactive (multiple choice) tutorials are now included on most topics. Assessment of exercises using the interactive editor was carried out by professional evaluators for several institutions,more »
Step-based tutoring systems, in which each step of a student’s work is accepted by a computer using special interfaces and provided immediate feedback, are known to be more effective in promoting learning than traditional and more common answer-based tutoring systems, in which only the final (usually numerical) answer is evaluated. Prior work showed that this approach can be highly effective in the domain of linear circuit analysis in teaching topics involving relatively simple solution procedures. Here, we demonstrate a novel application of this approach to more cognitively complex, multi-step procedures used to analyze linear circuits using the superposition and source transformation methods. Both methods require that students interactively edit a circuit diagram repeatedly, interspersed with the writing of relevant equations. Scores on post-tests and student opinions are compared using a blind classroom-based experiment where students are randomly assigned to use either the new system or a commercially published answer-based tutoring system on these topics. Post-test scores are not statistically significantly different but students prefer the step-based system by a margin of 84 to 11% for superposition and 68 to 23% for source transformations.