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In this paper we describe the historical background of the introductory course in Electric Circuits I, how it has been taught, and the different modifications this course has undergone for the past few years. We describe preliminary results of a new step-based method on student learning which has been applied at the University of Texas at El Paso (UTEP) to improve students’ understanding of the topics covered in this course, and describe the step-based tutoring System, dubbed Circuit Tutor, developed by researchers at the UTEP. The results indicate Circuit Tutor platform can be used as a self-learning tool according to survey answers from students and the increasing passing rate in the Circuits I course. 

Step-based tutoring consists in breaking down complicated problem-solving procedures into individual steps whose inputs can be immediately evaluated to promote effective student learning. Here, recent progress on the extension of a step-based tutoring for linear circuit analysis to cover new topics requiring complex, multi-step solution procedures is described. These topics include first and second-order transient problems solved using classical differential equation approaches. Students use an interactive circuit editor to modify the circuit appropriately for each step of the analysis, followed by writing and solving equations using methods of their choice as appropriate. Initial work on Laplace transform-based circuit analysis is also discussed. Detailed feedback is supplied at each step along with fully worked examples, supporting introductory multiple-choice tutorials and YouTube videos, and a full record of the student's work is created in a PDF document for later study and review. Further, results of a comprehensive independent evaluation involving both quantitative and qualitative analysis and users across four participating institutions are discussed. Overall, students had very favorable experiences using the step-based system across Fall 2020 and Spring 2021. At least 48% of students in the Fall 2020 semester and 60% of students in the Spring 2021 semester agreed or strongly agreed with all survey questions about positive features of the system. Those who had used the step-based system and the commercial MasteringEngineering system preferred the former by 69% to 12% margins in surveys. Instructors were further surveyed and 86% would recommend the system to others. 

Step-based tutoring consists in breaking down complicated problem-solving procedures into individual steps whose inputs can be immediately evaluated to promote effective student learning. Here, recent progress on the extension of a step-based tutoring for linear circuit analysis to cover new topics requiring complex, multi-step solution procedures is described. These topics include first and second-order transient problems solved using classical differential equation approaches. Students use an interactive circuit editor to modify the circuit appropriately for each step of the analysis, followed by writing and solving equations using methods of their choice as appropriate. Initial work on Laplace transform-based circuit analysis is also discussed. Detailed feedback is supplied at each step along with fully worked examples, supporting introductory multiple-choice tutorials and YouTube videos, and a full record of the student's work is created in a PDF document for later study and review. Further, results of a comprehensive independent evaluation involving both quantitative and qualitative analysis and users across four participating institutions are discussed. Overall, students had very favorable experiences using the step-based system across Fall 2020 and Spring 2021. At least 48% of students in the Fall 2020 semester and 60% of students in the Spring 2021 semester agreed or strongly agreed with all survey questions about positive features of the system. Those who had used the step-based system and the commercial MasteringEngineering system preferred the former by 69% to 12% margins in surveys. Instructors were further surveyed and 86% would recommend the system to others. 

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% and 87%, respectively. Large improvements were observed at every institution including five minority-serving ones. The posttest score is increased by a statistically significant amount after introducing the new definition of series elements. Students preferred the new definition of series and recommended its use, and very strongly endorsed color coding. 

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, and the zero of all mesh currents is now arbitrary just as it is for node voltages. Use of supermeshes is sometimes obviated by the new approach, and the analysis is sometimes simplified. This new approach has been used in two sections of a linear circuit analysis course in Fall 2019, and student survey data is presented to show preference for the new method over the usual textbook method. An interactive multiple-choice tutorial describing the new method has been integrated into a step-based tutoring system for linear circuit analysis. 

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, including three that heavily serve underrepresented minorities. Both quantitative and qualitative methods were used, including focus groups, surveys, and interviews. Controlled, randomized, blind evaluations were carried out in three different course sections in Spring and Fall 2019 to evaluate three tutorials using the interactive editor, comparing use of Circuit Tutor to both a commercial answer-based system and to conventional textbook-based paper homework. In Fall 2019, students rated the software a mean of 4.14/5 for being helpful to learn the material vs. 3.05/5 for paper homework (HW), p < 0.001 and effect size d = 1.11σ. On relevant exam questions that semester, students scored significantly (p = 0.014) higher with an effect size of d = 0.64σ when using Circuit Tutor compared to paper HW in one class section, with no significant difference in the other section. 

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.