A Systematic Literature Review of Misconceptions in Linear Circuit Analysis

Misconceptions in circuit analysis have been investigated by many researchers. However, we could not find a literature review from the last 20 years. We conducted a systematic literature review on circuit analysis misconceptions from the last 20 years, finding 15 articles meeting the search criteria, relevance, and accessibility. In total, the articles identified 20 misconceptions (e.g., term confusion in physics, algebraic manipulations, and failure to consider local changes in context of entire circuit), which we grouped into 8 misconception categories (e.g., Physics, Math, Sequential reasoning, and Application of Ohm's Law). Interestingly, none of the articles addressed the misconceptions, which may be low-hanging fruit. We also created a conceptual dependency graph to help point out foundational misconceptions within the misconception categories, yielding Physics, Math, and Application of Ohm's Law as the most foundational misconceptions. Physics had 5 misconceptions (the most) and in total cited by 7 articles. Within Physics, the most cited was term confusion, cited by 4 articles. Math had 2 misconceptions, cited by 3 articles. Application of Ohm's Law had 2 misconceptions, cited by 7 articles. Interestingly, none of the articles attempted to address misconceptions. Thus, there appears to be a need for research that addresses misconceptions. We might suggest focusing on prevalently reported misconceptions, such as physics term confusion and appropriate application of Ohm's Law. Introduction Misconceptions in circuit analysis have been investigated by many researchers, and researchers have identified numerous issues: Conceptual [1][2][3][4], term confusion [5][6], fundamental mathematical skills [7][8], incomplete metaphor [9][10], and diagnostics to identify such misconceptions [5][11]. Further, researchers have investigated many aspects: Community college through research university levels, laboratory and lecture settings, and across different learning materials. However, there does not appear to have been a systematic literature review of this work in over 20 years. Thus, we undertook a literature search to provide a more updated systematic review of misconception research. Misconceptions are important to identify and address because such misconceptions may follow the student into subsequent courses. Thus, focusing on linear circuit analysis is important because linear circuit analysis is a foundational course in electrical engineering. The concepts learned in linear circuit analysis, such as Ohm’s Law, source transformations, and basic calculations for solving for voltage, resistance, and current in circuit components, are built upon in later courses, such as digital system design and semiconductor devices. Thus, misconceptions found in linear circuit analysis may persist. Such misconceptions can arise from various sources, such as textbooks [10][12], previous courses, classroom lectures, or laboratory experiences [13]. In this paper, we systematically reviewed the literature on circuit analysis misconceptions. We analyzed the literature by analyzing the research methodologies, categorizing the misconceptions, enumerating the types of research, and building a conceptual dependency graph. Methods The goal of our literature search was to identify research conducted in the past 20 years that was relevant to misconceptions in circuit analysis engineering courses, typically taken by students in their first year. To that end, the search was conducted in Google Scholar [14] using the search: misconceptions "circuit analysis" "electrical engineering" "first-year" -electrochemistry The notation means: Each search term is either a single word or combined words (inside double-quotes). Combined words must be found together and as written. The search terms are combined using an AND Boolean operation. A NOT operation was applied to "electrochemistry". To identify the topic of linear circuit analysis, the broader term “circuit analysis” was included, as specifying “linear circuit analysis” narrowed the results to 6 papers and eliminated relevant articles. The term “electrical engineering” was included to pinpoint research done within engineering courses. Because circuit analysis is done across multiple courses, the term “first-year” was included to identify papers relevant to the topics taught in the beginning foundational circuit analysis courses. "First-year" in many papers refers to the first year of learning the major-specific topics. Many articles were specific to electrochemistry, so -​electrochemistry​ was included to eliminate electrochemistry articles. We included peer-reviewed articles and dissertations between the years 1997 to 2018. Our main inclusion criteria required articles to specifically discuss misconceptions relevant to topics taught in basic circuit analysis engineering courses (e.g. articles discussing more advanced engineering courses, such as electromagnetism, were discounted). For each article, the following data was extracted: The location of where the research was conducted, the number of participants in the study, the type of study conducted, and every misconception identified. We noticed often several papers would refer to the same misconception but using different terminology, so we selected the most succinct term that well-described the misconception. Literature review results A total of 93 articles were found from this search. 72 were found to be irrelevant to our topic. 6 articles were unable to be accessed. Thus, 15 articles met the inclusion criteria. This section briefly describes each article. Several researchers relied on validated assessments to develop their diagnostic test. Some tests included questions from combination of validated assessments. Hussain picked 12 questions specific to Thevenin and Norton equivalents [15] from assessments developed by Engelhardt (DIRECT) [5] and Sabah [16]. Other tests used a subset of questions from only one validated assessment. For example, Underwood [17] used a selection of questions from the Circuits Concept Inventory (CCI) [11] for a diagnostic test. Some researchers developed their own in-house assessments [18][19][20]. Smaill developed an in-house assessment based on previous work [5][21][22], which included 20 multiple choice and 2 free response questions. Students had 30 minutes to complete the questions [18][19][20]. Smaill administered the assessment to three groups of students: 560 students in 2007 [19], 543 students in 2008 [18], and over 1600 students from 2007 to 2009 [20]. Participants consisted of students from New Zealand and the United States. Other researchers developed in-house assessments based on their classroom and laboratory experiences, sampling questions from class quizzes and exams [9][23]. After informally studying student responses in lectures and and recitation lessons, Kautz developed diagnostic questions optional for students to complete during class lectures, or at the end of their final exam. Another popular method for observing misconceptions in circuit analysis courses was through student interviews, typically done after the diagnostic test. Biswas identified specific misconceptions students had about AC circuits through a series of interviews with a total of 18 students, who gave walk-through explanations of their circuit analysis steps [9]. Finally, one paper analyzed learning materials to identify potential misconceptions in explanations of concepts. Sangam and Jesiek analyzed circuit analysis concepts and links between the concepts to pinpoint misconceptions common across 5 textbooks [10]. A suggest for future research is to combine a validated assessment, such as DIRECT [5], with an interview to help dive deeper into the misconception. A validated assessment has already been verified to have questions that accurately predict conceptual understanding across a large population. An interview enable a researcher to better explore why the misconception exists. Interestingly, none of the articles attempted to address the misconceptions, so there exists a need for addressing misconceptions experimentally. Analysis of Misconception Categories Many of the misconception topics found shared commonalities in the overall concept being taught, or the type of circuit being analyzed. Thus, we grouped the misconceptions into the following 8 misconception categories: ● Physics: 5 misconceptions pertaining to the fundamentals of physics. Ex: Charge as a property of matter. ● Math: 2 misconceptions pertaining to the use of math in circuit analysis. Ex: Algebraic manipulations. ● Sequential reasoning: 1 misconception pertaining to the failure to consider effects on the circuit as a whole during analysis. Ex: ​General failure to consider local changes in context of entire circuit. ● Application of Ohm’s Law: 2 misconceptions pertaining to the understanding and application of Ohm’s Law. Ex: Inappropriate application or blind reliance of Ohm's Law. ● Elements in series and parallel: 2 misconceptions pertaining to identifying and analyzing circuit elements in series and parallel. Ex: Misidentifying if components are in series or in parallel. ● Open and short circuits: 4 misconceptions pertaining to analyzing effects in a circuit when circuits are open or shorted. Ex: Recognizing voltage effects in open and closed circuits. ● Kirchoff’s circuit laws: 2 misconceptions pertaining to the application of Kirchoff’s Current Law and Kirchoff’s Voltage Law. Ex: Belief the direction of mesh currents matter in mesh analysis. ● AC circuits: 2 misconceptions pertaining to analyzing AC circuits. Ex: Identifying what is alternating in an AC circuit. Table 1 includes each specific misconception organized by misconception categories. Each specific misconception is briefly described. For example, in physics, a misconception is related to charge as a property of matter. Specifically, some students thought that electrons carry positive charge [7