Addressing barriers to learning in linear circuit analysis

Some possible barriers to student success in introductory linear circuit analysis courses are analyzed, particularly for DC circuits and general circuit topology issues. We argue that certain concepts actually needed to solve circuit problems are often not taught as explicit principles, and that conventional instruction often fails to address typical conceptual misunderstandings. In particular, we discuss the concepts of hinged circuits, redundant circuit elements, and voltage and current-splittability of circuit problems, the replacement theorem, iterative calculations, and the several types of problems to which one can actually apply voltage and current division. We emphasize the importance of comparing and contrasting when teaching concepts, particularly for the cases of voltage and current sources, short and open circuits (as special cases of voltage and current sources, respectively), voltage and current dividers, series and parallel connections, and voltage and current measurements. We highlight the importance of contrasting the various functions of terminals in a circuit. We propose various models that can promote understanding of basic electrical concepts, such as a microscopic Drude model of conduction, a "balls in tube" analogy to explain the constancy of current through circuit elements, and a "control loop" model to explain the operation of voltage and current sources. We use the DIRECT 1.0 concept inventory of Engelhardt & Beichner to assess conceptual understanding, administering it as both a pre- and post-test in 20 sections of a linear circuits class involving over 1100 students over two years. Pre-test scores are around 50% as found by others. Post-test scores typically rise to only 59% (averaged over many instructors), showing that conventional instruction does not address qualitative misunderstandings very effectively. By introducing targeted instruction in one section to address misconceptions, the post-test score rose to 69% in Spring 2013 (higher than any other section) and with further refinement reached 79% in Fall 2013.